Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space-time construct are consistent with the existence of a dynamical 3-space, and absolute motion. We illustrate this mapping first with the standard theory of sound, as vibrations of a medium, which itself may be undergoing fluid motion, and which is covariant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under Lorentz transformations wherein the speed of sound is now the invariant speed. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian spacetime description of sound, with a metric characterised by an invariant speed of sound. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equations were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a allowing dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Formal language constrained path problems
Energy Technology Data Exchange (ETDEWEB)
Barrett, C.; Jacob, R.; Marathe, M.
1997-07-08
In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space- time construct are consistent with the existence of a dynamical 3-space, and “absolute motion”. We illustrate this mapping first with the standard theory of sound, as vibra- tions of a medium, which itself may be undergoing fluid motion, and which is covari- ant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under “Lorentz transformations” wherein the speed of sound is now the “invariant speed”. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian “spacetime” description of sound, with a metric characterised by an “invariant speed of sound”. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equa- tions were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a “flowing” dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-12-01
Given an arbitrary Lagrangian function on {R}^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a "Fubini theorem" expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by "cutting and pasting" and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic "formal path integral" for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Studying conformally flat spacetimes with an elastic stress energy tensor using 1 + 3 formalism
Brito, I.; Ramos, M. P. Machado
2015-12-01
Conformally flat spacetimes with an elastic stress-energy tensor having diagonal trace-free anisotropic pressure are investigated using 1 + 3 formalism. The 1 + 3 Bianchi and Jacobi identities and Einstein field equations are written for a particular case with a conformal factor dependent on only one spatial coordinate. Solutions with non zero anisotropic pressure are obtained.
Quantum Spacetime: Mimicry of Paths and Black Holes
Spaans, Marco
Since its inception, general relativity has been unreceptive to a marriage with the quantum aspects of our universe. Following the ideas of Einstein, one may pursue an approach that allows spacetime itself to take center stage. The quantum properties of matter are then carried by the dynamics of
Feng, Justin C.; Matzner, Richard A.
2017-11-01
We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general relativity by way of boundary variations. One feature of this approach is that it does not require an explicit 3 +1 splitting of spacetime in the bulk. For spacetimes with a spatial boundary, we show that the dependence of the transition amplitudes on spatial boundary conditions is determined by a Wheeler-DeWitt equation for the spatial boundary surface. We find that variations in the induced metric at the spatial boundary can be used to describe time evolution—time evolution in quantum general relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary. We then briefly describe a formalism for computing the dependence of transition amplitudes on spatial boundary conditions. Finally, we argue that for nonsmooth boundaries meaningful transition amplitudes must depend on boundary conditions at the joint surfaces.
Schmitz, Oliver; Soenario, Ivan; Vaartjes, Ilonca; Strak, Maciek; Hoek, Gerard; Brunekreef, Bert; Dijst, Martin; Karssenberg, Derek
2016-04-01
Air pollution is one of the major concerns for human health. Associations between air pollution and health are often calculated using long-term (i.e. years to decades) information on personal exposure for each individual in a cohort. Personal exposure is the air pollution aggregated along the space-time path visited by an individual. As air pollution may vary considerably in space and time, for instance due to motorised traffic, the estimation of the spatio-temporal location of a persons' space-time path is important to identify the personal exposure. However, long term exposure is mostly calculated using the air pollution concentration at the x, y location of someone's home which does not consider that individuals are mobile (commuting, recreation, relocation). This assumption is often made as it is a major challenge to estimate space-time paths for all individuals in large cohorts, mostly because limited information on mobility of individuals is available. We address this issue by evaluating multiple approaches for the calculation of space-time paths, thereby estimating the personal exposure along these space-time paths with hyper resolution air pollution maps at national scale. This allows us to evaluate the effect of the space-time path and resulting personal exposure. Air pollution (e.g. NO2, PM10) was mapped for the entire Netherlands at a resolution of 5×5 m2 using the land use regression models developed in the European Study of Cohorts for Air Pollution Effects (ESCAPE, http://escapeproject.eu/) and the open source software PCRaster (http://www.pcraster.eu). The models use predictor variables like population density, land use, and traffic related data sets, and are able to model spatial variation and within-city variability of annual average concentration values. We approximated space-time paths for all individuals in a cohort using various aggregations, including those representing space-time paths as the outline of a persons' home or associated parcel
Path Integral Quantum Mechanics in Curved Space-Time a New Perspective
Singh, Dinesh; Mobed, Nader
2012-07-01
A new approach to path integral quantum mechanics in curved space-time for a scalar particle is presented in terms of local curvature involving Fermi or Riemann normal co-ordinates. This approach involves use of a local time translation operator with Lie transport that, while strictly non-unitary in form, nonetheless yields the correct expression for the curved space-time free-particle Lagrangian in the sum-over-histories, with additional terms corresponding to a curvature-dependent violation of probability. These terms simultaneously induce a breakdown of time-reversal symmetry at the quantum mechanical level, and also a violation of the weak equivalence principle at the particle's Compton wavelength scale. Furthermore, the scalar propagator generates a gravitational analogue of the Aharonov-Bohm effect and Berry's phase through the appearance of an overall gauge-invariant phase factor. Future directions to follow from this initial research are presented.
On the coordinate (in)dependence of the formal path integral
DEFF Research Database (Denmark)
Johnson-Freyd, Theo
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path integral on the coordinates becomes much less obvious....... In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal...... path integral does not depend on the choice of coordinates, but only on a choice of fiberwise volume form. Our outline is an honest proof when the formal path integral is defined without ultraviolet divergences....
Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes
Brink, Jeandrew
2009-01-01
An analytic understanding of the geodesic structure around non-Kerr spacetimes will result in a powerful tool that could make the mapping of spacetime around massive quiescent compact objects possible. To this end, I present an analytic closed form expression for the components of a the fourth order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is as yet unclear what subset of SAV spacetimes admit this solution. The solution is written in terms of an integral expression involving the metric functions and two specific Greens functions. A second integral expression has to vanish in order for the solution to be exact. In the event that the second integral does not vanish it is likely that the best fourth order approximation to the invariant has been found. This solution can be viewed as a generalized Carter constant providing an explicit expression for the fourth invariant, in addition to the energy, azimuthal angular momentum and rest mass, associated with geodesic motion in SAV spaceti...
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
Zilhão, Miguel; Witek, Helvi; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea
2010-04-01
The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
Uncertainty-Based Map Matching: The Space-Time Prism and k-Shortest Path Algorithm
Directory of Open Access Journals (Sweden)
Bart Kuijpers
2016-11-01
Full Text Available Location-aware devices can be used to record the positions of moving objects for further spatio-temporal data analysis. For instance, we can analyze the routes followed by a person or a group of people, to discover hidden patterns in trajectory data. Typically, the positions of moving objects are registered by GPS devices, and most of the time, the recorded positions do not match the road actually followed by the object carrying the device, due to different sources of errors. Thus, matching the moving object’s actual position to a location on a digital map is required. The problem of matching GPS-recorded positions to a road network is called map matching (MM. Although many algorithms have been proposed to solve this problem, few of them consider the uncertainty caused by the absence of information about the moving object’s position in-between consecutive recorded locations. In this paper, we study the relationship between map matching and uncertainty, and we propose a novel MM algorithm that uses space-time prisms in combination with weighted k-shortest path algorithms. We applied our algorithm to real-world cases and to computer-generated trajectory samples with a variety of properties. We compare our results against a number of well-known algorithms that we have also implemented and show that it outperforms existing algorithms, allowing us to obtain better matches, with a negligible loss in performance. In addition, we propose a novel accuracy measure that allows a better comparison between different MM algorithms. We applied this novel measure to compare our algorithm against existing algorithms.
Efficient Calculation of Energy Expectation Values in the Path Integral Formalism
Grujic, J
2006-01-01
The path integral formalism, originally introduced by Richard Feynman, represents a powerful general framework for dealing with quantum and statistical theories, as well as an extremely useful tool in many other areas of science. Their numerical integration, however, is notoriously demanding of computer time and it is one of the most challenging computational problems.
Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
Aron, Camille; Barci, Daniel G.; Cugliandolo, Leticia F.; González Arenas, Zochil; Lozano, Gustavo S.
2014-09-01
We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown (1963 Phys. Rev. 130 1677), with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hugo [Tuebingen Univ. (Germany). Inst. fuer Theoretische Physik
2012-11-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Directory of Open Access Journals (Sweden)
David S. Hardin
2013-04-01
Full Text Available As Graphics Processing Units (GPUs have gained in capability and GPU development environments have matured, developers are increasingly turning to the GPU to off-load the main host CPU of numerically-intensive, parallelizable computations. Modern GPUs feature hundreds of cores, and offer programming niceties such as double-precision floating point, and even limited recursion. This shift from CPU to GPU, however, raises the question: how do we know that these new GPU-based algorithms are correct? In order to explore this new verification frontier, we formalized a parallelizable all-pairs shortest path (APSP algorithm for weighted graphs, originally coded in NVIDIA's CUDA language, in ACL2. The ACL2 specification is written using a single-threaded object (stobj and tail recursion, as the stobj/tail recursion combination yields the most straightforward translation from imperative programming languages, as well as efficient, scalable executable specifications within ACL2 itself. The ACL2 version of the APSP algorithm can process millions of vertices and edges with little to no garbage generation, and executes at one-sixth the speed of a host-based version of APSP coded in C – a very respectable result for a theorem prover. In addition to formalizing the APSP algorithm (which uses Dijkstra's shortest path algorithm at its core, we have also provided capability that the original APSP code lacked, namely shortest path recovery. Path recovery is accomplished using a secondary ACL2 stobj implementing a LIFO stack, which is proven correct. To conclude the experiment, we ported the ACL2 version of the APSP kernels back to C, resulting in a less than 5% slowdown, and also performed a partial back-port to CUDA, which, surprisingly, yielded a slight performance increase.
Path integral Monte Carlo ground state approach: formalism, implementation, and applications
Yan, Yangqian; Blume, D.
2017-11-01
Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.
Roldán, Édgar; Gupta, Shamik
2017-08-01
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.
Saniga, Metod
2001-01-01
A sequence of integers generated by the number of conjugated pairs of homaloidal nets of plane algebraic curves of even order is found to provide an >exact< integer-valued match for El Naschie's primordial set of fractal dimensions characterizing transfinite heterotic string space-time.
Directory of Open Access Journals (Sweden)
Lucian Gideon Conway
2016-11-01
Full Text Available It has been an accepted scientific fact in physics for almost 100 years that time speeds up and slows down for an observer based on factors—such as motion and gravity—that affect space. Yet this fact, drawn from the theory of relativity, has not been widely integrated into the study of the psychology of time. The present article helps to fill in this gap between physics and psychology by reviewing evidence concerning what a psychological spacetime processor—one that accounted for the theory of relativity’s empirically validated predictions of the compensatory relationship between time and space—would look like. This model of the spacetime processor suggests that humans should have a psychological mechanism for slowing time down as motion speeds up, a prediction that already has widespread research support. We also discuss several novel hypotheses directly suggested by the spacetime model and a set of related speculations that emerge when considering spacetime (some of which have already received empirical support. Finally, we compare and contrast three very different potential reasons why we might have developed a spacetime processor in the first place. We conclude that the spacetime model shows promise for organizing existing data on time perception and generating novel hypotheses for researchers to pursue. Considering how humans might process spacetime helps reduce the existing gap between our understanding of physics and our understanding of human psychology.
Electrodynamics and spacetime geometry: Astrophysical applications
Cabral, Francisco
2016-01-01
After a brief review of the foundations of (pre-metric) electromagnetism in differential forms, we proceed with the tensor formulation and explore physical consequences of Maxwell's equations in curved spacetime. The generalized Gauss and Maxwell-Amp\\`ere laws, as well as the wave equations, reveal potentially interesting astrophysical applications. The physical implications of these equations are explored and some solutions are obtained. In all cases new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. In general, new electromagnetic effects induced by spacetime curvature include the following: Gravitational contributions for the decay of electric and magnetic fields in...
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
Quantum healing of spacetime singularities: A review
Konkowski, D. A.; Helliwell, T. M.
2018-02-01
Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.
Energy Technology Data Exchange (ETDEWEB)
Nomura, Yasunori [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583 (Japan); Salzetta, Nico, E-mail: nsalzetta@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sanches, Fabio; Weinberg, Sean J. [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-12-10
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
Electrodynamics and spacetime geometry: Astrophysical applications
Cabral, Francisco; Lobo, Francisco S. N.
2017-07-01
After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws, where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena, such as the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.
Fractional and noncommutative spacetimes
Arzano, M.|info:eu-repo/dai/nl/32616443X; Calcagni, M.; Oriti, D.; Scalisi, M.
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale
Quantum-Spacetime Phenomenology
Directory of Open Access Journals (Sweden)
Giovanni Amelino-Camelia
2013-06-01
Full Text Available I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.
Perko, Howard
2017-01-01
Concepts from physical chemistry and more specifically surface tension are introduced to spacetime. Lagrangian equations of motion for membranes of curved spacetime manifold are derived. The equations of motion in spatial directions are dispersion equations and can be rearranged to Schrodinger's equation where Plank's constant is related to membrane elastic modulus. The equation of motion in the time-direction has two immediately recognizable solutions: electromagnetic waves and corpuscles. The corpuscular membrane solution can assume different genus depending on quantized amounts of surface energy. A metric tensor that relates empty flat spacetime to energetic curved spacetime is found that satisfies general relativity. Application of the surface tension to quantum electrodynamics and implications for quantum chromodynamics are discussed. Although much work remains, it is suggested that spacetime surface tension may provide a classical explanation that combines general relativity with field theories in quantum mechanics and atomic particle physics.
Geometry of Minkowski Space-Time
Catoni, Francesco; Cannata, Roberto; Catoni, Vincenzo; Zampetti, Paolo
2011-01-01
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity co...
The Spacetime Memory of Geometric Phases and Quantum Computing
Binder, B
2002-01-01
Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.
Teleparallel formalism of galilean gravity
Ulhoa, S. C.; Khanna, F. C.; Santana, A.E.
2011-01-01
A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant ...
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Krylov, Piotr
2017-01-01
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...
Space-Time Fractional DKP Equation and Its Solution
Bouzid, N.; Merad, M.
2017-05-01
In this paper, a fractional Hamiltonian formulation for Duffin-Kemmer-Petiau' (DKP) fields is presented and, as done in the framework of the Lagrangian formalism, the fractional DKP equation is deduced. The space-time fractional DKP equation is then solved for both scalar and vectorial cases. The wave functions obtained are expressed in terms of Mittag-Leffler function.
IR finite graviton propagators in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Upadhyay, Sudhaker; Mandal, Bhabani Prasad [Banaras Hindu University, Department of Physics, Varanasi (India)
2016-04-15
The graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are a symmetry of the classical action, but they do not leave the path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such a finite transformation the path integral measure changes and hence the FFBRST transformation is capable of relating theories in two different gauges. We explicitly construct the FFBRST transformation which relates the theory with a diverging graviton two-point function to a theory with an infrared finite graviton. The FFBRST transformation thus establishes that the divergence in a graviton two-point function may be only a gauge artifact. (orig.)
Schrödinger, Erwin
1985-01-01
In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.
Universal spacetimes in four dimensions
Hervik, S.; Pravda, V.; Pravdová, A.
2017-10-01
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.
Energy Technology Data Exchange (ETDEWEB)
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)
2016-04-29
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
Ohanian, Hans C
2013-01-01
The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...
Revisiting quantum mechanics on non-commutative space-time
Nandi, Partha; Pal, Sayan Kumar; Bose, Aritra N.; Chakraborty, Biswajit
2017-11-01
We construct an effective commutative Schrödinger equation in Moyal space-time in (1 + 1) -dimension where both t and x are operator-valued and satisfy [ t ˆ , x ˆ ] = iθ. Beginning with a time-reparametrised invariant form of an action we identify the actions of various space-time coordinates and their conjugate momenta on quantum states, represented by Hilbert-Schmidt operators. Since time is also regarded as a configuration space variable, we show how an 'induced' inner product can be extracted, so that an appropriate probabilistic interpretation is obtained. We then discuss several other applications of the formalism developed so far.
Classification of spacetimes with symmetry
Hicks, Jesse W.
Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we. i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein's Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov's paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.
Mädler, Thomas
2016-01-01
The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group.
Hervik, S.; Málek, T.; Pravda, V.; Pravdová, A.
2015-12-01
We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L({{Riemann}}) gravities.
Discrete causal theory emergent spacetime and the causal metric hypothesis
Dribus, Benjamin F
2017-01-01
This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation.
Directory of Open Access Journals (Sweden)
Arthur D. Gorman
1986-01-01
Full Text Available The Lagrange manifold (WKB formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning points. Here the formalism is adapted to determine a class of asymptotic solutions at caustic points for those equations modelling wave propagation in media with both spatial and temporal inhomogeneities. The analogous Schrodinger equation is also considered.
Emergent universe from noncommutative spacetime
Energy Technology Data Exchange (ETDEWEB)
Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Ewha Womans University, Seoul (Korea, Republic of)
2010-09-15
The Big Bang, which was the birth of our Universe, happened at the Planck epoch. It was not an event that developed in a pre-existing space-time. Rather, it was a cosmological event simultaneously generating space-time as well as all other matter fields. Therefore, in order to describe the origin of our Universe, it is necessary to have a background-independent theory for quantum gravity in which no space-time structure is a priori assumed, but is defined from the theory. The emergent gravity based on noncommutative gauge theory provides such a background-independent formulation of quantum gravity, and the emergent space-time leads to a novel picture of the dynamical origin of space-time. We address some issues about the origin of our Universe and discuss the implications to cosmology of the emergent gravity.
Deformed Spacetime Geometrizing Interactions in Four and Five Dimensions
Cardone, Fabio
2007-01-01
This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity, DSR) allows one to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense) to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational) Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism. The mathematical pr...
Springer handbook of spacetime
Petkov, Vesselin
2014-01-01
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Han...
Schild Action and Space-Time Uncertainty Principle in String Theory
Yoneya, Tamiaki
1997-01-01
We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microca...
Ambient cosmology and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Interactions Between Real and Virtual Spacetimes
DEFF Research Database (Denmark)
Javadi, Hossein; Forouzbakhsh, Farshid
2014-01-01
. In this article, we analyzed that c is the edge of visible and invisible particles such as virtual photons and graviton. It leads us passing the real spacetime and enter into the virtual spacetime and describe interactions between real spacetime and virtual spacetime and reach to non-obvious space....
Assche, van K.; Beunen, R.; Duineveld, M.
2014-01-01
In this chapter we discuss the concept of governance paths and the forms of dependency marking paths. The forms of dependency constitute rigidities in governance evolution, but leave space for flexibility, for path creation.
Quasilocal Energy in Kerr Spacetime
Liu, Jian-Liang
2016-01-01
In this work we study the quasilocal energy as in [11] for a constant radius surface in Kerr spacetime in Boyer-Lindquist coordinates. We show that under suitable conditions for isometric embedding, for a stationary observer the quasilocal energy defined in [11] for constant radius in a Kerr like spacetime is exactly equal to the Brown-York quasilocal energy [2]. By some careful estimations, we show that for a constant radius surface in the Kerr spacetime which is outside the ergosphere the embedding conditions for the previous result are satisfied. Finally we discuss extremal solutions as described in [14] and show that near the horizon of the Kerr spacetime for the small rotation case the extremal solutions are trivial.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
Directory of Open Access Journals (Sweden)
L. Román Juarez
2008-07-01
Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
Averaging Schwarzschild spacetime
Tegai, S. Ph.; Drobov, I. V.
2017-07-01
We tried to average the Schwarzschild solution for the gravitational point source by analogy with the same problem in Newtonian gravity or electrostatics. We expected to get a similar result, consisting of two parts: the smoothed interior part being a sphere filled with some matter content and an empty exterior part described by the original solution. We considered several variants of generally covariant averaging schemes. The averaging of the connection in the spirit of Zalaletdinov's macroscopic gravity gave unsatisfactory results. With the transport operators proposed in the literature it did not give the expected Schwarzschild solution in the exterior part of the averaged spacetime. We were able to construct a transport operator that preserves the Newtonian analogy for the outward region but such an operator does not have a clear geometrical meaning. In contrast, using the curvature as the primary averaged object instead of the connection does give the desired result for the exterior part of the problem in a fine way. However for the interior part, this curvature averaging does not work because the Schwarzschild curvature components diverge as 1 /r3 near the center and therefore are not integrable.
Mark Setterfield
2015-01-01
Path dependency is defined, and three different specific concepts of path dependency – cumulative causation, lock in, and hysteresis – are analyzed. The relationships between path dependency and equilibrium, and path dependency and fundamental uncertainty are also discussed. Finally, a typology of dynamical systems is developed to clarify these relationships.
Path-based Queries on Trajectory Data
DEFF Research Database (Denmark)
Krogh, Benjamin Bjerre; Pelekis, Nikos; Theodoridis, Yannis
2014-01-01
In traffic research, management, and planning a number of path-based analyses are heavily used, e.g., for computing turn-times, evaluating green waves, or studying traffic flow. These analyses require retrieving the trajectories that follow the full path being analyzed. Existing path queries cannot...... sufficiently support such path-based analyses because they retrieve all trajectories that touch any edge in the path. In this paper, we define and formalize the strict path query. This is a novel query type tailored to support path-based analysis, where trajectories must follow all edges in the path....... To efficiently support strict path queries, we present a novel NETwork-constrained TRAjectory index (NETTRA). This index enables very efficient retrieval of trajectories that follow a specific path, i.e., strict path queries. NETTRA uses a new path encoding scheme that can determine if a trajectory follows...
Domain walls and spacetime-filling branes
Bergshoeff, E; Wess, J; Ivanov, EA
1999-01-01
We discuss branes with one transversal direction (domain walls) and no transversal direction (spacetime-filling branes). In particular, we briefly discuss a relationship between spacetime-filling branes and superstring theories with sixteen supercharges.
Radiation Transport in Dynamic Spacetimes
Schnittman, Jeremy; Baker, John G.; Etienne, Zachariah; Giacomazzo, Bruno; Kelly, Bernard J.
2017-08-01
We present early results from a new radiation transport calculation of gas accretion onto merging binary black holes. We use the Monte Carlo radiation transport code Pandurata, now generalized for application to dynamic spacetimes. The time variability of the metric requires careful numerical techniques for solving the geodesic equation, particularly with tabulated spacetime data from numerical relativity codes. Using a new series of general relativistic magneto-hydrodynamical simulations of magnetized flow onto binary black holes, we investigate the possibility for detecting and identifying unique electromagnetic counterparts to gravitational wave events.
Role of spacetime boundaries in a vierbein formulation of gravity
Oshita, Naritaka; Wu, Yi-Peng
2017-08-01
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms that reside in the metric formulation of general relativity, in the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black hole entropy from the free energy due to the spacetime boundary. These results indicate that the vierbein formulation of gravity generally exhibits a well-posed action principle and readily admits the path-integral approach to quantization.
A computational approach to the twin paradox in curved spacetime
Fung, Kenneth K. H.; Clark, Hamish A.; Lewis, Geraint F.; Wu, Xiaofeng
2016-09-01
Despite being a major component in the teaching of special relativity, the twin ‘paradox’ is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often neglected entirely, and students are left with an incomplete understanding of the relativistic behaviour of time. This article outlines a project, undertaken by undergraduate physics students at the University of Sydney, in which a novel computational method was derived in order to predict the time experienced by a twin following a number of paths between two given spacetime coordinates. By utilising this method, it is possible to make clear to students that following a geodesic in curved spacetime does not always result in the greatest experienced proper time.
A computational approach to the twin paradox in curved spacetime
Fung, Kenneth K H; Lewis, Geraint F; Wu, Xiaofeng
2016-01-01
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often neglected entirely, and students are left with an incomplete understanding of the relativistic behaviour of time. This article outlines a project, undertaken by undergraduate physics students at the University of Sydney, in which a novel computational method was derived in order to predict the time experienced by a twin following a number of paths between two given spacetime coordinates. By utilising this method, it is possible to make clear to students that following a geodesic in curved spacetime does not always result in the greatest experienced proper time.
Jing, Yindi
2014-01-01
Distributed Space-Time Coding (DSTC) is a cooperative relaying scheme that enables high reliability in wireless networks. This brief presents the basic concept of DSTC, its achievable performance, generalizations, code design, and differential use. Recent results on training design and channel estimation for DSTC and the performance of training-based DSTC are also discussed.
Spacetime Metrics from Gauge Potentials
Directory of Open Access Journals (Sweden)
Ettore Minguzzi
2014-03-01
Full Text Available I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2 (or the Lie algebra of quaternions. If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S3 cosmological metric.
Space-time foam in 2D and the sum over topologies
Loll, R.; Westra, W.
2003-01-01
It is well-known that the sum over topologies in quantum gravity is ill- defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravita- tional path integral. Not even in dimension 2, where a
Indian Academy of Sciences (India)
Section 4 describes my first, aborted, attempt at a formalization, while Sections 5 to 7 present the formalization that was finished. Section 5 explains how I formalized orders and preorders. Section 6 presents a fragment of the formalization in detail, and Section 7 gives an example of how the formalization can be used to get ...
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. no reference of conformal rescaling nor conformal spacetime is made, at least not explicitly. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $\\sigma^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we obtain the Bondi mass-loss formula by integrating the Bianchi identity involving $D'\\Psi_2$ over a compact 2-surface on $\\mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $\\Lambd...
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Dark energy from discrete spacetime.
Directory of Open Access Journals (Sweden)
Aaron D Trout
Full Text Available Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Embedding Graphs in Lorentzian Spacetime
Clough, James R
2016-01-01
Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Euclidean signature, to manifolds of any metric signature. We then use this general method to develop an algorithm to be used on networks which have causal structure allowing them to be embedded in Lorentzian manifolds. The method is demonstrated by calculating embeddings for both causal sets and citation networks in Minkowski spacetime. We finally suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
Massive gravitons in arbitrary spacetimes
Mazuet, Charles; Volkov, Mikhail S.
2017-12-01
We present two different versions of the consistent theory of massive gravitons in arbitrary spacetimes which are simple enough for practical applications. The theory is described by a nonsymmetric rank-2 tensor whose equations of motion imply six algebraic and five differential constraints, reducing the number of independent components to five. The theory reproduces the standard description of massive gravitons in Einstein spaces. In generic spacetimes it does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. We find that the gravitons are stable if they are sufficiently massive, hence they may be a part of dark matter at present. We also discuss other possible applications.
Ringing in de Sitter spacetime
Directory of Open Access Journals (Sweden)
Alex Buchel
2018-03-01
Full Text Available Hydrodynamics is a universal effective theory describing relaxation of quantum field theories towards equilibrium. Massive QFTs in de Sitter spacetime are never at equilibrium. We use holographic gauge theory/gravity correspondence to describe relaxation of a QFT to its Bunch–Davies vacuum — an attractor of its late-time dynamics. Specifically, we compute the analogue of the quasinormal modes describing the relaxation of a holographic toy model QFT in de Sitter.
Black Hole: The Interior Spacetime
Ong, Yen Chin
2016-01-01
The information loss paradox is often discussed from the perspective of the observers who stay outside of a black hole. However, the interior spacetime of a black hole can be rather nontrivial. We discuss the open problems regarding the volume of a black hole, and whether it plays any role in information storage. We also emphasize the importance of resolving the black hole singularity, if one were to resolve the information loss paradox.
Directory of Open Access Journals (Sweden)
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Lorentz violations in multifractal spacetimes
Calcagni, Gianluca
2016-01-01
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would manifest an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is $E_*>10^{14}\\,\\text{GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not...
Embedding graphs in Lorentzian spacetime.
Directory of Open Access Journals (Sweden)
James R Clough
Full Text Available Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG into Minkowski spacetime using Multidimensional scaling (MDS. First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
Lorentz violations in multifractal spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)
Thermal dimension of quantum spacetime
Energy Technology Data Exchange (ETDEWEB)
Amelino-Camelia, Giovanni, E-mail: amelino@roma1.infn.it [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy); Brighenti, Francesco [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Dipartimento di Fisica e Astronomia dell' Università di Bologna and Sez. Bologna INFN, Via Irnerio 46, 40126 Bologna (Italy); Gubitosi, Giulia [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Santos, Grasiele [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)
2017-04-10
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of “dynamical dimensional reduction” which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the “spectral dimension”, which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the “thermal dimension” which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.
Thermal dimension of quantum spacetime
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Giovanni Amelino-Camelia
2017-04-01
Full Text Available Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of “dynamical dimensional reduction” which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the “spectral dimension”, which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the “thermal dimension” which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.
Multiloop string vertices from the path integral
Energy Technology Data Exchange (ETDEWEB)
Bochicchio, M.; Lerda, A.
1989-02-02
We derive the multiloop vertices for the bosonic string using path integral methods and establish a precise equivalence between the functional approach to string perturbation theory and the operator formalism on Riemann surfaces recently developed by various authors.
A Metaphysical Reflection on the Notion of Background in Modern Spacetime Physics
Vassallo, Antonio
2016-01-01
The paper presents a metaphysical characterization of spatiotemporal backgrounds from a realist perspective. The conceptual analysis is based on a heuristic sketch that encompasses the common formal traits of the major spacetime theories, such as Newtonian mechanics and general relativity. It is shown how this framework can be interpreted in a fully realist fashion, and what is the role of background structures in such a picture. In the end it is argued that, although backgrounds are a source of metaphysical discomfort, still they make a spacetime theory easy to interpret. It is also suggested that this conclusion partially explains why the notion of background independence carries a lot of conceptual difficulties.
Gauge theory of massless spin- field in de Sitter space-time
Parsamehr, S.; Mohsenzadeh, M.
2016-11-01
On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian density in de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detail for a massless spin- gauge field.
In-Out Formalism for One-Loop Effective Actions in QED and Gravity
Kim, S. P.
2017-03-01
The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes complex when pairs of charged particles are produced due to an electric field and curved spacetime. This may lead to a conjecture of one-to-one correspondence between the vacuum polarization (real part) and the vacuum persistence (imaginary part). We illustrate the one-loop effective action in a constant electric field in a Minkowski spacetime and in a uniform electric field in a two-dimensional (anti-) de Sitter space.
DEFF Research Database (Denmark)
Tastu, Julija; Pinson, Pierre; Madsen, Henrik
2015-01-01
Emphasis is placed on generating space-time trajectories of wind power generation, consisting of paths sampled from high-dimensional joint predictive densities, describing wind power generation at a number of contiguous locations and successive lead times. A modelling approach taking advantage......-correlations. Estimation is performed in a maximum likelihood framework. Based on a test case application in Denmark, with spatial dependencies over 15 areas and temporal ones for 43 hourly lead times (hence, for a dimension of n = 645), it is shown that accounting for space-time effects is crucial for generating skilful...
Mapping curved spacetimes into Dirac spinors.
Sabín, Carlos
2017-01-11
We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.
DEFF Research Database (Denmark)
Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions....
Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
Lee, Sunggeun; Roychowdhury, Raju; Yang, Hyun Seok
2012-01-01
Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a spacetime with symplectic structure. In this approach, the spacetime geometry is defined by U(1) gauge fields on noncommutative (NC) spacetime. Accordingly the topology of spacetime is determined by the topology of NC U(1) gauge fields. We show that the topolog...
Minkowski Spacetime and QED from Ontology of Time
Baumgarten, C.
Classical mechanics, relativity, electrodynamics, and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover an intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concepts with theobvious conditions for the possibility of measurements. The derived consequences put the measurement problem of quantum mechanics and the Copenhagen interpretation of the quantum mechanical wave function into perspective. According to our (onto-) logic, we find that spacetime cannot be fundamental. We argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding Lie algebra and the representation of a Clifford algebra. Within this conceptional framework, we derive the dimensionality of spacetime, the form of Lorentz transformations and of the Lorentz force and fundamental laws of physics as the Planck-Einstein relation, the Maxwell equations, and finally the Dirac equation.
Conformal symmetry inheritance in null fluid spacetimes
Tupper, B O J; Hall, G S; Coley, Alan A; Carot, J
2003-01-01
We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addition, it is shown that there are two distinct classes of non-conformally flat generalized plane wave spacetimes which possess the maximum dimension, and one class in the conformally flat case.
Path integral measure for gravitational interactions
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Kazuo Fujikawa
1983-10-01
Full Text Available It is pointed out that the path-integral variables as well as the local measure for gravitational interactions are uniquely specified if one imposes the anomaly-free condition on the Becchi-Rouet-Stora supersymmetry associated with general coordinate transformations. This prescription is briefly illustrated for the Einstein gravity and supergravity in four space-time dimensions and the relativistic string theory in two dimensions.
Directory of Open Access Journals (Sweden)
Bruchholz U. E.
2009-10-01
Full Text Available The geometry of the space-time is deduced from gravitational and electromagnetic fields. We have to state that Rainich's "already unified field theory" is the ground work of the proposed theory. The latter is deduced independently on Rainich. Rainich's analogies are brilliantly validated. His formulae are verified this way. Further reaching results and insights demonstrate that Rainich's theory is viable. In final result, we can formulate an enhanced equivalence principle. It is the equivalence of Newton's force with the Lorentz force.
Unstable Fields in Kerr Spacetimes
Dotti, Gustavo; Ranea-Sandoval, Ignacio F
2011-01-01
We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary $s=\\pm 1$ representing electromagnetic perturbations, $s=\\pm 1/2$ representing a perturbation by a Dirac field and $s=0$ representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.
Probing Gravity with Spacetime Sirens
Deffayet, Cédric; Menou, Kristen
2007-10-01
A gravitational observatory such as LISA will detect coalescing pairs of massive black holes, accurately measure their luminosity distance, and help identify a host galaxy or an electromagnetic counterpart. If dark energy is a manifestation of modified gravity on large scales, gravitational waves from cosmologically distant spacetime sirens are direct probes of this new physics. For example, a gravitational Hubble diagram based on black hole pair luminosity distances and host galaxy redshifts could reveal a large distance extradimensional leakage of gravity. Various additional signatures may be expected in a gravitational signal propagated over cosmological scales.
Cosmic Censorship for Gowdy Spacetimes
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Hans Ringström
2010-04-01
Full Text Available Due to the complexity of Einstein’s equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
Cosmic Censorship for Gowdy Spacetimes.
Ringström, Hans
2010-01-01
Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
An, Xinliang; Wong, Willie Wai Yeung
2018-01-01
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis on the Kodama vector field and the Hawking energy; the construction is signature independent. This leads to proofs of general Birkhoff-type theorems for warped product manifolds; our theorems in particular apply to situations where the warped product manifold is not necessarily Einstein, and thus can be applied to solutions with matter content in general relativity. Next we specialize to the Lorentzian case and study the propagation of null expansions under the assumption of the dominant energy condition. We prove several non-existence results relating to the Yamabe class of the fibers, in the spirit of the black-hole topology theorem of Hawking–Galloway–Schoen. Finally we discuss the effect of the warped product ansatz on matter models. In particular we construct several cosmological solutions to the Einstein–Euler equations whose spatial geometry is generally not isotropic.
Pragmatics for formal semantics
DEFF Research Database (Denmark)
Danvy, Olivier
2011-01-01
This tech talk describes how to write and how to inter-derive formal semantics for sequential programming languages. The progress reported here is (1) concrete guidelines to write each formal semantics to alleviate their proof obligations, and (2) simple calculational tools to obtain a formal...
Minkowski Spacetime A Hundred Years Later
Petkov, Vesselin
2009-01-01
This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's ...
Traversable acausal retrograde domains in spacetime
Tippett, Benjamin K.; Tsang, David
2017-05-01
In this paper we present geometry which has been designed to fit a layperson’s description of a ‘time machine’. It is a box which allows those within it to travel backwards and forwards through time and space, as interpreted by an external observer. Timelike observers travel within the interior of a ‘bubble’ of geometry which moves along a circular, acausal trajectory through spacetime. If certain timelike observers inside the bubble maintain a persistent acceleration, their worldlines will close. Our analysis includes a description of the causal structure of our spacetime, as well as a discussion of its physicality. The inclusion of such a bubble in a spacetime will render the background spacetime non-orientable, generating additional consistency constraints for formulations of the initial value problem. The spacetime geometry is geodesically incomplete, contains naked singularities, and requires exotic matter.
Evolving spacetimes with purely radial tension
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B. Nasre Esfahani
2000-12-01
Full Text Available In this study time-dependent and spherically symmetric solutions of the Einstein field equations in an anisotropic background with a purely radial tension are presented. There exist three classes of solutions,1 An open spacetime with a wormhole at its center. 2 A conical spacetime. 3 A closed spacetime. These inhomogeneous solutions are reduced to FRW spacetimes in matter-dominated era, asymptotically. Therefore, they can be used to describe local inhomogeneities that are not considered in the standard model. For the wormhole solution. it is explicity shown that the considered matter is non-exotic, that is, it does not violate the energy conditions. Also, static solutions are studied. There is only one static solution,a conical spacetime. In this case, the matter satisfies the energy condition critically.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
On the quantisation of gravity by embedding spacetime in a higher dimensional space
Pavšič, Matej
2014-01-01
Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise this 4-surface. Our formal procedure generalises our version of Stueckelberg's proper time method of worldline quantisation. We write the equations of $V_4$ in the covariant canonical form starting from a model Lagrangian which contains the classical Einstein gravity as a particular case. Then we perform quantisation in the Schr\\"odinger picture by using the concepts of a phase functional and wave functional. As a result we obtain the uncertainty relations which imply that an observer is `aware' either of a particular spacetime surface and has no information about other spacetime surfaces (which represent alternative histories); or conversely, he loses information about a particular $V_4$ whilst he obtains some information about other spacetimes (and histories). Equivalentl...
DEFF Research Database (Denmark)
Madsen, Mogens Ove
Begrebet Path Dependence blev oprindelig udviklet inden for New Institutionel Economics af bl.a. David, Arthur og North. Begrebet har spredt sig vidt i samfundsvidenskaberne og undergået en udvikling. Dette paper propagerer for at der er sket så en så omfattende udvikling af begrebet, at man nu kan...... tale om 1. og 2. generation af Path Dependence begrebet. Den nyeste udvikling af begrebet har relevans for metodologi-diskusionerne i relation til Keynes...
Differential Space-Time Block Code Modulation for DS-CDMA Systems
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Liu Jianhua
2002-01-01
Full Text Available A differential space-time block code (DSTBC modulation scheme is used to improve the performance of DS-CDMA systems in fast time-dispersive fading channels. The resulting scheme is referred to as the differential space-time block code modulation for DS-CDMA (DSTBC-CDMA systems. The new modulation and demodulation schemes are especially studied for the down-link transmission of DS-CDMA systems. We present three demodulation schemes, referred to as the differential space-time block code Rake (D-Rake receiver, differential space-time block code deterministic (D-Det receiver, and differential space-time block code deterministic de-prefix (D-Det-DP receiver, respectively. The D-Det receiver exploits the known information of the spreading sequences and their delayed paths deterministically besides the Rake type combination; consequently, it can outperform the D-Rake receiver, which employs the Rake type combination only. The D-Det-DP receiver avoids the effect of intersymbol interference and hence can offer better performance than the D-Det receiver.
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is ex- plored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman’s path integral for superposition andWheeler’s quan- tum foam of Planck mass mini black
Spaans, M.
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Schenkel, Alexander
2011-10-24
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Constraining spacetime torsion with LAGEOS
March, Riccardo; Bellettini, Giovanni; Tauraso, Roberto; Dell'Agnello, Simone
2011-11-01
We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.
Newtonian gravity on quantum spacetime
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Majid Shahn
2014-04-01
Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.
An accurate metric for the spacetime around rotating neutron stars
Pappas, George
2017-04-01
The problem of having an accurate description of the spacetime around rotating neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a rotating neutron star. Furthermore, an accurate appropriately parametrized metric, I.e. a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work, we present such an approximate stationary and axisymmetric metric for the exterior of rotating neutron stars, which is constructed using the Ernst formalism and is parametrized by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parametrization of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a three-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.
Path finding on high-dimensional free energy landscapes
Díaz Leines, G.; Ensing, B.
2012-01-01
We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the
Industrial use of formal methods formal verification
Boulanger, Jean-Louis
2012-01-01
At present the literature gives students and researchers of the very general books on the formal technics. The purpose of this book is to present in a single book, a return of experience on the used of the "formal technics" (such proof and model-checking) on industrial examples for the transportation domain. This book is based on the experience of people which are completely involved in the realization and the evaluation of safety critical system software based. The implication of the industrialists allows to raise the problems of confidentiality which could appear and so allow
Particle Physics Probes of Extra Spacetime Dimensions
Energy Technology Data Exchange (ETDEWEB)
Hewett, JoAnne L
2002-05-13
The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher dimensional spacetimes have been developed to resolve the hierarchy problem in particle physics. These scenarios make distinct predictions which allow for experiment to probe the existence of extra dimensions in new ways. We review the conceptual framework of these scenarios, their implications in collider and short-range gravity experiments, their astrophysical and cosmological effects, as well as the constraints placed on these models from present data.
Bona, Carles; Bona-Casas, Carles; Palenzuela-Luque, Carlos
The general covariant approach to general relativity is not adapted to our experience from everyday life. The most intuitive concept is not that of spacetime geometry, but rather that of a time succession of space geometries. This ‘flowing geometries’ picture could be easily put into the computer, by discretizing the time coordinate, in the same way that the continuous time flow of the real life is coded in terms of a discrete set of photograms in a movie.
Cylindrical symmetry locally isometric $AdS_{4}$ spacetime
Ahmed, Faizuddin; Sarma, Debojit; Myrzakulov, Ratbay
2016-01-01
We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from curvature singularities and an $4D$ extension of the Misner space in curved spacetime with identical causality violating properties.
No Smooth Beginning for Spacetime
Feldbrugge, Job; Lehners, Jean-Luc; Turok, Neil
2017-10-01
We identify a fundamental obstruction to any theory of the beginning of the Universe, formulated as a semiclassical path integral. The Hartle-Hawking no boundary proposal and Vilenkin's tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. We introduce a new mathematical tool—Picard-Lefschetz theory—for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is mathematically meaningful in this approach, but the Euclidean version is not. The Lorentzian-Picard-Lefschetz formulation yields unambiguous predictions. Unfortunately, the outcome is that primordial tensor (gravitational wave) fluctuations are unsuppressed. We prove a general theorem to this effect, in a wide class of theories.
Lake, Kayll
2010-12-01
example, does not contain reference to the insights found by Pretorius and Israel [2]. This is perhaps justifiable in view of the many specialized texts devoted to the Kerr space-time (e.g. [3]). The large clear diagrams that one becomes accustomed to in this book show off the Taub-NUT (and related) space-times in the next chapter. After perhaps a somewhat standard discussion of stationary axially symmetric space-times, there is a very informative discussion of accelerating black holes. For example, the global structure of the C-metric is considered in detail. This is followed by a brief discussion of solutions for uniformly accelerating particles. The discussion of the Plebański-Demiański solutions contains two very useful flow charts that help to systematize two rather complex families of solutions. After a somewhat brief discussion of plane and pp-waves, the authors give an extensive discussion of the Kunt solutions. I note here that after this text was in production the importance of the Kunt space-times as regards the characterization of space-times by scalar curvature invariants was made clear [4]. The discussion of the Robinson-Trautman solutions that follows is extensive, containing, for example, details of the singularity structure and of the global structure. The final formal chapter in this text covers colliding plane waves. This contains, for example, discussions of the Khan-Penrose, Ferrari-Ibañez and Chandrasekhar-Xanthopoulos solutions. The text ends with a `final miscellany'. This covers a number of interesting topics, but I found the discussion of the Lemaître-Tolman solutions rather weak (compare e.g. [5]). The book has two quite useful appendices covering 2-spaces and 3-spaces of constant curvature. To conclude, I will quote from the dust jacket: `The book is an invaluable resource for both graduate students and academic researchers working in gravitational physics'. I highly recommend it. References [1] Stephani H, Kramer D, MacCallum M
Gravitational geons in asymptotically anti-de Sitter spacetimes
Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter
2017-06-01
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.
An accurate metric for the spacetime around neutron stars
Pappas, George
2016-01-01
The problem of having an accurate description of the spacetime around neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a neutron star. Furthermore, an accurate appropriately parameterised metric, i.e., a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work we present such an approximate stationary and axisymmetric metric for the exterior of neutron stars, which is constructed using the Ernst formalism and is parameterised by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical propert...
Measuring Space-Time Geometry over the Ages
Energy Technology Data Exchange (ETDEWEB)
Stebbins, Albert; /Fermilab
2012-05-01
Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.
Relativity as the quantum mechanics of space-time measurements
Lieu, Richard
2016-01-01
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) {\\it alone} if space-time quantization is a fundamental law of physics which must be included as part of the Postulate. An important corollary, however, is that when measuring devices which carry the basic units of lengths and time (e.g. a clock ticking every time quantum) are `moving' uniformly, they appear to be measuring with larger units. Secondly, such an apparent increase in the sizes of the quanta can be attributed to extra fluctuations associated with motion, which are precisely described in terms of a thermally agitated harmonic oscillator by using a temperature parameter. This provides a stringent constraint on the microscopic properties of flat space-time: it is an array of quantized oscillators. Thirdly, sin...
Spacetime Encodings III - Second Order Killing Tensors
Brink, Jeandrew
2009-01-01
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher- order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require...
Metastring theory and modular space-time
National Research Council Canada - National Science Library
Freidel, Laurent; Leigh, Robert G; Minic, Djordje
2015-01-01
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory...
Field Theory on Curved Noncommutative Spacetimes
Directory of Open Access Journals (Sweden)
Alexander Schenkel
2010-08-01
Full Text Available We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005, 3511 and Classical Quantum Gravity 23 (2006, 1883], we describe noncommutative spacetimes by using (Abelian Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.
The bizarre anti-de Sitter spacetime
Sokolowski, Leszek M
2016-01-01
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we derive \\textit{ab initio\\/} all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five--dimensional space. Employing the latter space one is able to explain these bizarre features of anti--de Sitter spacetime; in this sense the spacetime is not self--contained. This is not a physical world.
General formalism for the stability of thin-shell wormholes in 2 + 1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia [Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina); Eiroa, Ernesto F. [Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Simeone, Claudio [Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); IFIBA-CONICET, Buenos Aires (Argentina)
2014-08-15
In this article we theoretically construct circular thin-shell wormholes in a 2 + 1-dimensional spacetime. The construction is symmetric with respect to the throat. We present a general formalism for the study of the mechanical stability under perturbations preserving the circular symmetry of the configurations, adopting a linearized equation of state for the exotic matter at the throat. We apply the formalism to several examples. (orig.)
The space-time cube revisited it potential to visualize mobile data
DEFF Research Database (Denmark)
Kveladze, Irma; Kraak, Menno-Jan
2010-01-01
in transportation (Miller, 2003), gender studies (Kwan, 1999) among others. Stations are locations of no-movement and are the vertical lines in a path. They can also be used separately of the paths as done by Gatalski (2004), while analyzing earthquake information. Or by Kraak & Madzudzo (2007) to analyze the Black...... Death locations in 14th century in Europe. The STP, representing a reachable space by individual in an available time and is utilized in the study of space-time accessibility. It has been used by Neutens (2010), and as taxels (volume of cells) by Forer and Huisman (1998), with the aim to aggregate...
Double conformal space-time algebra
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Exact Philosophy of Space-Time
Vucetich, Héctor
2011-01-01
Starting from Bunge's (1977) scientific ontology, we expose a materialistic relational theory of space-time, that carries out the program initiated by Leibniz, and provides a protophysical basis consistent with any rigorous formulation of General Relativity. Space-time is constructed from general concepts which are common to any consistent scientific theory and they are interpreted as emergent properties of the greatest assembly of things, namely, the world.
Twin Paradox in de Sitter Spacetime
Boblest, Sebastian; Wunner, Günter
2010-01-01
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the traveling observer and an observer at rest.
Dynamical Space-Time and Gravitational Waves
van Holten, J W
2016-01-01
According to General Relativity gravity is the result of the interaction between matter and space-time geometry. In this interaction space-time geometry itself is dynamical: it can store and transport energy and momentum in the form of gravitational waves. We give an introductory account of this phenomenon and discuss how the observation of gravitational waves may open up a fundamentally new window on the universe.
Space-Time Disarray and Visual Awareness
Directory of Open Access Journals (Sweden)
Jan Koenderink
2012-04-01
Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.
Geometry and Formal Linguistics.
Huff, George A.
This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
Over recent decades, institutions exhibiting high degrees of formality have come in for severe criticism. From the private to the public sector, and across a whole spectrum of actors spanning from practitioners to academics, formal organization is viewed with increasing doubt and skepticism. In a...
Griffies, Stephen Matthew
1993-01-01
Field theoretic and spacetime aspects of nontrivial planar supersymmetric bosonic field configurations in d = 3 + 1, N = 1 supergravity coupled to a chiral superfield are presented. They are topologically stable and static domain walls interpolating between non -positive cosmological constant (Lambdaequations. The induced spacetime is static. An especially novel solution is the Minkowski--anti-de Sitter (AdS_4) wall (Type I wall). Supersymmetric vacua are shown to be absolutely stable (to all orders in Newton's constant) towards quantum decay into another supersymmetric vacuum. The methods of supersymmetry and the language of Coleman's quantum tunneling are employed. This result proves the degeneracy of all supersymmetric vacua in N = 1 supergravity regardless of the relative value of their LambdaCauchy horizons inherited from AdS_4. Lattices of these walls are possible when completing the spacetime manifold which possess causal structures similar to extreme black holes. In these lattices, the time-like boundary of pure AdS_4 is replaced by a wall thus making all affine boundaries null. Quantum field theory on the Type I background indicates that it has zero Hawking temperature and zero spacetime entropy. Generalizations of the supergravity walls to non -supersymmetric non- and ultra-extreme walls are presented. These walls are compact two-spheres corresponding to topological walls formed from the Kibble mechanism (non-extreme: bubbles with two insides) and the classical evolution of quantum tunneling bubbles (ultra-extreme: bubbles with an inside and an outside). Israel's formalism for singular hypersurfaces is used to deduce the local spacetime properties working in the wall's comoving frame. Geodesically complete manifolds are given, some of which exhibit natural generalizations of the extreme wall lattices. Analysis of the non-supersymmetric bubbles, in the context of Tolman's effective gravitation, indicates the absence of observers outside of negatively
DEFF Research Database (Denmark)
Karnøe, Peter; Garud, Raghu
2012-01-01
. Competencies emerged through processes and mechanisms such as co-creation that implicated multiple learning processes. The process was not an orderly linear one as emergent contingencies influenced the learning processes. An implication is that public policy to catalyse clusters cannot be based......This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts...
DEFF Research Database (Denmark)
Garsten, Christina; Nyqvist, Anette
Ethnographic work in formal organizations involves learning to recognize the many layers of front stage and back stage of organized life, and to bracket formality. It means to be alert to the fact that what is formal and front stage for one some actors, and in some situations, may in fact be back...... stage and informal for others. Walking the talk, donning the appropriate attire, wearing the proper suit, may be part of what is takes to figure out the code of formal organizational settings – an entrance ticket to the backstage, as it were. Oftentimes, it involves a degree of mimicry, of ‘following...... suits’ (Nyqvist 2013), and of doing ‘ethnography by failure’ (Garsten 2013). In this paper, we explore the layers of informality and formality in our fieldwork experiences among financial investors and policy experts, and discuss how to ethnographically represent embodied fieldwork practices. How do we...
Thermodynamics of quantum spacetime histories
Smolin, Lee
2017-11-01
We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez [Phys. Rev. D 87, 121503 (2013); , 10.1103/PhysRevD.87.121503Phys. Rev. D 89, 084069 (2014); , 10.1103/PhysRevD.89.084069Phys. Rev. Lett. 107, 241301 (2011); , 10.1103/PhysRevLett.107.241301Phys. Rev. Lett.108, 169901(E) (2012)., 10.1103/PhysRevLett.108.169901] and Bianchi [arXiv:1204.5122.]. This allows us to apply a recent argument of Jacobson [Phys. Rev. Lett. 116, 201101 (2016).10.1103/PhysRevLett.116.201101] to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.
Quantum cosmology based on discrete Feynman paths
Energy Technology Data Exchange (ETDEWEB)
Chew, Geoffrey F.
2002-10-10
Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''.
Levy, Joseph
2008-01-01
The aim of this first volume of papers is to examine the different paths by which the modern ether concept has been developed and to highlight the part it plays in major departments of 21st century physics. The evidence for its existence is reviewed, and it is hoped, widespread misconceptions concerning ether are corrected. It is anticipated that the emerging modern concept of ether will play a fundamental part in the development of 21st century physical science.
Imprint of quantum gravity in the dimension and fabric of spacetime
Amelino-Camelia, Giovanni; Calcagni, Gianluca; Ronco, Michele
2017-11-01
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within the framework of multifractional theories, whose key assumption is an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared. This sole ingredient is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements that was reported in studies combining quantum mechanics and general relativity heuristically. This allows us to fix two free parameters of the theory and leads, in one of the scenarios we contemplate, to a value of the ultraviolet dimension which had already found support in other quantum-gravity analyses. We also formalize a picture such that fuzziness originates from a fundamental discrete scale invariance at short scales and corresponds to a stochastic spacetime geometry.
DEFF Research Database (Denmark)
Rand, John; Torm, Nina Elisabeth
2012-01-01
Based on unique panel data consisting of both formal and informal firms, this paper uses a matched double difference approach to examine the relationship between legal status and firm level outcomes in micro, small and medium manufacturing enterprises (SMEs) in Vietnam. Controlling for determining...... factors and observable time-variant factors that may simultaneously influence the decision to formalize and subsequent firm performance, we find evidence that becoming officially registered leads to an increase in profits and investments, and a decrease in the use of casual labor (improved contract...... conditions for workers). Thus, we conclude that formalizing is beneficial both to firms and the workers in these firms....
Indian Academy of Sciences (India)
Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...
Integrated formal operations plan
Energy Technology Data Exchange (ETDEWEB)
Cort, G.; Dearholt, W.; Donahue, S.; Frank, J.; Perkins, B.; Tyler, R.; Wrye, J.
1994-01-05
The concept of formal operations (that is, a collection of business practices to assure effective, accountable operations) has vexed the Laboratory for many years. To date most attempts at developing such programs have been based upon rigid, compliance-based interpretations of a veritable mountain of Department of Energy (DOE) orders, directives, notices, and standards. These DOE dictates seldom take the broad view but focus on highly specialized programs isolated from the overall context of formal operations. The result is a confusing array of specific, and often contradictory, requirements that produce a patchwork of overlapping niche programs. This unnecessary duplication wastes precious resources, dramatically increases the complexity of our work processes, and communicates a sense of confusion to our customers and regulators. Coupled with the artificial divisions that have historically existed among the Laboratory`s formal operations organizations (quality assurance, configuration management, records management, training, etc.), this approach has produced layers of increasingly vague and complex formal operations plans, each of which interprets its parent and adds additional requirements of its own. Organizational gridlock ensues whenever an activity attempts to implement these bureaucratic monstrosities. The integrated formal operations plan presented is to establish a set of requirements that must be met by an integrated formal operations program, assign responsibilities for implementation and operation of the program, and specify criteria against which the performance of the program will be measured. The accountable line manager specifies the items, processes, and information (the controlled elements) to which the formal operations program specified applies. The formal operations program is implemented using a graded approach based on the level of importance of the various controlled elements and the scope of the activities in which they are involved.
DEFF Research Database (Denmark)
Levinsen, Karin Tweddell; Sørensen, Birgitte Holm
2013-01-01
are examined and the relation between network society competences, learners’ informal learning strategies and ICT in formalized school settings over time is studied. The authors find that aspects of ICT like multimodality, intuitive interaction design and instant feedback invites an informal bricoleur approach....... When integrated into certain designs for teaching and learning, this allows for Formalized Informal Learning and support is found for network society competences building....
Mapping superintegrable quantum mechanics to resonant spacetimes
Evnin, Oleg; Demirchian, Hovhannes; Nersessian, Armen
2018-01-01
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to nonrelativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in application to (typically, superintegrable) problems whose energy spectrum is given by a quadratic function of the energy level number, since for such systems the spacetimes one obtains possess evenly spaced, resonant spectra of frequencies for scalar fields of a certain mass. This construction emerges as a generalization of the previously studied correspondence between the Higgs oscillator and anti-de Sitter spacetime, which has been useful for both understanding weakly nonlinear dynamics in anti-de Sitter spacetime and algebras of conserved quantities of the Higgs oscillator. Our conversion procedure ("Klein-Gordonization") reduces to a nonlinear elliptic equation closely reminiscent of the one emerging in relation to the celebrated Yamabe problem of differential geometry. As an illustration, we explicitly demonstrate how to apply this procedure to superintegrable Rosochatius systems, resulting in a large family of spacetimes with resonant spectra for massless wave equations.
Noncommutative effects of spacetime on holographic superconductors
Directory of Open Access Journals (Sweden)
Debabrata Ghorai
2016-07-01
Full Text Available The Sturm–Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born–Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that the higher value of noncommutative parameter and Born–Infeld parameter make the condensate harder to form. We also observe that the noncommutative structure of spacetime makes the critical temperature depend on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
Noncommutative effects of spacetime on holographic superconductors
Energy Technology Data Exchange (ETDEWEB)
Ghorai, Debabrata, E-mail: debanuphy123@gmail.com [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700098 (India); Gangopadhyay, Sunandan, E-mail: sunandan.gangopadhyay@gmail.com [Department of Physics, West Bengal State University, Barasat (India); Inter University Centre for Astronomy & Astrophysics, Pune (India)
2016-07-10
The Sturm–Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born–Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that the higher value of noncommutative parameter and Born–Infeld parameter make the condensate harder to form. We also observe that the noncommutative structure of spacetime makes the critical temperature depend on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
On the reconstruction of Lifshitz spacetimes
Energy Technology Data Exchange (ETDEWEB)
Gentle, Simon A. [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States); Keeler, Cynthia [Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK 2100, Copenhagen (Denmark)
2016-03-30
We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or ‘hole-ography’), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of http://dx.doi.org/10.1007/JHEP10(2014)149. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.
Scalar fields in black hole spacetimes
Thuestad, Izak; Khanna, Gaurav; Price, Richard H.
2017-07-01
The time evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, timelike infinity, and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index ℓ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.
Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime
Directory of Open Access Journals (Sweden)
Zhiming Huang
2017-10-01
Full Text Available We investigate the dynamics of entanglement between two atoms in de Sitter spacetime and in thermal Minkowski spacetime. We treat the two-atom system as an open quantum system which is coupled to a conformally coupled massless scalar field in the de Sitter invariant vacuum or to a thermal bath in the Minkowski spacetime, and derive the master equation that governs its evolution. We compare the phenomena of entanglement creation, degradation, revival and enhancement for the de Sitter spacetime case with that for the thermal Minkowski spacetime case. We find that the entanglement dynamics of two atoms for these two spacetime cases behave quite differently. In particular, the two atoms interacting with the field in the thermal Minkowski spacetime (with the field in the de Sitter-invariant vacuum, under certain conditions, could be entangled, while they would not become entangled in the corresponding de Sitter case (in the corresponding thermal Minkowski case. Thus, although a single static atom in the de Sitter-invariant vacuum responds as if it were bathed in thermal radiation in a Minkowski universe, with the help of the different dynamic evolution behaviors of entanglement for two atoms one can in principle distinguish these two universes.
The Dirac point electron in zero-gravity Kerr–Newman spacetime
Energy Technology Data Exchange (ETDEWEB)
Kiessling, M. K.-H.; Tahvildar-Zadeh, A. S. [Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854 (United States)
2015-04-15
Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
The birth of spacetime atoms as the passage of time
Dowker, Fay
2014-01-01
The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new spacetime atoms.
Racing a quantum computer through Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Biamonte, Jacob D [Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD (United Kingdom)
2010-05-01
The Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers.
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Wave regularity in curve integrable spacetimes
Sanchez, Yafet Sanchez
2015-01-01
The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In particular, the concept of wave regularity is introduced which serves to show that the classical singularities in curve integrable spacetimes do not interrupt the well-posedness of the wave equation. The techniques used also provide arguments that can be extended to establish when a classically singular spacetime remains singular in a semi-classical picture.
Special relativity derived from spacetime magma.
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Special relativity derived from spacetime magma.
Directory of Open Access Journals (Sweden)
Fred Greensite
Full Text Available We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Space-time system architecture for the neural optical computing
Lo, Yee-Man V.
1991-02-01
The brain can perform the tasks of associative recall detection recognition and optimization. In this paper space-time system field models of the brain are introduced. They are called the space-time maximum likelihood associative memory system (ST-ML-AMS) and the space-time adaptive learning system (ST-ALS). Performance of the system is analyzed using the probability of error in memory recall (PEMR) and the space-time neural capacity (ST-NC). 1.
Stability of generic thin shells in conformally flat spacetimes
Amirabi, Z.
2017-07-01
Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p=ω σ . It is shown that, for the physical domain of ω , i.e., 0Mannheim spacetime as the outer region is also investigated.
Formalizing Restriction Categories
Directory of Open Access Journals (Sweden)
James Chapman
2017-03-01
Full Text Available Restriction categories are an abstract axiomatic framework by Cockett and Lack for reasoning about (generalizations of the idea of partiality of functions. In a restriction category, every map defines an endomap on its domain, the corresponding partial identity map. Restriction categories cover a number of examples of different flavors and are sound and complete with respect to the more synthetic and concrete partial map categories. A partial map category is based on a given category (of total maps and a map in it is a map from a subobject of the domain. In this paper, we report on an Agda formalization of the first chapters of the theory of restriction categories, including the challenging completeness result. We explain the mathematics formalized, comment on the design decisions we made for the formalization, and illustrate them at work.
Formalizing Probabilistic Safety Claims
Herencia-Zapana, Heber; Hagen, George E.; Narkawicz, Anthony J.
2011-01-01
A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.
Fermionic currents in AdS spacetime with compact dimensions
Bellucci, S.; Saharian, A. A.; Vardanyan, V.
2017-09-01
We derive a closed expression for the vacuum expectation value (VEV) of the fermionic current density in a (D +1 )-dimensional locally AdS spacetime with an arbitrary number of toroidally compactified Poincaré spatial dimensions and in the presence of a constant gauge field. The latter can be formally interpreted in terms of a magnetic flux treading the compact dimensions. In the compact subspace, the field operator obeys quasiperiodicity conditions with arbitrary phases. The VEV of the charge density is zero and the current density has nonzero components along the compact dimensions only. They are periodic functions of the magnetic flux with the period equal to the flux quantum and tend to zero on the AdS boundary. Near the horizon, the effect of the background gravitational field is small and the leading term in the corresponding asymptotic expansion coincides with the VEV for a massless field in the locally Minkowski bulk. Unlike the Minkowskian case, in the system consisting of an equal number of fermionic and scalar degrees of freedom, with same masses, charges and phases in the periodicity conditions, the total current density does not vanish. In these systems, the leading divergences in the scalar and fermionic contributions on the horizon are canceled and, as a consequence of that, the charge flux, integrated over the coordinate perpendicular to the AdS boundary, becomes finite. We show that in odd spacetime dimensions the fermionic fields realizing two inequivalent representations of the Clifford algebra and having equal phases in the periodicity conditions give the same contribution to the VEV of the current density. Combining the contributions from these fields, the current density in odd-dimensional C -,P - and T -symmetric models are obtained. As an application, we consider the ground state current density in curved carbon nanotubes described in terms of a (2 +1 )-dimensional effective Dirac model.
Žáček, Martin
2017-07-01
Ontology or formal ontology? Which word is correct? The aim of this article is to introduce correct terms and explain their basis. Ontology describes a particular area of interest (domain) in a formal way - defines the classes of objects that are in that area, and relationships that may exist between them. Meaning of ontology consists mainly in facilitating communication between people, improve collaboration of software systems and in the improvement of systems engineering. Ontology in all these areas offer the possibility of unification of view, maintaining consistency and unambiguity.
DEFF Research Database (Denmark)
Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard
2015-01-01
The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.......The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe....
Riemann curvature of a boosted spacetime geometry
Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco
2016-10-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.
Space-time modeling of timber prices
Mo Zhou; Joseph Buongriorno
2006-01-01
A space-time econometric model was developed for pine sawtimber timber prices of 21 geographically contiguous regions in the southern United States. The correlations between prices in neighboring regions helped predict future prices. The impulse response analysis showed that although southern pine sawtimber markets were not globally integrated, local supply and demand...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event ...
Twin Paradox in de Sitter Spacetime
Boblest, Sebastian; Muller, Thomas; Wunner, Gunter
2011-01-01
The "twin paradox" of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline…
Wave Equations in Bianchi Space-Times
Directory of Open Access Journals (Sweden)
S. Jamal
2012-01-01
Full Text Available We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.
Superconformal quantum field theory in curved spacetime
de Medeiros, Paul; Hollands, Stefan
2013-09-01
By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.
Kundt spacetimes minimally coupled to scalar field
Energy Technology Data Exchange (ETDEWEB)
Tahamtan, T. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic); Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic); Svitek, O. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic)
2017-06-15
We derive an exact solution belonging to the Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations. (orig.)
Quantum fluctuations in FRLW space-time
Rabochaya, Y.
2015-01-01
In this paper we study a quantum field theoretical approach, where a quantum probe is used to investigate the properties of generic non-flat FRLW space time. The fluctuations related to a massless conformal coupled scalar field defined on a space-time with horizon is identified with a probe and the procedure to measure the local temperature is presented.
The Thermal Entropy Density of Spacetime
Directory of Open Access Journals (Sweden)
Rongjia Yang
2013-01-01
Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.
Schellhorn, Gerhard
2002-01-01
Formal fault tree semantics / G. Schellhorn, A. Thums, and W. Reif. - In: IDPT : Proceedings of the Sixth World Conference on Integrated Design and Process Technology : June 23 - 27, 2003, Pasadena, California / SDPS, Society for Design & Process Science. - 2002. - 1CD-ROM
Formalizing physical security procedures
Meadows, C.; Pavlovic, Dusko
Although the problems of physical security emerged more than 10,000 years before the problems of computer security, no formal methods have been developed for them, and the solutions have been evolving slowly, mostly through social procedures. But as the traffic on physical and social networks is now
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
2016-01-01
term this ‘fear of the formal’, outlining key elements of its genealogy and exploring its contemporary manifestation in relation to recent and ongoing reforms of organisational life in a range of contexts. At the same time, we seek to indicate the continuing constitutive significance of formality...
2009-09-01
automated enforcement [52]. Other policy languages such as P3P [15], which has a formal notation, inform website visitors of the site’s privacy practices...Lorrie Faith Cranor. Web Privacy with P3P . O’Reilly, September 2002. [16] Lorrie Faith Cranor, Praveen Guduru, and Manjula Arjula. User interfaces for
Comparing Formal Specification Languages
Harmelen, van F.A.H.; Lopez de Mantaras, R.; Malec, J.; Treur, J.
This paper presents a comparison between eight specification languages discussed during the Workshop on Formal Specification Techniques for Complex Reasoning Systems held in Vienna during the ECAI'92 conference. The languages as discussed here possess many important common characteristics, but also
Methodologies for tracking learning paths
DEFF Research Database (Denmark)
Frølunde, Lisbeth; Gilje, Øystein; Lindstrand, Fredrik
2009-01-01
The article concerns the design of a collaborative research project (2008-09) entitled Making a Filmmaker, which examines how young Scandinavian filmmakers create their own learn- ing paths in formal and/or informal contexts. Our interest is how learning experiences and contexts motivate the young...... filmmakers: what furthers their interest and/or hinders it, and what learning patterns emerge. The aim of this article is to present and discuss issues regarding the methodology and meth- ods of the study, such as developing a relationship with interviewees when conducting inter- views online (using MSN). We...... platform that is familiar to our participants....
Feynman’s path integral seen as a Henstock integral
Guadalupe Morales, M.; Gaitán, Ricardo
2017-10-01
The motivation of this paper is to give mathematical formalism to the Feynman path integral using the Henstock integral. This integral saves some of Feynman’s integral difficulties and justifies Feynman’s intuition: to interpret the state function as “a sum of complex contributions, one from each path in the region”.
The space-time outside a source of gravitational radiation: the axially symmetric null fluid
Energy Technology Data Exchange (ETDEWEB)
Herrera, L. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Universidad de Salamanca, Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain); Di Prisco, A. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Ospino, J. [Universidad de Salamanca, Departamento de Matematica Aplicada and Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain)
2016-11-15
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric space-times. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the 1 + 3 formalism. (orig.)
Emergence of spacetime in stochastic gravity
Mattingly, James
2013-08-01
I focus on the stochastic gravity program, a program that conceptualizes spacetime as the hydrodynamic limit of the correlation hierarchy of an underlying quantum theory, that is, a theory of the microscopic theory of gravity. This approach is relatively obscure, and so I begin by outlining the stochastic gravity program in enough detail to make clear the basic sense in which, on this approach, spacetime emerges from more fundamental physical structures. The theory, insofar as it is a univocal theory, is quite clear in its basic features, and so issues of philosophical interpretation can be readily isolated. The most obvious reason to investigate the theory as a model for the emergence of spacetime structure is how close it is to the stage at which the behavior that we recognize as spacetime actually emerges from the micro gravitational system. Approaches that begin with fully quantum gravity (insofar as there is such a thing) treat a system that is conceptually quite far removed from the stage at which emergence is relevant. The stochastic approach however begins by identifying the point at which spacetime emerges as a phenomena of interest. I begin with an analysis of the emergence question generally and ask how best we should understand it, especially from the point of view of thinking of spacetime as emergent. A nice feature of the stochastic program is how clear the question of emergence is on this approach. In part this is because of its similarity by design to the kinetic theory of gases and solid state physics. And so many of the analyses of the emergence of macroscopic variables in the thermodynamic limit can be repurposed to understand how an apparently continuous metrical space emerges from the behavior of a non-spatial system. A serious interpretive problem looms however. The problem is that there is no clear connection between features of the kinetic theory of gravity, as a quantum theory, and any final theory of gravity. In the third part of the paper
Talebian-Ashkezari, Alireza; Abolhasani, Ali Akbar
2016-01-01
We study the evolution of the "non-perturbative" metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the "{\\delta}M formalism" for calculating the evolution of the tensor perturbations in anisotropic inflation models in almost similar way as the so-called {\\delta}N formula for the super-horizon dynamics of the curvature perturbations. Likewise its ancestor, {\\delta}N formalism, this new method can substantially reduce the amount of calculations related to the evolution of the tensor modes.
Readings in Formal Epistemology
DEFF Research Database (Denmark)
‘Formal epistemology’ is a term coined in the late 1990s for a new constellation of interests in philosophy,the roots of which are found in earlier works of epistemologists, philosophers of science, and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty......, rationality, deliberation, decision, strategy, action and agent interaction – and it does so using methods from logic, probability, computability, decision, and game theory. This volume presents 42 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy...... and its neighbouring intellectual disciplines. The editors provide introductions to five basic subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Logics of Knowledge and Belief. The volume also includes a thorough index and suggestions for further reading...
Talebian-Ashkezari, Alireza; Ahmadi, Nahid; Abolhasani, Ali Akbar
2016-01-01
We study the evolution of the "non-perturbative" metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the "{\\delta}M formalism" for calculating the evolution of the tensor perturbations in anisotropic inflation models in almost similar way as the so...
Formal groups and applications
Hazewinkel, Michiel
2012-01-01
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
TASI Lectures on Holographic Space-Time, SUSY, and Gravitational Effective Field Theory
Banks, Tom
2012-11-01
I argue that the conventional field theoretic notion of vacuum state is not valid in quantum gravity. The arguments use gravitational effective field theory, as well as results from string theory, particularly the AdS/CFT correspondence. Different solutions of the same low energy gravitational field equations correspond to different quantum systems, rather than different states in the same system. I then introduce holographic space-time a quasi-local quantum mechanical construction based on the holographic principle. I argue that models of quantum gravity in asymptotically flat space-time will be exactly super-Poincare invariant, because the natural variables of holographic space-time for such a system, are the degrees of freedom of massless superparticles. The formalism leads to a non-singular quantum Big Bang cosmology, in which the asymptotic future is required to be a de Sitter space, with cosmological constant (c.c.) determined by cosmological initial conditions. It is also approximately SUSic in the future, with the gravitino mass KΛ1/4.
Petrov classification and holographic reconstruction of spacetime
Energy Technology Data Exchange (ETDEWEB)
Gath, Jakob [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Mukhopadhyay, Ayan [Department of Physics, University of Crete,Heraklion 71003 (Greece); Petkou, Anastasios C. [Department of Physics, Institute of Theoretical Physics,Aristotle University of Thessaloniki,54124, Thessaloniki (Greece); Petropoulos, P. Marios [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Siampos, Konstantinos [Albert Einstein Center for Fundamental Physics,Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-09-01
Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov’s classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebański-Demiański Petrov D family.
Geometric inequalities in spherically symmetric spacetimes
Csukás, Károly Z.
2017-07-01
In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner-Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.
spacetime : Spatio-Temporal Data in R
Directory of Open Access Journals (Sweden)
Edzer Pebesma
2012-11-01
Full Text Available This document describes classes and methods designed to deal with different types of spatio-temporal data in R implemented in the R package spacetime, and provides examples for analyzing them. It builds upon the classes and methods for spatial data from package sp, and for time series data from package xts. The goal is to cover a number of useful representations for spatio-temporal sensor data, and results from predicting (spatial and/or temporal interpolation or smoothing, aggregating, or subsetting them, and to represent trajectories. The goals of this paper is to explore how spatio-temporal data can be sensibly represented in classes, and to find out which analysis and visualisation methods are useful and feasible. We discuss the time series convention of representing time intervals by their starting time only. This document is the main reference for the R package spacetime, and is available (in updated form as a vignette in this package.
Black hole evaporation rates without spacetime.
Braunstein, Samuel L; Patra, Manas K
2011-08-12
Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high dimensionality of black holes, global conservation of the no-hair quantities, and the existence of Penrose processes. Our analysis is not wedded to standard general relativity and so should apply to extended gravity theories where we find that the black hole area must be replaced by some other property in any generalized area theorem.
Twin paradox in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Boblest, Sebastian; Wunner, Guenter [Institut fuer Theoretische Physik, Universitaet Stuttgart, Pfaffenwaldring 57 IV, 70550 Stuttgart (Germany); Mueller, Thomas, E-mail: sebastian.boblest@itp1.uni-stuttgart.de, E-mail: Thomas.Mueller@vis.uni-stuttgart.de, E-mail: guenter.wunner@itp1.uni-stuttgart.de [Visualisierungsinstitut der Universitaet Stuttgart (VISUS), Allmandring 19, 70569 Stuttgart (Germany)
2011-09-15
The 'twin paradox' of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the travelling observer and an observer at rest. This paper is intended to give graduate students who are familiar with special relativity and have some basic experience of general relativity a deeper insight into accelerated motion in general relativity, into the relationship between the proper times of different observers and the propagation of light signals between them, and into the use of compactification to describe the global structure of a relativistic model.
An Uncertainty Relation of Space-Time
Sasakura, N.
1999-01-01
We propose an uncertainty relation of space-time. This relation is characterized by GhT \\lesssim \\delta V, where T and \\delta V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of 't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmi...
Space-time fractional Zener wave equation.
Atanackovic, T M; Janev, M; Oparnica, Lj; Pilipovic, S; Zorica, D
2015-02-08
The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.
Measuring space-time fuzziness with high energy γ-ray detectors
Directory of Open Access Journals (Sweden)
Cattaneo Paolo Walter
2017-01-01
Full Text Available There are several suggestions to probe space-time fuzziness (also known as space-time foam due to the quantum mechanics nature of space-time. These effects are predicted to be very small, being related to the Planck length, so that the only hope to experimentally detect them is to look at particles propagating along cosmological distances. Some phenomenological approaches suggest that photons originating from pointlike sources at cosmological distance experience path length fluctuation that could be detected. Also the direction of flight of such photons may be subject to a dispersion such that the image of a point-like source is blurred and detected as a disk. An experimentally accessible signature may be images of point-like sources larger that the size due to the Point Spread Function of the instrument. This additional broadening should increase with distance and photon energy. Some concrete examples that can be studied with the AGILE and FERMI-LAT γ -ray satellite experiments are discussed.
Space-time modeling of soil moisture
Chen, Zijuan; Mohanty, Binayak P.; Rodriguez-Iturbe, Ignacio
2017-11-01
A physically derived space-time mathematical representation of the soil moisture field is carried out via the soil moisture balance equation driven by stochastic rainfall forcing. The model incorporates spatial diffusion and in its original version, it is shown to be unable to reproduce the relative fast decay in the spatial correlation functions observed in empirical data. This decay resulting from variations in local topography as well as in local soil and vegetation conditions is well reproduced via a jitter process acting multiplicatively over the space-time soil moisture field. The jitter is a multiplicative noise acting on the soil moisture dynamics with the objective to deflate its correlation structure at small spatial scales which are not embedded in the probabilistic structure of the rainfall process that drives the dynamics. These scales of order of several meters to several hundred meters are of great importance in ecohydrologic dynamics. Properties of space-time correlation functions and spectral densities of the model with jitter are explored analytically, and the influence of the jitter parameters, reflecting variabilities of soil moisture at different spatial and temporal scales, is investigated. A case study fitting the derived model to a soil moisture dataset is presented in detail.
Entwinement and the emergence of spacetime
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Vijay [David Rittenhouse Laboratories, University of Pennsylvania, 209 S 33 Street, Philadelphia, PA 19104 (United States); CUNY Graduate Center, Initiative for the Theoretical Sciences, 365 Fifth Avenue, New York, NY 10016 (United States); Chowdhury, Borun D. [Department of Physics, Arizona State University, Tempe, Arizona 85287 (United States); Czech, Bartłomiej [Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States); Boer, Jan de [Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2015-01-12
It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by “internal”, possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow — the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario — a 2d conformal field theory (CFT) that is dual to a conical defect in AdS{sub 3} space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.
Inequivalence of coset constructions for spacetime symmetries
Energy Technology Data Exchange (ETDEWEB)
Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34151 Trieste (Italy); Institute for Advanced Study, Princeton, NJ 08540 (United States); Serone, Marco [SISSA, via Bonomea 265, 34136 Trieste (Italy); Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34151 Trieste (Italy); INFN - Sezione di Trieste, 34151 Trieste (Italy); Trevisan, Gabriele [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN - Sezione di Trieste, 34151 Trieste (Italy); Trincherini, Enrico [Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa (Italy); INFN - Sezione di Pisa, 56100 Pisa (Italy)
2015-02-05
Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios.
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
Nonclassical paths in quantum interference experiments.
Sawant, Rahul; Samuel, Joseph; Sinha, Aninda; Sinha, Supurna; Sinha, Urbasi
2014-09-19
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
Directory of Open Access Journals (Sweden)
Alexei Serna A.
2012-12-01
Full Text Available The application of formal methods in industry has progressed extensively over the past decade and the results are promising. But despite these achievements and it have been documented in numerous studies, it is still very common the skepticism about its usefulness and applicability. The goal of this paper is to show that its evolution over the past decade exceeds all previous processes and each time they do a better job to satisfy industrial needs. This is achieved by the description of some experiments and the result of various applications in industry and through an analyzing of the needs of companies that must be satisfy the research community in this field.
Langevin formalism for solidification
Energy Technology Data Exchange (ETDEWEB)
Karma, A. (Department of Physics, Northeastern University, Boston, Massachusetts 02115 (United States))
1993-05-31
The question of how thermal noise should be incorporated in the continuum equations of solidification in a way which is consistent with both bulk and interfacial equilibrium fluctuations is investigated. The proper Langevin formalism which accomplishes this task is found to consist of the usual bulk forces, which remain unaffected by the presence of a two-phase boundary, and an extra stochastic force on the interface associated with its kinetics. The relevance of this force in the context of pattern formation is examined.
Diffusion formalism and applications
Dattagupta, Sushanta
2013-01-01
Within a unifying framework, Diffusion: Formalism and Applications covers both classical and quantum domains, along with numerous applications. The author explores the more than two centuries-old history of diffusion, expertly weaving together a variety of topics from physics, mathematics, chemistry, and biology. The book examines the two distinct paradigms of diffusion-physical and stochastic-introduced by Fourier and Laplace and later unified by Einstein in his groundbreaking work on Brownian motion. The author describes the role of diffusion in probability theory and stochastic calculus and
Formalizing the concept of sound.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-08-03
The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.
Zero mass limit of Kerr spacetime is a wormhole
Gibbons, Gary W.; Volkov, Mikhail S.
2017-07-01
We show that, contrary to what is usually claimed in the literature, the zero mass limit of Kerr spacetime is not flat Minkowski space but a spacetime whose geometry is only locally flat. This limiting spacetime, as the Kerr spacetime itself, contains two asymptotic regions and hence cannot be topologically trivial. It also contains a curvature singularity, because the power-law singularity of the Weyl tensor vanishes in the limit but there remains a distributional contribution of the Ricci tensor. This spacetime can be interpreted as a wormhole sourced by a negative tension ring. We also extend the discussion to similarly interpret the zero mass limit of the Kerr-(anti-)de Sitter spacetime.
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
Hack, Thomas-Paul
2015-01-01
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology and a fundamental study of the perturbations in Inflation. The two central sections of the book dealing with these applications are preceded by sections containing a pedagogical introduction to the subject as well as introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation. The target reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but does not need to have a background in QFT on curved spacetimes or the algebraic approach to QFT. In particul...
Formalization of Database Systems -- and a Formal Definition of {IMS}
DEFF Research Database (Denmark)
Bjørner, Dines; Løvengreen, Hans Henrik
1982-01-01
come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics......Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....
Guidelines for Formal Verification Systems
1989-04-01
This document explains the requirements for formal verification systems that are candidates for the NCSC’s Endorsed Tools List (ETL). This document...is primarily intended for developers of verification systems to use in the development of production-quality formal verification systems. It explains...the requirements and the process used to evaluate formal verification systems submitted to the NCSC for endorsement.
Topical Roots of Formal Dialectic
Krabbe, Erik C. W.
Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin's book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la
Novel Applications of Space-Time Processing for Wireless Systems
Hult, Tommy
2006-01-01
Space-time processing techniques have emerged as one of the most promising areas of research and development in wireless communications. Space-time processing signifies the signal processing performed on a system consisting of several antenna elements, whose signals are processed adaptively in order to exploit both the spatial (space) and temporal (time) dimensions of the radio channel. Space-time processing techniques can be applied at the transmitter, the receiver or both. The use of space-...
Path integral for multi-field inflation
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Department of Physics, Postech, Pohang 37673 (Korea, Republic of); Seo, Min-Seok [Center for Theoretical Physics of the Universe, Institute for Basic Science, 34051 Daejeon (Korea, Republic of); Shiu, Gary [Department of Physics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Department of Physics & Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
2016-07-20
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
On the usefulness of relativistic space-times for the description of the Earth's gravitational field
Soffel, Michael; Frutos, Francisco
2016-12-01
The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.
Stability of generic thin shells in conformally flat spacetimes
Energy Technology Data Exchange (ETDEWEB)
Amirabi, Z. [Eastern Mediterranean Univ., Gazimagusa (Turkey). Dept. of Physics
2017-07-15
Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p = ωσ. It is shown that, for the physical domain of ω, i.e., 0 < ω ≤ 1, such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated. (orig.)
Matter collineations of spacetime homogeneous Gödel-type metrics
Camci, U
2003-01-01
The spacetime homogeneous Gödel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The results obtained are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have an infinite number of matter collineations in the degenerate case, i.e. det(T sub a sub b) = 0, and do not admit proper matter collineations in the non-degenerate case, i.e. det(T sub a sub b) not = 0. The degenerate case has the new constraints on the parameters m and w which characterize the causality features of the Gödel-type spacetimes.
Practical path planning among movable obstacles
Energy Technology Data Exchange (ETDEWEB)
Chen, Pang C.; Hwang, Yong K.
1990-09-05
Path planning among movable obstacles is a practical problem that is in need of a solution. In this paper an efficient heuristic algorithm that uses a generate-and-test paradigm: a good'' candidate path is hypothesized by a global planner and subsequently verified by a local planner. In the process of formalizing the problem, we also present a technique for modeling object interactions through contact. Our algorithm has been tested on a variety of examples, and was able to generate solutions within 10 seconds. 5 figs., 27 refs.
Formal Verification of Security Policy Implementations in Enterprise Networks
Bera, P.; Ghosh, S. K.; Dasgupta, Pallab
In enterprise networks, the management of security policies and their configurations becoming increasingly difficult due to complex security constraints of the organizations. In such networks, the overall organizational security policy (global policy) is defined as a collection of rules for providing service accesses between various network zones. Often, the specification of the global policy is incomplete; where all possible service access paths may not be covered explicitly by the "permit" and "deny" rules. This policy is implemented in a distributed manner through appropriate sets of access control rules (ACL rules) in the network interfaces. However, the implementation must be complete i.e., all service access paths across the network must be implemented as "permit" and "deny" ACL rules. In that case, the unspecified access paths in a given policy must be implemented as either "permit" or "deny" rules; hence there may exist multiple ACL implementations corresponding to that policy. Formally verifying that the ACL rules distributed across the network interfaces guarantees proper enforcement of the global security policy is an important requirement and a major technical challenge. The complexity of the problem is compounded by the fact that some combination of network services may lead to inconsistent hidden access paths in the network. The ACL implementations ignoring these hidden access paths may result in violation of one or more policy rules implicitly. This paper presents a formal verification framework for analyzing security policy implementations in enterprise networks. It stems from boolean modeling of the network topology, network services and security policy where the unspecified access paths are modeled as "don't-care" rules. The framework formally models the hidden access rules and incorporates them in the distributed ACL implementations for extracting a security implementation model, and finally formulates a QSAT (satisfiability of quantified boolean
Colosi, Daniele; Dohse, Max
2017-04-01
We use the General Boundary Formulation (GBF) of Quantum Field Theory to compute the S-matrix for a general interacting scalar field in a wide class of curved spacetimes. As a by-product we obtain the general expression of the Feynman propagator for the scalar field, defined in the following three types of spacetime regions. First, there are the familiar interval regions (e.g. a time interval times all of space). Second, we consider the rod hypercylinder regions (all of time times a solid ball in space). Third, the tube hypercylinders (all of time times a solid shell in space) are related to interval regions, and result from removing a smaller rod from a concentric larger one. Using the Schrödinger representation for the quantum states combined with Feynman's path integral quantization, we obtain the S-matrix as the asymptotic limit of the GBF amplitude associated with finite interval, and rod regions. For interval regions, whose boundary consists of two Cauchy surfaces, the asymptotic GBF-amplitude becomes the standard S-matrix. Our work generalizes previous results (obtained in Minkowski, Rindler, de Sitter, and Anti de Sitter spacetimes) to a wide class of curved spacetimes.
Efficient Geo-Computational Algorithms for Constructing Space-Time Prisms in Road Networks
Directory of Open Access Journals (Sweden)
Hui-Ping Chen
2016-11-01
Full Text Available The Space-time prism (STP is a key concept in time geography for analyzing human activity-travel behavior under various Space-time constraints. Most existing time-geographic studies use a straightforward algorithm to construct STPs in road networks by using two one-to-all shortest path searches. However, this straightforward algorithm can introduce considerable computational overhead, given the fact that accessible links in a STP are generally a small portion of the whole network. To address this issue, an efficient geo-computational algorithm, called NTP-A*, is proposed. The proposed NTP-A* algorithm employs the A* and branch-and-bound techniques to discard inaccessible links during two shortest path searches, and thereby improves the STP construction performance. Comprehensive computational experiments are carried out to demonstrate the computational advantage of the proposed algorithm. Several implementation techniques, including the label-correcting technique and the hybrid link-node labeling technique, are discussed and analyzed. Experimental results show that the proposed NTP-A* algorithm can significantly improve STP construction performance in large-scale road networks by a factor of 100, compared with existing algorithms.
Directory of Open Access Journals (Sweden)
Diana-Maria Drigă
2015-12-01
Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.
DEFF Research Database (Denmark)
Levinsen, Karin; Sørensen, Birgitte Holm
2011-01-01
This paper presents findings from a large-scale longitudinal, qualitative study - Project ICT and Learning (PIL) - that engaged the participation of eight primary schools in Denmark, and was conducted between 2006 and 2008. The research design was based on action research, involving teachers...... and other relevant stakeholders, as well as participant observations in the classroom documented by thick descriptions, formal and informal interviews and focus group interviews. The aim of the study was to explore and identify relations between designs for teaching and learning and the students' learning...... of school subjects within defined learning goals and curricula, along with various implementations of ICT in the pedagogical everyday practice (Levinsen & Sørensen 2008). However, another research strand - the topic of this paper - emerged during the project's life cycle as a consequence of ongoing changes...
Directory of Open Access Journals (Sweden)
Alan Smart
2017-12-01
Full Text Available Addressing a variety of locations and subjects across several social contexts and countries, this forum intends to stimulate novel ways of conceptualizing the inevitable interpenetration and entanglement of formalization and informalization as two interlinked social processes. Rather than proposing a new coherent definition of “informality”, we propose to consider “in/formalization” as a space of practice and reflection which is crucial for engaging with contemporary economy, law and politics and their current local and global articulations and scenarios. The forum features contributions by Stamatis Amarianakis, Lenka Brunclíková, Dolores Koenig, B. Lynne Milgram, Sarah Muir, Antonio Maria Pusceddu, Alan Smart, Mechthild von Vacano, Filippo M. Zerilli & Julie Trappe.
Bertolami, Orfeu
Since the nineteenth century, it is known, through the work of Lobatchevski, Riemann, and Gauss, that spaces do not need to have a vanishing curvature. This was for sure a revolution on its own, however, from the point of view of these mathematicians, the space of our day to day experience, the physical space, was still an essentially a priori concept that preceded all experience and was independent of any physical phenomena. Actually, that was also the view of Newton and Kant with respect to time, even though, for these two space-time explorers, the world was Euclidean.
An Uncertainty Relation of Space-Time
Naoki, SASAKURA; Department of Physics, Kyoto University
1999-01-01
We propose an uncertainty relation of space-time. This relation is characterized by Gh^^-T IsimδV, where T and δV denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic p...
An Uncertainty Relation of Space-Time
Sasakura, N.
1999-07-01
We propose an uncertainty relation of space-time. This relation is characterized by G hbar T Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula sqrt{EV/Ghbar2, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER / hbar with R denoting the length scale of the system.
The emergence of spacetime in string theory
Vistarini, Tiziana
2018-01-01
The nature of space and time is one of the most fascinating and fundamental philosophical issues which presently engages at the deepest level with physics. During the last thirty years this notion has been object of an intense critical review in the light of new scientific theories which try to combine the principles of both general relativity and quantum theory—called theories of quantum gravity. This book considers the way string theory shapes its own account of spacetime disappearance from the fundamental level.
Charged black holes in colored Lifshitz spacetimes
Directory of Open Access Journals (Sweden)
Zhong-Ying Fan
2015-04-01
Full Text Available We consider Einstein gravities coupled to a cosmological constant and SU(2 Yang–Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents z>1. We study the wave equations of the SU(2 scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that approach the D=4, z=3 and D=5, z=4 colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes.
Asymptotically flat spacetimes with BMS3 symmetry
Compère, Geoffrey; Fiorucci, Adrien
2017-10-01
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.
Generalising the coupling between spacetime and matter
Carloni, Sante
2017-03-01
We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We then show that the introduction of this tensor can account for dark phenomenology in General Relativity, maintaining a weak field limit compatible with standard Newtonian gravitation. The same paradigm can be applied any other theory of gravitation. We show, as an example, that in the context of conformal gravity a generalised coupling is able to solve compatibility issues between the matter and the gravitational sector.
Generalising the coupling between spacetime and matter
Directory of Open Access Journals (Sweden)
Sante Carloni
2017-03-01
Full Text Available We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We then show that the introduction of this tensor can account for dark phenomenology in General Relativity, maintaining a weak field limit compatible with standard Newtonian gravitation. The same paradigm can be applied any other theory of gravitation. We show, as an example, that in the context of conformal gravity a generalised coupling is able to solve compatibility issues between the matter and the gravitational sector.
Discreteness of Curved Spacetime from GUP
Directory of Open Access Journals (Sweden)
Ahmad Adel Abutaleb
2013-01-01
Full Text Available Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP. It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric. We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.
Generalising the coupling between spacetime and matter
Energy Technology Data Exchange (ETDEWEB)
Carloni, Sante, E-mail: sante.carloni@gmail.com
2017-03-10
We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We then show that the introduction of this tensor can account for dark phenomenology in General Relativity, maintaining a weak field limit compatible with standard Newtonian gravitation. The same paradigm can be applied any other theory of gravitation. We show, as an example, that in the context of conformal gravity a generalised coupling is able to solve compatibility issues between the matter and the gravitational sector.
R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2013-01-01
textabstractA path-neighborhood graph is a connected graph in which every neighborhood induces a path. In the main results the 3-sun-free path-neighborhood graphs are characterized. The 3-sun is obtained from a 6-cycle by adding three chords between the three pairs of vertices at distance 2. A Pk
Space-time discontinuous Galerkin method for compressible flow
Klaij, C.M.
2006-01-01
The space-time discontinuous Galerkin method allows the simulation of compressible flow in complex aerodynamical applications requiring moving, deforming and locally refined meshes. This thesis contains the space-time discretization of the physical model, a fully explicit solver for the resulting
Quantum mechanics in fractional and other anomalous spacetimes
Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco
2012-01-01
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Photoelectric effect for twist-deformed space-time
Daszkiewicz, Marcin
2016-01-01
In this article, we investigate the impact of twisted space-time on the photoelectric effect, \\ie, we derive the $\\theta$-deformed threshold frequency. In such a way, we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
Space-time algebra for the generalization of gravitational field ...
Indian Academy of Sciences (India)
The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of ...
Inflationary scenario from higher curvature warped spacetime
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2017-10-15
We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR{sup 2} in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n{sub s}) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)
Spacetime-bridge solutions in vacuum gravity
Sengupta, Sandipan
2017-11-01
Vacuum spacetime solutions, which are representations of a bridgelike geometry, are constructed as purely geometric sources of curvature in gravity theory. These configurations satisfy the first-order equations of motion everywhere. Each of them consists of two identical sheets of asymptotically flat geometry, connected by a region of finite extension where the tetrad is noninvertible. The solutions can be classified into nonstatic and static spacetimes. The first class represents a single causal universe equipped (locally) with a timelike coordinate everywhere. The latter, on the other hand, could be interpreted as a sum of two self-contained universes which are causally disconnected. These geometries, even though they have different metrical dimensions in the regions within and away from the bridge, are regular. This is reflected through the associated gauge-covariant fields, which are continuous across the hypersurfaces connecting the invertible and noninvertible phases of the tetrad and are finite everywhere. These vacuum bridge solutions have no analogue in the Einsteinian theory of gravity.
Macroscopic Spacetime Shortcuts in the Manyfold Universe
Loup, F
2004-01-01
Recently the idea of a Manyfold Universe was proposed by some authors to explain Dark Matter . In this study we assume that the Standard Model(SM) of particles and fields with gravity propagating in the Higher Dimensional Spacetime(Bulk) while other interactions are confined to 3+1 Einsteinian spacetime(Brane) is not due to open strings and closed loops but instead is due to the capability of gravity as the weakest and "smallest" interaction to penetrate these small Bulk size ($10^{-31}$m to $10^{-35}$m) while protons,neutrons and other interactions stronger and "larger" than gravity do not "fits" in the size of the Bulk and remains trapped on the Brane and we present a equation to justify this point of view. Our picture relies over the geometrical beauty of the Manyfold Universe proposal that Dark Matter is chemically identical to ordinary matter but lies on other Folds. Also the geometrical point of view for the small size of the Bulk eliminates the need of trapping mechanisms to confine matter in the Brane...
Radiation memory, boosted Schwarzschild spacetimes and supertranslations
Mädler, Thomas; Winicour, Jeffrey
2017-06-01
We investigate gravitational radiation memory and its corresponding effect on the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild spacetime. First, in the context of linearized theory, we consider such a Schwarzschild body which is initially at rest, then goes through a radiative stage and finally emerges as a boosted Schwarzschild body. We show that the proper retarded solution of the exterior Schwarzschild spacetime for this process can be described in terms of the ingoing Kerr-Schild form of the Schwarzschild metric for both the initial and final states. An outgoing Kerr-Schild or time symmetric metric does not give the proper solution. The special property of Kerr-Schild metrics that their linearized and nonlinear forms are identical allows us to extend this result to processes in the nonlinear regime. We then discuss how the nonlinear memory effect, and its associated supertranslation, affect angular momentum conservation. Our approach provides a new framework for studying nonlinear aspects of the memory effect.
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Energy Technology Data Exchange (ETDEWEB)
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Singularities and the geometry of spacetime
Hawking, Stephen
2014-11-01
The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove
Formal verification of AI software
Rushby, John; Whitehurst, R. Alan
1989-01-01
The application of formal verification techniques to Artificial Intelligence (AI) software, particularly expert systems, is investigated. Constraint satisfaction and model inversion are identified as two formal specification paradigms for different classes of expert systems. A formal definition of consistency is developed, and the notion of approximate semantics is introduced. Examples are given of how these ideas can be applied in both declarative and imperative forms.
Resonant-state perturbation formalisms
Energy Technology Data Exchange (ETDEWEB)
Romo, W.J. (Carleton Univ., Ottawa, Ontario (Canada). Dept. of Physics)
1983-05-02
Three different formalisms for determining bound-state, virtual-state, and resonant-state energies of a perturbed system are developed. Two of the formalisms are based on expansions of the unperturbed Green function in terms of bound-state, resonant-state and deformed-continuum-state contributions of the form developed by T. Berggren. The third formalism is based on a Mittag-Leffler expansion of the unperturbed Green function. The three formalisms are compared and the relative merits of calculation schemes based on them are examined.
Counting paths with Schur transitions
Energy Technology Data Exchange (ETDEWEB)
Díaz, Pablo [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Kemp, Garreth [Department of Physics, University of Johannesburg, P.O. Box 524, Auckland Park 2006 (South Africa); Véliz-Osorio, Alvaro, E-mail: aveliz@gmail.com [Mandelstam Institute for Theoretical Physics, University of the Witwatersrand, WITS 2050, Johannesburg (South Africa); School of Physics and Astronomy, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2016-10-15
In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which is valid for any rank of the unitary group, reproduces known asymptotic results. We proceed to establish the general validity of this expression by a formal proof. The form of this equation strongly hints towards a quantum generalization. Thus, we introduce a notion of quantum relative dimension and subject it to the appropriate consistency tests. This new quantity finds its natural environment in the context of RCFTs and fractional statistics; where the already established notion of quantum dimension has proven to be of great physical importance.
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
A Formalization of Linkage Analysis
DEFF Research Database (Denmark)
Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.
In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been ...
Obligationes as Formal Dialogue Systems
Uckelman, S.L.; Ågotnes, T.
2011-01-01
Formal Dialogue Systems (FDSs) model rule-based interaction between agents. Their conceptual roots go back to Hamblin's [11,12], which cites the medieval theory of obligationes as inspiration for his development of a formal system of argumentation. In an obligatio, two agents, Opponent and
Yang-Feldman formalism on noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Doescher, C.
2006-12-15
We examine quantum field theory on noncummutative spacetime. For this we choose an approach which lives explicitly on the noncommutative Minkowski space, namely the Yang-Feldman formalism. Here the ansatz is to try to solve the field equation of the quantum fields. In this setting we first take a look at an additional mass term, and use this to discuss possible IR cutoffs. We find classes of IR cutoffs which indeed yield the expected limit. Furthermore, we look at interacting models, namely the {phi}{sup 3} model in four and six dimensions, the {phi}{sup 4} model and the Wess-Zumino model. For these we calculate dispersion relations. We see that there exist huge differences in the orders of magnitude between logarithmically and quadratically divergent models. Integrals which are made finite by twisting factors are calculated rigorously in the sense of the theory of oscillatory integrals. (orig.)
On quadrupole and octupole gravitational radiation in the ANK formalism
Kozameh, Carlos N.; Ortega, R. G.; Rojas, T. A.
2017-04-01
Following the approach of Adamo-Newman-Kozameh (ANK) we derive the equations of motion for the center of mass and intrinsic angular moment for isolated sources of gravitational waves in axially symmetric spacetimes. The original ANK formulation is generalized so that the angular momentum coincides with the Komar integral for a rotational Killing symmetry. This is done using the Winicour-Tamburino Linkages which yields the mass dipole-angular momentum tensor for the isolated sources. The ANK formalism then provides a complex worldline in a fiducial flat space to define the notions of center of mass and spin. The equations of motion are derived and then used to analyse a very simple astrophysical process where only quadrupole and octupole contributions are included. The results are then compared with those coming from the post newtonian approximation.
Transition path time distributions
Laleman, M.; Carlon, E.; Orland, H.
2017-12-01
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the barrier. Average transition path times and, recently, their full probability distribution have been measured for several biomolecular systems, e.g., in the folding of nucleic acids or proteins. Motivated by these experiments, we have calculated the full transition path time distribution for a single stochastic particle crossing a parabolic barrier, including inertial terms which were neglected in previous studies. These terms influence the short time scale dynamics of a stochastic system and can be of experimental relevance in view of the short duration of transition paths. We derive the full transition path time distribution as well as the average transition path times and discuss the similarities and differences with the high friction limit.
New procedure for departure formalities
HR & GS Departments
2011-01-01
As part of the process of simplifying procedures and rationalising administrative processes, the HR and GS Departments have introduced new personalised departure formalities on EDH. These new formalities have applied to students leaving CERN since last year and from 17 October 2011 this procedure will be extended to the following categories of CERN personnel: Staff members, Fellows and Associates. It is planned to extend this electronic procedure to the users in due course. What purpose do departure formalities serve? The departure formalities are designed to ensure that members of the personnel contact all the relevant services in order to return any necessary items (equipment, cards, keys, dosimeter, electronic equipment, books, etc.) and are aware of all the benefits to which they are entitled on termination of their contract. The new departure formalities on EDH have the advantage of tailoring the list of services that each member of the personnel must visit to suit his individual contractual and p...
Formal connections in deformation quantization
DEFF Research Database (Denmark)
Masulli, Paolo
manifold. Gammelgaard gave an explicit formula for a class of star products in this setting. We review his construction, which is combinatorial and based on a certain family of graphs and extend it, to provide the graph formalism with the notions of composition and differentiation. We shall focus our...... attention on symplectic manifolds equipped with a family of star products, indexed by a parameter space. In this situation we can define a connection in the trivial bundle over the parameter space with fibres the formal smooth functions on the manifold, which relates the star products in the family...... and is called a formal connection. We study the question of classifying such formal connections. To each star product we can associate a certain cohomology class called the characteristic class. It turns out that a formal connection exists if and only if all the star products in the family have the same...
Newman-Janis Ansatz in conformastatic spacetimes
Gutiérrez-Piñeres, Antonio C
2016-01-01
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.
Superluminal propagation: Light cone and Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Mugnai, D. [' Nello Carrara' Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)]. E-mail: d.mugnai@ifac.cnr.it
2007-05-14
Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some experimental results showed that these waves have both phase and group velocities greater that light velocity c. However, because of the lack of an exact definition of signal velocity, no definite answer about the signal propagation (or velocity of information) has been found. The present Letter is a short note that deals in a general way with this vexed question. By analyzing the field of existence of the Bessel X-pulse in pseudo-Euclidean spacetime, it is possible to give a general description of the propagation, and to overcome the specific question related to a definition of signal velocity.
Relativistic Magnetic Reconnection in Kerr Spacetime.
Asenjo, Felipe A; Comisso, Luca
2017-02-03
The magnetic reconnection process is analyzed for relativistic magnetohydrodynamical plasmas around rotating black holes. A simple generalization of the Sweet-Parker model is used as a first approximation to the problem. The reconnection rate, as well as other important properties of the reconnection layer, has been calculated taking into account the effect of spacetime curvature. Azimuthal and radial current sheet configurations in the equatorial plane of the black hole have been studied, and the case of small black hole rotation rate has been analyzed. For the azimuthal configuration, it is found that the black hole rotation decreases the reconnection rate. On the other hand, in the radial configuration, it is the gravitational force created by the black hole mass that decreases the reconnection rate. These results establish a fundamental interaction between gravity and magnetic reconnection in astrophysical contexts.
Phantom space-times in fake supergravity
Bu Taam, Maryam; Sabra, Wafic A.
2015-12-01
We discuss phantom metrics admitting Killing spinors in fake N = 2, D = 4 supergravity coupled to vector multiplets. The Abelian U (1) gauge fields in the fake theory have kinetic terms with the wrong sign. We solve the Killing spinor equations for the standard and fake theories in a unified fashion by introducing a parameter which distinguishes between the two theories. The solutions found are fully determined in terms of algebraic conditions, the so-called stabilisation equations, in which the symplectic sections are related to a set of functions. These functions are harmonic in the case of the standard supergravity theory and satisfy the wave-equation in flat (2 + 1)-space-time in the fake theory. Explicit examples are given for the minimal models with quadratic prepotentials.
A quantum kinematics for asymptotically flat spacetimes
Campiglia, Miguel
2014-01-01
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\\em states} and the background electric fields which label the {\\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We...
Relative-locality effects in Snyder spacetime
Energy Technology Data Exchange (ETDEWEB)
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Samsarov, A., E-mail: andjelo.samsarov@irb.hr [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia)
2017-05-18
Most models of noncommutative geometry and doubly special relativity suggest that the principle of absolute locality should be replaced by the milder notion of relative locality. In particular, they predict the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. Distant observers may however measure different times of flight for massive particles. - Highlights: • We discuss the dynamics of the Snyder model from the point of view of relative locality. • We show that no time delay is present for particles emitted by distant observers. • We ascribe this fact to the Lorentz invariance of the model. • Distant observers may however measure different times of flight for massive particle.
Selective reconstruction of space-time spectra
Voronin, E. N.
1985-12-01
The relationship between the active component of mutual resistance and radiation patterns of arbitrary receive-transmit antennas is simplified on the basis of the reciprocity theorem. The simplification does not violate the identity of the relationship, and has a useful application to the correction of the near-field holograms of arbitrary sources with the aim of the selective reconstruction of the space-time spectra of homogeneous or inhomogeneous waves. The version of the relationship obtained can also be extended to acoustic antennas. Numerical simulation results are presented concerning the reconstruction of the radiation pattern of a half-wave dipole on the basis of near-field sounding in a cylindrical shielded chamber.
Mass ladder operators from spacetime conformal symmetry
Cardoso, Vitor; Houri, Tsuyoshi; Kimura, Masashi
2017-07-01
Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators, which map a scalar field onto another massive scalar field. We construct such operators, in arbitrary dimensions, from closed conformal Killing vector fields, eigenvectors of the Ricci tensor. As an example, we explicitly construct these objects in anti-de Sitter (A d S ) spacetime and show that they exist for masses above the Breitenlohner-Freedman bound. Starting from a regular seed solution of the massive Klein-Gordon equation, mass ladder operators in AdS allow one to build a variety of regular solutions with varying boundary condition at spatial infinity. We also discuss mass ladder operator in the context of spherical harmonics, and the relation between supersymmetric quantum mechanics and so-called Aretakis constants in an extremal black hole.
Emergent spacetime in stochastically evolving dimensions
Afshordi, Niayesh; Stojkovic, Dejan
2014-12-01
Changing the dimensionality of the space-time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field theories, it is possible to quantize gravity, and the theory of matter plus gravity is free of divergencies or renormalizable. If the space is higher dimensional at cosmological scales, then some cosmological problems (including the cosmological constant problem) can be attacked from a completely new perspective. In this paper, we construct an explicit model of ;evolving dimensions; in which the dimensions open up as the temperature of the universe drops. We adopt the string theory framework in which the dimensions are fields that live on the string worldsheet, and add temperature dependent mass terms for them. At the Big Bang, all the dimensions are very heavy and are not excited. As the universe cools down, dimensions open up one by one. Thus, the dimensionality of the space we live in depends on the energy or temperature that we are probing. In particular, we provide a kinematic Brandenberger-Vafa argument for how a discrete causal set, and eventually a continuum (3 + 1)-dim spacetime along with Einstein gravity emerges in the Infrared from the worldsheet action. The (3 + 1)-dim Planck mass and the string scale become directly related, without any compactification. Amongst other predictions, we argue that LHC might be blind to new physics even if it comes at the TeV scale. In contrast, cosmic ray experiments, especially those that can register the very beginning of the shower, and collisions with high multiplicity and density of particles, might be sensitive to the dimensional cross-over.
Adolescent thinking ála Piaget: The formal stage.
Dulit, E
1972-12-01
Two of the formal-stage experiments of Piaget and Inhelder, selected largely for their closeness to the concepts defining the stage, were replicated with groups of average and gifted adolescents. This report describes the relevant Piagetian concepts (formal stage, concrete stage) in context, gives the methods and findings of this study, and concludes with a section discussing implications and making some reformulations which generally support but significantly qualify some of the central themes of the Piaget-Inhelder work. Fully developed formal-stage thinking emerges as far from commonplace among normal or average adolescents (by marked contrast with the impression created by the Piaget-Inhelder text, which chooses to report no middle or older adolescents who function at less than fully formal levels). In this respect, the formal stage differs appreciably from the earlier Piagetian stages, and early adolescence emerges as the age for which a "single path" model of cognitive development becomes seriously inadequate and a more complex model becomes essential. Formal-stage thinking seems best conceptualized, like most other aspects of psychological maturity, as a potentiality only partially attained by most and fully attained only by some.
An xp model on AdS{sub 2} spacetime
Energy Technology Data Exchange (ETDEWEB)
Molina-Vilaplana, Javier, E-mail: xavmol@gmail.com [Universidad Politécnica de Cartagena, Cartagena (Spain); Sierra, Germán [Instituto de Física Teórica, UAM-CSIC, Madrid (Spain)
2013-12-01
In this paper we formulate the xp model on the AdS{sub 2} spacetime. We find that the spectrum of the Hamiltonian has positive and negative eigenvalues, whose absolute values are given by a harmonic oscillator spectrum, which in turn coincides with that of a massive Dirac fermion in AdS{sub 2}. We extend this result to generic xp models which are shown to be equivalent to a massive Dirac fermion on spacetimes whose metric depend of the xp Hamiltonian. Finally, we construct the generators of the isometry group SO(2,1) of the AdS{sub 2} spacetime, and discuss the relation with conformal quantum mechanics.
Quantum relativistic fluid at global thermodynamic equilibrium in curved spacetime
Becattini, F
2015-01-01
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
Quaternion wave equations in curved space-time
Edmonds, J. D., Jr.
1974-01-01
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
Classical black holes: the nonlinear dynamics of curved spacetime.
Thorne, Kip S
2012-08-03
Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.
Theory and Phenomenology of Space-Time Defects
Directory of Open Access Journals (Sweden)
Sabine Hossenfelder
2014-01-01
Full Text Available Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of spacetime is discrete, typically represented in terms of a graph or network, then the apparent smoothness of geometry on large scales should be imperfect—it should have defects. Here, we review a model for space-time defects and summarize the constraints on the prevalence of these defects that can be derived from observation.
Formal verification - Robust and efficient code: Introduction to Formal Verification
CERN. Geneva
2016-01-01
In general, FV means "proving that certain properties hold for a given system using formal mathematics". This definition can certainly feel daunting, however, as we will learn, we can reap benefits from the paradigm without digging too deep into ...
Multi-Dimensional Path Queries
DEFF Research Database (Denmark)
Bækgaard, Lars
1998-01-01
to create nested path structures. We present an SQL-like query language that is based on path expressions and we show how to use it to express multi-dimensional path queries that are suited for advanced data analysis in decision support environments like data warehousing environments......We present the path-relationship model that supports multi-dimensional data modeling and querying. A path-relationship database is composed of sets of paths and sets of relationships. A path is a sequence of related elements (atoms, paths, and sets of paths). A relationship is a binary path...
On the covariant formalism of the effective field theory of gravity and leading order corrections
DEFF Research Database (Denmark)
Codello, Alessandro; Jain, Rajeev Kumar
2016-01-01
We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases of pure gravity with cosmological constant as well...... as gravity coupled to matter. By means of heat kernel methods we renormalize and compute the leading quantum corrections to quadratic order in a curvature expansion. The final effective action in our covariant formalism is generally non-local and can be readily used to understand the phenomenology...... on different spacetimes. In particular, we point out that on curved backgrounds the observable leading quantum gravitational effects are less suppressed than on Minkowski spacetime....
Scalable Techniques for Formal Verification
Ray, Sandip
2010-01-01
This book presents state-of-the-art approaches to formal verification techniques to seamlessly integrate different formal verification methods within a single logical foundation. It should benefit researchers and practitioners looking to get a broad overview of the spectrum of formal verification techniques, as well as approaches to combining such techniques within a single framework. Coverage includes a range of case studies showing how such combination is fruitful in developing a scalable verification methodology for industrial designs. This book outlines both theoretical and practical issue
Formal Component-Based Semantics
Directory of Open Access Journals (Sweden)
Ken Madlener
2011-08-01
Full Text Available One of the proposed solutions for improving the scalability of semantics of programming languages is Component-Based Semantics, introduced by Peter D. Mosses. It is expected that this framework can also be used effectively for modular meta theoretic reasoning. This paper presents a formalization of Component-Based Semantics in the theorem prover Coq. It is based on Modular SOS, a variant of SOS, and makes essential use of dependent types, while profiting from type classes. This formalization constitutes a contribution towards modular meta theoretic formalizations in theorem provers. As a small example, a modular proof of determinism of a mini-language is developed.
Formal Methods: Practice and Experience
DEFF Research Database (Denmark)
Woodcock, Jim; Larsen, Peter Gorm; Bicarregui, Juan
2009-01-01
Formal methods use mathematical models for analysis and verification at any part of the program life-cycle. We describe the state of the art in the industrial use of formal methods, concentrating on their increasing use at the earlier stages of specification and design. We do this by reporting....... Based on this, we discuss the issues surrounding the industrial adoption of formal methods. Finally, we look to the future and describe the development of a Verified Software Repository, part of the worldwide Verified Software Initiative. We introduce the initial projects being used to populate...
Leibniz' First Formalization of Syllogistics
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
In his Dissertatio de Arte Combinatoria from 1666 Leibniz provides a formal presentation of syllogistics within the framework of his general-combinatoric program. He does not set up an axiomatic system for the derivation of all valid syllogistic mode, rather he formulates a set of rules which...... of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity...
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Spin coefficients and gauge fixing in the Newman-Penrose formalism
Nerozzi, Andrea
2017-03-01
Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einstein's equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in numerical relativity. Despite the many applications, Einstein's equations in the Newman-Penrose formalism appear complicated and not easily applicable to general studies of spacetimes, mainly because physical and gauge degrees of freedom are mixed in a nontrivial way. In this paper we approach the whole formalism with the goal of expressing the spin coefficients as functions of tetrad invariants once a particular tetrad is chosen. We show that it is possible to do so, and give for the first time a general recipe for the task, as well as an indication of the quantities and identities that are required.
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Directory of Open Access Journals (Sweden)
Andrzej Borowiec
2010-10-01
Full Text Available Some classes of Deformed Special Relativity (DSR theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called ''q-analog'' version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
DEFF Research Database (Denmark)
Bessenrodt, Christine; Olsson, Jørn Børling; Sellers, James A.
2013-01-01
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.......We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions....
DEFF Research Database (Denmark)
Garud, Raghu; Karnøe, Peter
the place of agency in these theories that take history so seriously. In the end, they are as interested in path creation and destruction as they are in path dependence. This book is compiled of both theoretical and empirical writing. It shows relatively well-known industries such as the automobile...
Loup, F
2004-01-01
We use the Higher Dimensional Spacetime of the Manyfold Universe(as is our previous works) and Dark Matter to explain the Tate Anomally observed when measuring the mass of Cooper Pairs of Rotating Superconductors as a proof that Quantum Materials are not tied to $3+1$ Spacetime according to Matos-Tajmar studies. We demonstrate that the Dutch Equation can enlarge a Extra Dimension of the Manyfold Universe from Planck size and this enlargement can affect the Cooper Pair mass explaining the Tate Anomally. We adopt a slight deviation from the Fractal Spacetime of Matos-Tajmar with fractionary Dimensions because in the formalism of General Relativity it is difficult to conceive a Einstein Tensor with fractionary Dimensions(fractionary scripts).But the idea of Matos-Tajmar is excellent because if a Superconductor in Rotation can enlarge the Planck Size Dimension of the Manyfold Universe we can perhaps probe the Extra Dimensions in a way more acessible than TeV collisions and perhaps probe the Geometry of the Spacet...
The Universe of Fluctuations The Architecture of Spacetime and the Universe
Sidharth, B G
2005-01-01
The Universe of Fluctuations: The Architecture of Spacetime and the Universe is a path-breaking work which proposes solutions to the impasse and crisis facing fundamental physics and cosmology. It describes a cosmological model based on fuzzy spacetime that has correctly predicted a dark-energy-driven acceleration of our expanding universe - with a small cosmological constant - at a time when the popular belief was quite the contrary. It describes how the Universe is made up of an underpinning of Planck oscillators in a Quantum Vacuum. This leads to, amongst other things, a characterization of gravitation as being distributional over the entire Universe, thereby providing an answer to a puzzle brought to light by Weinberg years ago and since overlooked. There is also a simple formula for the mass spectrum of all known elementary particles, based on QCD dynamics. Many other interesting ramifications and experimental tests for the future are also discussed. This apart, there is a brief survey of some of the exi...
Time-dependent photon migration using path integrals
Perelman, Lev T.; Wu, Jun; Wang, Yang; Itzkan, Irving; Dasari, Ramachandra R.; Feld, Michael S.
1995-06-01
We present an approach to the problem of light propagation in turbid media based on the path integral formalism. The method of analysis provides solutions to the time-dependent equation of radiative transfer for a number of cases for which known approximations, including the diffusion approximation, are not applicable. The theory and experiments show that trajectories of photon traversing a turbid medium cluster around a well defined, time-resolved path called a classical path. This concept is a powerful tool, and it provides physical insight into optical propagation in turbid media.
The standard electroweak model in the noncommutative DFR space-time
Neves, Mario J.; Abreu, Everton M. C.
2017-11-01
The noncommutative (NC) framework elaborated by Doplicher, Fredenhagen and Roberts (DFR) has a Lorentz invariant space-time structure in order to be considered as a candidate to understand the physics of the early Universe. In DFR formalism, the NC parameter (𝜃μν) is a coordinate operator in an extended Hilbert space and it has a conjugate momentum. Since x and 𝜃μν are independent coordinates, the Moyal-Weyl (MW) product can be used in this framework. With these elements, in this work, we have constructed the standard electroweak model. To accomplish this task, we have begun with the MW-product basis group of symmetry. After that we have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed. Finally, the gauge symmetry and gauge transformations were discussed.
Two-parameter nonlinear spacetime perturbations gauge transformations and gauge invariance
Bruni, M; Sopuerta, C F
2003-01-01
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity OMEGA), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by lambda) are then built on top of the axisymmetric perturbations in OMEGA. Clearly, any interesting physics requires nonlinear perturbations, as at least terms lambda OMEGA need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge ...
Aspects of quantum field theory in curved space-time
Fulling, Stephen A
1989-01-01
The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology
Generalized Timelike Mannheim Curves in Minkowski Space-Time
Directory of Open Access Journals (Sweden)
M. Akyig~it
2011-01-01
Full Text Available We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.
Exact solutions and spacetime singularities in nonlocal gravity
National Research Council Canada - National Science Library
Li, Yao-Dong; Modesto, Leonardo; Rachwał, Lesław
2015-01-01
.... We prove that maximally symmetric spacetimes are exact solutions in both classes, while in dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant...
Formal Verification of UML Profil
DEFF Research Database (Denmark)
Bhutto, Arifa; Hussain, Dil Muhammad Akbar
2011-01-01
The Unified Modeling Language (UML) is based on the Model Driven Development (MDD) approach which capturing the system functionality using the platform-independent model (PMI) and appropriate domain-specific languages. In UML base system notations, structural view is model by the class, components...... and object diagrams and behavioral view model by the activity, use case, state, and sequence diagram. However, UML does not provide the formal syntax, therefore its semantics is not formally definable, so for assure of correctness, we need to incorporate semantic reasoning through verification, specification......, refinement, and incorporate into the development process. Our motivation of research is to make an easy structural view and suggest formal technique/ method which can be best applied or used for the UML based development system. We investigate the tools and methods, which broadly used for the formal...
Readings in Formal Epistemology : Sourcebook
Arló-Costa, H.; Hendricks, V.F.; van Benthem, J.
2016-01-01
This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory,
Concepts of formal concept analysis
Žáček, Martin; Homola, Dan; Miarka, Rostislav
2017-07-01
The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.
El Salvador - Formal Technical Education
Millennium Challenge Corporation — With a budget of nearly $20 million, the Formal Technical Education Sub-Activity was designed to strengthen technical and vocational educational institutions in the...
Formalism and functionalism in linguistics.
Newmeyer, Frederick J
2010-05-01
Formalism and functionalism in linguistics are often taken to be diametrically opposed approaches. However, close examination of the relevant phenomena reveals that the two are complementary, rather than being irrevocably in opposition to each other. One can be a formal linguist and a functional linguist at the same time, without there being any contradiction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Analogue transformation acoustics and the compression of spacetime
García Meca, Carlos; Carloni, Sante; Barceló, Carlos; Jannes, Gil Georges Paul; Sánchez-Dehesa Moreno-Cid, José; Martínez Abietar, Alejandro José
2014-01-01
A recently developed technique known as analogue transformation acoustics has allowed the extension of the transformational paradigm to general spacetime transformations under which the acoustic equations are not form invariant. In this paper, we review the fundamentals of analogue transformation acoustics and show how this technique can be applied to build a device that increases the density of events within a given spacetime region by simultaneously compressing space and t...
Clocks, computers, black holes, spacetime foam, and holographic principle
Ng, Y. Jack
2000-01-01
What do simple clocks, simple computers, black holes, space-time foam, and holographic principle have in common? I will show that the physics behind them is inter-related, linking together our concepts of information, gravity, and quantum uncertainty. Thus, the physics that sets the limits to computation and clock precision also yields Hawking radiation of black holes and the holographic principle. Moreover, the latter two strongly imply that space-time undergoes much larger quantum fluctuati...
Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes
Directory of Open Access Journals (Sweden)
Nungesser Ernesto
2013-09-01
Full Text Available The problem of determinism in General Relativity appears even if one assumes that the spacetime is globally hyperbolic, i.e. that it contains a hypersurface that is intersected by any causal curve exactly once. The strong cosmic censorship hypothesis is essentially the hypothesis that General Relativity is a predictable theory and thus a crucial issue in Classical General Relativity. We sketch here the proof for the case of Electrogowdy spacetimes.
Visualizing Flat Spacetime: Viewing Optical versus Special Relativistic Effects
Black, Don V; Wessel, F; Pajarola, R; Kuester, F
2012-01-01
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as predicted by special relativity theory. The contributions of relativistic aberration as compared to classical pre-relativistic aberration to the geometry are discussed in the context of its visual representation.
Hopf-algebra description of noncommutative-spacetime symmetries
Agostini, A; D'Andrea, F; Andrea, Francesco D'
2003-01-01
In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a large literature is already available, we propose a line of analysis of noncommutative-spacetime symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski) and of a compatible notion of integration in the noncommutative spacetime. We confirm (and we establish more robustly) previous suggestions that the commutative-spacetime notion of Lie-algebra symmetries must be replaced, in the noncommutative-spacetime context, by the one of Hopf-algebra symmetries. We prove that in kappaMinkowski it is possible to construct an action which is invariant under a Poincare-like Hopf algebra of symmetries with 10 generators, in which the noncommutativity length scale has the r...
Simons, Jacob V., Jr.
2017-01-01
The critical path method/program evaluation and review technique method of project scheduling is based on the importance of managing a project's critical path(s). Although a critical path is the longest path through a network, its location in large projects is facilitated by the computation of activity slack. However, logical fallacies in…
Deformed space-time transformations in Mercury
Cardone, F.; Albertini, G.; Bassani, D.; Cherubini, G.; Guerriero, E.; Mignani, R.; Monti, M.; Petrucci, A.; Ridolfi, F.; Rosada, A.; Rosetto, F.; Sala, V.; Santoro, E.; Spera, G.
2017-09-01
A mole of Mercury was suitably treated by ultrasound in order to generate in it the same conditions of local Lorentz invariance violation that were generated in a sonicated cylindrical bar of AISI 304 steel and that are the cause of neutron emission during the sonication. After 3 min, part of the mercury turned into a solid material which turned out to contain isotopes having a different mass (higher and lower) with respect to the isotopes already present in the initial material (mercury). These transformations in the atomic weight without gamma production above the background are brought about during Deformed Space-Time reactions. We present the results of the analyses performed on samples taken from the transformation product. The analyses have been done in two groups, the first one using five different analytical techniques: ICP-OES, XRF, ESEM-EDS, ICP-MS, INAA. In the second group of analyses, we used only two techniques: INAA and ICP-MS. The second group of analyses confirmed the occurring of the transformations in mercury.
Leptogenesis from loop effects in curved spacetime
Energy Technology Data Exchange (ETDEWEB)
McDonald, Jamie I.; Shore, Graham M. [Department of Physics, Swansea University,Singleton Park, Swansea, SA2 8PP (United Kingdom)
2016-04-05
We describe a new mechanism — radiatively-induced gravitational leptogenesis — for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how the size of the radiative corrections relevant for leptogenesis becomes enhanced by increasing the mass hierarchy of the sterile neutrinos, and show how the induced lepton asymmetry may be sufficiently large to play an important rôle in determining the baryon-to-photon ratio of the Universe.
Leptogenesis from loop effects in curved spacetime
McDonald, Jamie I.; Shore, Graham M.
2016-04-01
We describe a new mechanism — radiatively-induced gravitational leptogenesis — for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how the size of the radiative corrections relevant for leptogenesis becomes enhanced by increasing the mass hierarchy of the sterile neutrinos, and show how the induced lepton asymmetry may be sufficiently large to play an important rôle in determining the baryon-to-photon ratio of the Universe.
Formalization of an environmental model using formal concept analysis - FCA
Bourdon-García, Rubén D.; Burgos-Salcedo, Javier D.
2016-08-01
Nowadays, there is a huge necessity to generate novel strategies for social-ecological systems analyses for resolving global sustainability problems. This paper has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Ángel Maya, who without a doubt, was one of the most important environmental philosophers in South America; Ángel Maya proposed and established that Ecosystem-Culture relations, instead Human-Nature ones, are determinants in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept-superconcept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne-Guigues base), were determined for the ecosystem-culture relations.
Diósi, Lajos; Elze, Hans-Thomas; Fronzoni, Leone; Halliwell, Jonathan; Prati, Enrico; Vitiello, Giuseppe; Yearsley, James
2013-06-01
Presented in this volume are the Invited Lectures and the Contributed Papers of the Sixth International Workshop on Decoherence, Information, Complexity and Entropy - DICE 2012, held at Castello Pasquini, Castiglioncello (Tuscany), 17-21 September 2012. These proceedings may document to the interested public and to the wider scientific community the stimulating exchange of ideas at the meeting. The number of participants has been steadily growing over the years, reflecting an increasing attraction, if not need, of such conference. Our very intention has always been to bring together leading researchers, advanced students, and renowned scholars from various areas, in order to stimulate new ideas and their exchange across the borders of specialization. In this way, the series of meetings successfully continued from the beginning with DICE 20021, followed by DICE 20042, DICE 20063, DICE 20084, and DICE 20105, Most recently, DICE 2012 brought together more than 120 participants representing more than 30 countries worldwide. It has been a great honour and inspiration to have Professor Yakir Aharonov (Tel Aviv) with us, who presented the opening Keynote Lecture 'The two-vector quantum formalism'. With the overarching theme 'Spacetime - Matter - Quantum Mechanics - from the Planck scale to emergent phenomena', the conference took place in the very pleasant and inspiring atmosphere of Castello Pasquini - in beautiful surroundings, overlooking a piece of Tuscany's coast. The 5-day program covered these major topics: Quantum Mechanics, Foundations and Quantum-Classical Border Quantum-Classical Hybrids and Many-Body Systems Spectral Geometry, Path Integrals and Experiments Quantum -/- Gravity -/- Spacetime Quantum Mechanics on all Scales? A Roundtable Discussion under the theme 'Nuovi orizzonti nella ricerca scientifica. Ci troviamo di fronte ad una rivoluzione scientifica?' formed an integral part of the program. With participation of E Del Giudice (INFN & Università di
Charkiewicz, A
2000-01-01
Before the Career Path system, jobs were classified according to grades with general statutory definitions, guided by the "Job Catalogue" which defined 6 evaluation criteria with example illustrations in the form of "typical" job descriptions. Career Paths were given concise statutory definitions necessitating a method of description and evaluation adapted to their new wider-band salary concept. Evaluations were derived from the same 6 criteria but the typical descriptions became unusable. In 1999, a sub-group of the Standing Concertation Committee proposed a new guide for describing Career Paths, adapted to their wider career concept by expanding the 6 evaluation criteria into 9. For each criterion several levels were established tracing the expected evolution of job level profiles and personal competencies over their longer salary ranges. While providing more transparency to supervisors and staff, the Guide's official use would be by services responsible for vacancy notices, Career Path evaluations and rela...
Spanier, Graham B.; Glick, Paul C.
1980-01-01
Presents a demographic analysis of the paths to remarriage--the extent and timing of remarriage, social factors associated with remarriage, and the impact of the event which preceded remarriage (divorce or widowhood). (Author)
Origin of the pure spinor and Green-Schwarz formalisms
Energy Technology Data Exchange (ETDEWEB)
Berkovits, Nathan [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP - Universidade Estadual Paulista,Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil)
2015-07-20
The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂x{sup m}(γ{sub m}λ){sub α}=0 where λ{sup α} is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint ∂x{sup m}∂x{sub m}=0, and the Green-Schwarz fermionic spacetime spinor variables θ{sup α} arise as Faddeev-Popov ghosts for this constraint. In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor λ{sup α} with a d=10 projective pure spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and superstring are then obtained as different gauge-fixings of this purely bosonic classical action, and the Green-Schwarz kappa symmetry is directly related to the pure spinor BRST symmetry. Since a d=10 projective pure spinor parameterizes ((SO(10))/(U(5))), this action can be interpreted as a standard ĉ=5 topological action where one integrates over the ((SO(10))/(U(5))) choice of complex structure. Finally, a purely bosonic action for the d=11 supermembrane is proposed which reduces upon double-dimensional reduction to the purely bosonic action for the d=10 Type IIA superstring.
Path planning in changeable environments
Nieuwenhuisen, D.
2007-01-01
This thesis addresses path planning in changeable environments. In contrast to traditional path planning that deals with static environments, in changeable environments objects are allowed to change their configurations over time. In many cases, path planning algorithms must facilitate quick
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Bondas, Terese
2006-07-01
The aim was to explore why nurses enter nursing leadership and apply for a management position in health care. The study is part of a research programme in nursing leadership and evidence-based care. Nursing has not invested enough in the development of nursing leadership for the development of patient care. There is scarce research on nurses' motives and reasons for committing themselves to a career in nursing leadership. A strategic sample of 68 Finnish nurse leaders completed a semistructured questionnaire. Analytic induction was applied in an attempt to generate a theory. A theory, Paths to Nursing Leadership, is proposed for further research. Four different paths were found according to variations between the nurse leaders' education, primary commitment and situational factors. They are called the Path of Ideals, the Path of Chance, the Career Path and the Temporary Path. Situational factors and role models of good but also bad nursing leadership besides motivational and educational factors have played a significant role when Finnish nurses have entered nursing leadership. The educational requirements for nurse leaders and recruitment to nursing management positions need serious attention in order to develop a competent nursing leadership.
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Integrating Semi-formal and Formal Software Specification Techniques
Wieringa, Roelf J.; Dubois, Eric
1998-01-01
In this paper, we report on the integration of informal, semiformal and formal system specification techniques. We present a framework for system specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of structured
Formal verification of mathematical software
Sutherland, D.
1984-01-01
Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.
Formally Generating Adaptive Security Protocols
2013-03-01
RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) MAR 2013 2. REPORT TYPE FINAL TECHNICAL REPORT 3. DATES COVERED (From - To) May...receipt of messages. Formally, an event class of type T is a function that takes an event ordering and an event in that event ordering, and returns a bag...and Robert Constable. An exper- iment in formal design using meta-properties. In J. Lala , D. Mughan, C. McCollum, and B. Witten, editors, DARPA
Emergent spacetime in stochastically evolving dimensions
Energy Technology Data Exchange (ETDEWEB)
Afshordi, Niayesh [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1 (Canada); HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, NY 14260-1500 (United States); Stojkovic, Dejan, E-mail: ds77@buffalo.edu [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, NY 14260-1500 (United States)
2014-12-12
Changing the dimensionality of the space–time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field theories, it is possible to quantize gravity, and the theory of matter plus gravity is free of divergencies or renormalizable. If the space is higher dimensional at cosmological scales, then some cosmological problems (including the cosmological constant problem) can be attacked from a completely new perspective. In this paper, we construct an explicit model of “evolving dimensions” in which the dimensions open up as the temperature of the universe drops. We adopt the string theory framework in which the dimensions are fields that live on the string worldsheet, and add temperature dependent mass terms for them. At the Big Bang, all the dimensions are very heavy and are not excited. As the universe cools down, dimensions open up one by one. Thus, the dimensionality of the space we live in depends on the energy or temperature that we are probing. In particular, we provide a kinematic Brandenberger–Vafa argument for how a discrete causal set, and eventually a continuum (3+1)-dim spacetime along with Einstein gravity emerges in the Infrared from the worldsheet action. The (3+1)-dim Planck mass and the string scale become directly related, without any compactification. Amongst other predictions, we argue that LHC might be blind to new physics even if it comes at the TeV scale. In contrast, cosmic ray experiments, especially those that can register the very beginning of the shower, and collisions with high multiplicity and density of particles, might be sensitive to the dimensional cross-over.
Emergent spacetime in stochastically evolving dimensions
Directory of Open Access Journals (Sweden)
Niayesh Afshordi
2014-12-01
Full Text Available Changing the dimensionality of the space–time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field theories, it is possible to quantize gravity, and the theory of matter plus gravity is free of divergencies or renormalizable. If the space is higher dimensional at cosmological scales, then some cosmological problems (including the cosmological constant problem can be attacked from a completely new perspective. In this paper, we construct an explicit model of “evolving dimensions” in which the dimensions open up as the temperature of the universe drops. We adopt the string theory framework in which the dimensions are fields that live on the string worldsheet, and add temperature dependent mass terms for them. At the Big Bang, all the dimensions are very heavy and are not excited. As the universe cools down, dimensions open up one by one. Thus, the dimensionality of the space we live in depends on the energy or temperature that we are probing. In particular, we provide a kinematic Brandenberger–Vafa argument for how a discrete causal set, and eventually a continuum (3+1-dim spacetime along with Einstein gravity emerges in the Infrared from the worldsheet action. The (3+1-dim Planck mass and the string scale become directly related, without any compactification. Amongst other predictions, we argue that LHC might be blind to new physics even if it comes at the TeV scale. In contrast, cosmic ray experiments, especially those that can register the very beginning of the shower, and collisions with high multiplicity and density of particles, might be sensitive to the dimensional cross-over.
The Mond Limit from Spacetime Scale Invariance
Milgrom, Mordehai
2009-06-01
The modified Newtonian dynamics (MOND) limit is shown to follow from a requirement of spacetime scale invariance of the equations of motion for nonrelativistic, purely gravitational systems, i.e., invariance of the equations of motion under (t, r) → (λt, λr) in the limit a 0 → ∞. It is suggested that this should replace the definition of the MOND limit based on the low-acceleration behavior of a Newtonian-MOND interpolating function. In this way, the salient, deep-MOND results—asymptotically flat rotation curves, the mass-rotational-speed relation (baryonic Tully-Fisher relation), the Faber-Jackson relation, etc.,—follow from a symmetry principle. For example, asymptotic flatness of rotation curves reflects the fact that radii change under scaling, while velocities do not. I then comment on the interpretation of the deep-MOND limit as one of "zero mass": rest masses, whose presence obstructs scaling symmetry, become negligible compared to the "phantom," dynamical masses—those that some would attribute to dark matter. Unlike the former masses, the latter transform in a way that is consistent with the symmetry. Finally, I discuss the putative MOND-cosmology connection in light of another, previously known symmetry of the deep-MOND limit. In particular, it is suggested that MOND is related to the asymptotic de Sitter geometry of our universe. It is conjectured, for example that in an exact de Sitter cosmos, deep-MOND physics would exactly apply to local systems. I also point out, in this connection, the possible relevance of a de Sitter-conformal-field-theory (dS/CFT) duality.
Vaidya spacetime in massive gravity's rainbow
Heydarzade, Yaghoub; Rudra, Prabir; Darabi, Farhad; Ali, Ahmed Farag; Faizal, Mir
2017-11-01
In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Vaidya spacetime in massive gravity's rainbow
Directory of Open Access Journals (Sweden)
Yaghoub Heydarzade
2017-11-01
Full Text Available In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Formalization and implementation of topological visual navigation in two dimensions
Kender, John R.; Park, Il-Pyung; Yang, David
1991-03-01
In this paper we formalize and implement a model of topological visual navigation in two-dimensional spaces. Unlike much of traditional quantitative visual navigation the emphasis throughout is on the methods and the efficiency of qualitative visual descriptions of objects and environments and on the methods and the efficiency of direction-giving by means of visual landmarks. We formalize three domainsthe world itself the map-maker''s view of it and the navigator''s experience of itand the concepts of custom maps and landmarks. We specify for a simplified navigator (the " level helicopter" ) the several ways in which visual landmarks can be chosen depending on which of several costs (sensor distance or communication) should be minimized. We show that paths minimizing one measure can make others arbitrarily complex the algorithm for selecting the path is based on a form of Dijkstra''s algorithm and therefore automatically generates intelligent navigator overshooting and backtracking. We implement using an armheld camera such a navigator and detail its basic seek-and-adjust behaviors as it follows visual highways (or departs from them) to reach a goal. Seeking is based on topology and adjusting is based on symmetry there are essentially no quantitative measures. We describe under what circumstances its environment is visually difficult and perceptively shadowed and describe how errors in path-following impact landmark selection. Since visual landmark selection and direction-giving are in general NP-complete and rely on the nearly intractable
Unitarity and causality in generalized quantum mechanics for nonchronal spacetimes
Hartle, James B.
1994-06-01
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime possesses nonchronal regions which cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives on two spacelike surfaces lying in regions of spacetime where foliating families can be defined may be nonunitary if a nonchronal region lies between them. This paper describes a sum-over-histories generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such nonunitarity. The usual notion of state on a spacelike surface is lost in this generalization. Anomalies such as nonconservation of energy or ``Everett phones'' that are exhibited by some generalizations of quantum mechanics are not found in this one. However, the generalization is acausal in the sense that the existence of nonchronal regions of spacetime in the future can affect the probabilities of alternatives today and signaling outside the light cone is possible. The detectability of nonunitary evolution and violations of causality in measurement situations are briefly considered.
Formal systems for persuasion dialogue
Prakken, Henry
This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various
Formal monkey linguistics : The debate
Schlenker, Philippe; Chemla, Emmanuel; Schel, Anne M.; Fuller, James; Gautier, Jean Pierre; Kuhn, Jeremy; Veselinović, Dunja; Arnold, Kate; Cäsar, Cristiane; Keenan, Sumir; Lemasson, Alban; Ouattara, Karim; Ryder, Robin; Zuberbühler, Klaus
2016-01-01
We explain why general techniques from formal linguistics can and should be applied to the analysis of monkey communication - in the areas of syntax and especially semantics. An informed look at our recent proposals shows that such techniques needn't rely excessively on categories of human language:
Automatic Testing with Formal Methods
Tretmans, G.J.; Belinfante, Axel
1999-01-01
The use of formal system specifications makes it possible to automate the derivation of test cases from specifications. This allows to automate the whole testing process, not only the test execution part of it. This paper presents the state of the art and future perspectives in testing based on
HAMILTONIAN FORMALISM ON CHARACTERISTIC SURFACES.
The problem of the construction of a Hamiltonian formalism suitable for propagation of a field off characteristic or null surfaces is considered. In...is developed on characteristic surfaces. A Hamiltonian for gravitation (general relativity) is constructed, first on null surfaces described only by
Rotor and wind turbine formalism
DEFF Research Database (Denmark)
Branlard, Emmanuel Simon Pierre
2017-01-01
The main conventions used in this book for the study of rotors are introduced in this chapter. The main assumptions and notations are provided. The formalism specific to wind turbines is presented. The forces, moments, velocities and dimensionless coefficients used in the study of rotors...
Abrams, Gene; Siles Molina, Mercedes
2017-01-01
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...
TAT-based formal representation of medical guidelines: imatinib case-study.
Simalatsar, Alena; De Micheli, Giovanni
2012-01-01
Computer-based interpretation of medical guidelines (GLs) has drawn lots of attention in the past three decades. It is essential to use a formalism for GLs representation that would enable the validation of GLs structural properties, be able to map medical actions into the time scale and support the automatic formal verification of GLs without additional translation paths. In this paper we preset a novel approach based on Timed Automata extended with Tasks (TAT) for the medical protocol formal representation using the TIMES toolbox. We discuss the verification issues with the help of the Imatinib case study.
Sokołowski, L. M.; Golda, Z. A.
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain infinite number of equally separated conjugate points and there are no other cut points. Yet in these two spacetimes each outgoing or ingoing radial geodesic which does not cross the centre is globally of maximal length. Circular geodesics exist only in CAdS spacetime and contain an infinite sequence of equally separated conjugate points. The geodesic curves which intersect the circular ones at these points may either belong to the two-surface $\\theta=\\pi/2$ or lie outside it.
Derivation of Electromagnetism from the Elastodynamics of the Spacetime Continuum
Directory of Open Access Journals (Sweden)
Millette P. A.
2013-04-01
Full Text Available We derive Electromagnetism from the Elastodynamics of the Spacetime Continuum based on the identification of the theory’s antisymmetric rotation tensor with the elec- tromagnetic field-strength tensor. The theory provides a physical explanation of the electromagnetic potential, which arises from transverse ( shearing displacements of the spacetime continuum, in contrast to mass which arises from longitudinal (dilatational displacements. In addition, the theory provides a physical explanation of the current density four-vector, as the 4-gradient of the volume dilatation of the spacetime con- tinuum. The Lorentz condition is obtained directly from the theory. In addition, we obtain a generalization of Electromagnetism for the situation where a volume force is present, in the general non-macroscopic case. Maxwell’s equations are found to remain unchanged, but the current density has an additional term proportional to the volume force.
Conformal geodesics in spherically symmetric vacuum spacetimes with cosmological constant
García-Parrado Gómez-Lobo, A.; Gasperín, E.; Valiente Kroon, J. A.
2018-02-01
An analysis of conformal geodesics in the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that the congruence of conformal geodesics arising from this data cover the whole maximal extension of canonical conformal representations of the spacetimes without forming caustic points. For the Schwarzschild–de Sitter family, the resulting congruence can be used to obtain global conformal Gaussian systems of coordinates of the conformal representation. In the case of the Schwarzschild–anti-de Sitter family, the natural parameter of the curves only covers a restricted time span so that these global conformal Gaussian systems do not exist.
Dislocations in the Spacetime Continuum: Framework for Quantum Physics
Directory of Open Access Journals (Sweden)
Millette P. A.
2015-10-01
Full Text Available This paper provides a framework for the physical description of physical processes at the quantum level based on dislocations in the spacetime continuum within STCED (Spacetime Continuum Elastodynamics. In this framework, photon and particle self- energies and interactions are mediated by the strain energy density of the dislocations, replacing the role played by virtual particles in QED. We postulate that the spacetime continuum has a granularity characterized by a length b 0 corresponding to the smallest STC elementary Burgers dislocation-displacement vector. Screw dislocations corre- sponding to transverse displacements are identified with photons, and edge dislocations corresponding to longitudinal displacements are identified with particles. Mixed dislo- cations give rise to wave-particle duality. The strain energy density of the dislocations are calculated and proposed to explain the QED problem of mass renormalization.
Quantum field theory in curved spacetime and black hole thermodynamics
Wald, Robert M
1994-01-01
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth. This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum f...
Quantum nonlocality, and the end of classical space-time
Banerjee, Shreya; Singh, T P
2016-01-01
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that space-time is fundamentally non-commutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying non-commutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary space-time geometry. However, measurement on an entangled state can be correctly described only in the underlying non-commutative space-time, where there is no causality violation, nor a spooky action at a distance.
Generalized Poincare algebras, Hopf algebras and {kappa}-Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Kovacevic, D., E-mail: domagoj.kovacevic@fer.hr [Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb (Croatia); Meljanac, S., E-mail: meljanac@irb.hr [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia); Pachol, A., E-mail: pachol@raunvis.hi.is [Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik (Iceland); Strajn, R., E-mail: rina.strajn@gmail.com [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia)
2012-05-01
We propose a generalized description for the {kappa}-Poincare-Hopf algebra as a symmetry quantum group of underlying {kappa}-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of {kappa}-Minkowski algebra realization. For the given realization of {kappa}-Minkowski spacetime there is a unique {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with {kappa}-Poincare algebras which are related to {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of {kappa}-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the {kappa}-Minkowski spacetime is presented. Some physical applications are briefly discussed.
Space-Time Coding over Fading Channels with Stable Noise
Lee, Junghoon
2011-01-01
This paper addresses the performance of space-time coding over fading channels with impulsive noise which is known to accurately capture network interference. We use the symmetric alpha stable noise distribution and adopt two models which assume dependent and independent noise components across receive antennas. We derive pairwise error probability (PEP) of orthogonal space-time block codes (STBC) with a benchmark genie-aided receiver (GAR), or the minimum distance receiver (MDR) which is optimal in the Gaussian case. For general space-time codes we propose a maximum-likelihood (ML) receiver, and its approximation at high signal-to-noise ratio (SNR). The resulting asymptotically optimal receiver (AOR) does not depend on noise parameters and is computationally simple. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the receivers.
On the theory of Killing orbits in spacetime
Hall, G. S.
2003-09-01
This paper gives a theoretical discussion of the orbits and isotropies which arise in a spacetime which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a spacetime in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of 'stable' orbits and the possible misbehaviour of the 'unstable' ones is pointed out and, in particular, the fact that independent Killing vector fields in spacetime may not induce independent Killing vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.
Green-Schwarz superstring on doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Park, Jeong-Hyuck [Department of Physics, Sogang University,35 Baekbeom-ro, Mapo-gu, Seoul 04107 (Korea, Republic of); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science,Daejeon 34047 (Korea, Republic of)
2016-11-02
We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses O(10,10) T-duality, Spin(1,9)×Spin(9,1) Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms, world-sheet diffeomorphisms and Weyl symmetry. Further, restricted to flat backgrounds, it enjoys maximal spacetime supersymmetry and kappa-symmetry. After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action. Thanks to the twofold spin groups, the action is unique: it is specific choices of the NS-NS backgrounds that distinguish IIA or IIB, as well as lead to non-Riemannian or non-relativistic superstring a la Gomis-Ooguri which might deserve the nomenclature, type IIC.
Modified Theories of Gravitation behind the Spacetime Deformation
Directory of Open Access Journals (Sweden)
Gagik Ter-Kazarian
2015-01-01
Full Text Available In the framework of proposed theory of spacetime deformation/distortion, we have a way to deform the spacetime through a nontrivial choice of the distortion-complex, displaying different connections, which may reveal different post-Riemannian spacetime structures as corollary. We extend this theory to address, in particular, the gauge model of the most general metric-affine gravity carrying both nontrivial torsion and nonmetricity. This model is constructed in the framework of the first order Lagrangian expressed in terms of the gauge potentials and their first derivatives. The equations of the standard theory, which have no propagating modes for torsion, can be equivalently replaced in modified framework by the modified equations, which in the limit of reducing the affine group leads to the modified Einstein-Cartan theory with dynamical torsion and beyond. In testing the modified framework for various particular cases, we use the Lagrange multipliers for extinguishing nonmetricity and torsion.
Directory of Open Access Journals (Sweden)
Camillo Constantini
2003-10-01
Full Text Available We prove that the hyperspace of closed bounded sets with the Hausdor_ topology, over an almost convex metric space, is an absolute retract. Dense subspaces of normed linear spaces are examples of, not necessarily connected, almost convex metric spaces. We give some necessary conditions for the path-wise connectedness of the Hausdorff metric topology on closed bounded sets. Finally, we describe properties of a separable metric space, under which its hyperspace with the Wijsman topology is path-wise connected.
DEFF Research Database (Denmark)
Garud, Raghu; Karnøe, Peter
the place of agency in these theories that take history so seriously. In the end, they are as interested in path creation and destruction as they are in path dependence. This book is compiled of both theoretical and empirical writing. It shows relatively well-known industries such as the automobile......, biotechnology and semi-conductor industries in a new light. It also invites the reader to learn more about medical practices, wind power, lasers and synthesizers. Primarily for academicians, researchers and PhD students in fields related to technology management, this book is a research-oriented textbook...
MEST- avoid next extinction by a space-time effect
Cao, Dayong
2013-03-01
Sun's companion-dark hole seasonal took its dark comets belt and much dark matter to impact near our earth. And some of them probability hit on our earth. So this model kept and triggered periodic mass extinctions on our earth every 25 to 27 million years. After every impaction, many dark comets with very special tilted orbits were arrested and lurked in solar system. When the dark hole-Tyche goes near the solar system again, they will impact near planets. The Tyche, dark comet and Oort Cloud have their space-time center. Because the space-time are frequency and amplitude square of wave. Because the wave (space-time) can make a field, and gas has more wave and fluctuate. So they like dense gas ball and a dark dense field. They can absorb the space-time and wave. So they are ``dark'' like the dark matter which can break genetic codes of our lives by a dark space-time effect. So the upcoming next impaction will cause current ``biodiversity loss.'' The dark matter can change dead plants and animals to coal, oil and natural gas which are used as energy, but break our living environment. According to our experiments, which consciousness can use thought waves remotely to change their systemic model between Electron Clouds and electron holes of P-N Junction and can change output voltages of solar cells by a life information technology and a space-time effect, we hope to find a new method to the orbit of the Tyche to avoid next extinction. (see Dayong Cao, BAPS.2011.APR.K1.17 and BAPS.2012.MAR.P33.14) Support by AEEA
Revisiting Special Relativity: A Natural Algebraic Alternative to Minkowski Spacetime
Chappell, James M.; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension , with the unit imaginary producing the correct spacetime distance , and the results of Einstein’s then recently developed theory of special relativity, thus providing an explanation for Einstein’s theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary , with the Clifford bivector for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis and . We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton’s scattering formula, and a simple formulation of Dirac’s and Maxwell’s equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane. PMID:23300566
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
Chappell, James M; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
Directory of Open Access Journals (Sweden)
James M Chappell
Full Text Available Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
The Mode Solution of the Wave Equation in Kasner Spacetimes and Redshift
Energy Technology Data Exchange (ETDEWEB)
Petersen, Oliver Lindblad, E-mail: lindblad@uni-potsdam.de [Universität Potsdam, Institut für Mathematik (Germany)
2016-12-15
We study the mode solution to the Cauchy problem of the scalar wave equation □φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift.
Holographic analysis of dispersive pupils in space--time optics
Energy Technology Data Exchange (ETDEWEB)
Calatroni, J.; Vienot, J.C.
1981-06-01
Extension of space--time optics to objects whose transparency is a function of the temporal frequency v = c/lambda is examined. Considering the effects of such stationary pupils on white light waves, they are called temporal pupils. It is shown that simultaneous encoding both in the space and time frequency domains is required to record pupil parameters. The space-time impulse response and transfer functions are calculated for a dispersive nonabsorbent material. An experimental method providing holographic recording of the dispersion curve of any transparent material is presented.
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E
2015-01-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.
Three-generation neutrino oscillations in curved spacetime
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yu-Hao, E-mail: yhzhang1994@gmail.com; Li, Xue-Qian, E-mail: lixq@nankai.edu.cn
2016-10-15
Three-generation MSW effect in curved spacetime is studied and a brief discussion on the gravitational correction to the neutrino self-energy is given. The modified mixing parameters and corresponding conversion probabilities of neutrinos after traveling through celestial objects of constant densities are obtained. The method to distinguish between the normal hierarchy and inverted hierarchy is discussed in this framework. Due to the gravitational redshift of energy, in some extreme situations, the resonance energy of neutrinos might be shifted noticeably and the gravitational effect on the self-energy of neutrino becomes significant at the vicinities of spacetime singularities.
Axion particle production in a laser-induced dynamical spacetime
Wadud, M. A.; King, B.; Bingham, R.; Gregori, G.
2018-02-01
We consider the dynamics of a charged particle (e.g., an electron) oscillating in a laser field in flat spacetime and describe it in terms of the variable mass metric. By applying Einstein's equivalence principle, we show that, after representing the electron motion in a time-dependent manner, the variable mass metric takes the form of the Friedmann-Lemaître-Robertson-Walker metric. We quantize a pseudo-scalar field in this spacetime and derive the production rate of electrically neutral, spinless particles. We show that this approach can provide an alternative experimental method to axion searches.
On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime
Directory of Open Access Journals (Sweden)
Kazi Ashraful Alam
2017-01-01
Full Text Available Entropy bound for the photon gas in a noncommutative (NC spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.
BPS Wilson loops in Minkowski spacetime and Euclidean space
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-ju
2015-01-01
We give evidence that spacelike BPS Wilson loops do not exist in Minkowski spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot preserve any supersymmetries, in $d = 4$ $\\mathcal N = 4$ super Yang-Mills theory, $d = 3$ $\\mathcal N = 2$ super Chern-Simons-matter theory, and $d = 3$ $\\mathcal N = 6$ Aharony-Bergman-Jafferis-Maldacena theory. We not only show this using infinite straight lines and circles as examples, but also we give proofs for general curves. We attribu...
Space-time modeling of electricity spot prices
DEFF Research Database (Denmark)
Abate, Girum Dagnachew; Haldrup, Niels
In this paper we derive a space-time model for electricity spot prices. A general spatial Durbin model that incorporates the temporal as well as spatial lags of spot prices is presented. Joint modeling of space-time effects is necessarily important when prices and loads are determined in a network...... of power exchange areas. We use data from the Nord Pool electricity power exchange area bidding markets. Different spatial weight matrices are considered to capture the structure of the spatial dependence process across different bidding markets and statistical tests show significant spatial dependence...
Spinning scalar solitons in anti-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Radu, Eugen, E-mail: eugen.radu@uni-oldenburg.de [Institut fuer Physik, Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Subagyo, Bintoro [Institut fuer Physik, Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)
2012-10-31
We present spinning Q-balls and boson stars in four-dimensional anti-de Sitter spacetime. These are smooth, horizonless solutions for gravity coupled to a massive complex scalar field with a harmonic dependence on time and the azimuthal angle. Similar to the flat spacetime configurations, the angular momentum is quantized. We find that a class of solutions with a self-interaction potential has a limit corresponding to static solitons with axial symmetry only. An exact solution describing spherically symmetric Q-balls in a fixed AdS background is also discussed.
Noise kernels of stochastic gravity in conformally-flat spacetimes
Cho, H. T.; Hu, B. L.
2015-03-01
The central object in the theory of semiclassical stochastic gravity is the noise kernel, which is the symmetric two point correlation function of the stress-energy tensor. Using the corresponding Wightman functions in Minkowski, Einstein and open Einstein spaces, we construct the noise kernels of a conformally coupled scalar field in these spacetimes. From them we show that the noise kernels in conformally-flat spacetimes, including the Friedmann-Robertson-Walker universes, can be obtained in closed analytic forms by using a combination of conformal and coordinate transformations.
Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes
Bantilan, Hans; Figueras, Pau; Kunesch, Markus; Romatschke, Paul
2017-11-01
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.
Covariant information-density cutoff in curved space-time.
Kempf, Achim
2004-06-04
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.
Deformed Space-Time of the Piezonuclear Emissions
Cardone, F.; Calbucci, V.; Albertini, G.
2014-01-01
In this paper, an experimental verification of the relationship between the deformed Minkowsky space-time and the piezonuclear emission has been obtained by testing several cylindrical steel bars cyclically loaded in a mechanical fatigue machine. During the compression cycles, α-particles have been both detected by a ZnS(Ag) scintillator and a Geiger counter. Taking into account the theory of the deformed special relativity, we report that the emission only occurs after a specific value of energy is overcome. This value is strictly related to the weak and strong nuclear interactions, which in turn define the regions of Minkowsky and non-Minkowsky space-time.
On the Formal Verification of Conflict Detection Algorithms
Munoz, Cesar; Butler, Ricky W.; Carreno, Victor A.; Dowek, Gilles
2001-01-01
Safety assessment of new air traffic management systems is a main issue for civil aviation authorities. Standard techniques such as testing and simulation have serious limitations in new systems that are significantly more autonomous than the older ones. In this paper, we present an innovative approach, based on formal verification, for establishing the correctness of conflict detection systems. Fundamental to our approach is the concept of trajectory, which is a continuous path in the x-y plane constrained by physical laws and operational requirements. From the Model of trajectories, we extract, and formally prove, high level properties that can serve as a framework to analyze conflict scenarios. We use the Airborne Information for Lateral Spacing (AILS) alerting algorithm as a case study of our approach.
Horizon dynamics in perturbed Kerr spacetimes
Chu, Tony; Cohen, Michael I
2010-01-01
We present numerical simulations of a Kerr black hole perturbed by a pulse of ingoing gravitational radiation. For strong perturbations we find up to five concentric marginally outer trapped surfaces. These trapped surfaces appear and disappear in pairs, so that the total number of such surfaces at any given time is odd. The world tubes traced out by the marginally outer trapped surfaces are found to be spacelike during the highly dynamical regime, approaching a null hypersurface at early and late times. We analyze the structure of these marginally trapped tubes in the context of the dynamical horizon formalism, computing the expansion of outgoing and incoming null geodesics, as well as evaluating the dynamical horizon flux law and the angular momentum flux law. Finally, we compute the event horizon. The event horizon is well-behaved and approaches the apparent horizon before and after the highly dynamical regime. No new generators enter the event horizon during the simulation.
Hilditch, David; Bugner, Marcus; Rueter, Hannes; Bruegmann, Bernd
2016-01-01
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the `dual foliation' formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoglu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et. al., we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a...
The FGK formalism for black p-branes in d dimensions
de Antonio Martín, Antonio; Ortín, Tomás; Shahbazi, C. S.
2012-05-01
We present a generalization to an arbitrary number of spacetime ( d) and world-volume ( p + 1) dimensions of the formalism proposed by Ferrara, Gibbons and Kallosh to study black holes ( p = 0) in d = 4 dimensions. We include the special cases in which there can be dyonic and self- or anti-self-dual black branes. Most of the results valid for 4-dimensional black holes (relations between temperature, entropy and non-extremality parameter, and between entropy and black-hole potential on the horizon) are straightforwardly generalized. We apply the formalism to the case of black strings in N = 2 , d = 5 supergravity coupled to vector multiplets, in which the black-string potential can be expressed in terms of the dual central charge and work out an explicit example with one vector multiplet, determining supersymmetric and non-supersymmetric attractors and constructing the nonextremal black-string solutions that interpolate between them.
Directory of Open Access Journals (Sweden)
Peter Juhasz
2017-03-01
Full Text Available While risk management gained popularity during the last decades even some of the basic risk types are still far out of focus. One of these is path dependency that refers to the uncertainty of how we reach a certain level of total performance over time. While decision makers are careful in accessing how their position will look like the end of certain periods, little attention is given how they will get there through the period. The uncertainty of how a process will develop across a shorter period of time is often “eliminated” by simply choosing a longer planning time interval, what makes path dependency is one of the most often overlooked business risk types. After reviewing the origin of the problem we propose and compare seven risk measures to access path. Traditional risk measures like standard deviation of sub period cash flows fail to capture this risk type. We conclude that in most cases considering the distribution of the expected cash flow effect caused by the path dependency may offer the best method, but we may need to use several measures at the same time to include all the optimisation limits of the given firm
McGarvey, Lynn M.; Sterenberg, Gladys Y.; Long, Julie S.
2013-01-01
The authors elucidate what they saw as three important challenges to overcome along the path to becoming elementary school mathematics teacher leaders: marginal interest in math, low self-confidence, and teaching in isolation. To illustrate how these challenges were mitigated, they focus on the stories of two elementary school teachers--Laura and…
Bill, R. C.; Johnson, R. D. (Inventor)
1979-01-01
A gas path seal suitable for use with a turbine engine or compressor is described. A shroud wearable or abradable by the abrasion of the rotor blades of the turbine or compressor shrouds the rotor bades. A compliant backing surrounds the shroud. The backing is a yieldingly deformable porous material covered with a thin ductile layer. A mounting fixture surrounds the backing.
DEFF Research Database (Denmark)
Schürmann, Carsten; Sarnat, Jeffrey
2009-01-01
an induction principle that combines the comfort of structural induction with the expressive strength of transfinite induction. Using lexicographic path induction, we give a consistency proof of Martin-Löf’s intuitionistic theory of inductive definitions. The consistency of Heyting arithmetic follows directly...
Sokołowski, Leszek M
2014-01-01
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain...
Formal Verification for a Next-Generation Space Shuttle
Nelson, Stacy D.; Pecheur, Charles; Koga, Dennis (Technical Monitor)
2002-01-01
This paper discusses the verification and validation (V&2) of advanced software used for integrated vehicle health monitoring (IVHM), in the context of NASA's next-generation space shuttle. We survey the current VBCV practice and standards used in selected NASA projects, review applicable formal verification techniques, and discuss their integration info existing development practice and standards. We also describe two verification tools, JMPL2SMV and Livingstone PathFinder, that can be used to thoroughly verify diagnosis applications that use model-based reasoning, such as the Livingstone system.
Contextual approach to quantum formalism
Khrennikov, Andrei
2009-01-01
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems...
Musical Formalism and Political Performances
Directory of Open Access Journals (Sweden)
Jonathan A. Neufeld
2009-01-01
Full Text Available Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing any description of the music can tell us, is inconsistent with Kivy's quite compelling account of performance. This shows the difficulty that actual performances pose to overly rigid conceptions of music. Daniel Barenboim's unannounced performance of Wagner in Israel in 2001 shows that the problem of the boundaries of musical relevance is no mere philosophical puzzle. It is a pressing problem in the musical public sphere.
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Formal Validation of Aerospace Software
Lesens, David; Moy, Yannick; Kanig, Johannes
2013-08-01
Any single error in critical software can have catastrophic consequences. Even though failures are usually not advertised, some software bugs have become famous, such as the error in the MIM-104 Patriot. For space systems, experience shows that software errors are a serious concern: more than half of all satellite failures from 2000 to 2003 involved software. To address this concern, this paper addresses the use of formal verification of software developed in Ada.
Formal description of board games
Nowak, Stanislav
2011-01-01
The aim of thesis was to design a mathematical formalism that allows describing and exploring the properties of board games. The work benefits from the findings of automata theory and logic programming. First part of thesis deals with finite automata and their possible applications for the needs of board games. The result is an extension of finite-state automaton covering the specifics of board games called game automaton. Board games are a complex domain hight level tools should be used. Suc...
DEFF Research Database (Denmark)
Villesèche, Florence; Josserand, Emmanuel
2017-01-01
implications: The paper contributes to research showing that the social structure of interactions and context can impact women’s standing in the workplace. Originality/value: The paper sheds light on the under-studied and under-theorised phenomenon of formal women-only business networks. Beyond the individual...... member level, the authors suggest that such networks can be of value for organisations and the wider social group of women in management and leadership positions....
Stroh formalism and Rayleigh waves
Tanuma, Kazumi
2008-01-01
Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations
DEFF Research Database (Denmark)
Bjørner, Dines; George, Chris W.; Haxthausen, Anne Elisabeth
2004-01-01
these different UML views are unified, integrated, correlated or merely co-located is for others to dispute. We also seek to support multiple views, but are also in no doubt that there must be sound, well defined relations between such views. We thus report on ways and means of integrating formal techniques...... techniques, one that can be believably deployed for as wide a spectrum, or even a wider spectrum of software (and hardware) development, as, respectively than UML....
Formalizing narratives using nested circumscription
Energy Technology Data Exchange (ETDEWEB)
Baral, C.; Gabaldon, A. [Univ. of Texas, El Paso, TX (United States); Provetti, A. [Universita di Bologna (Italy)
1996-12-31
The representation of narratives of actions and observations is a current issue in Knowledge Representation, where traditional plan-oriented treatments of action seem to fall short. To address narratives, Pinto and Reiter have extended Situation Calculus axioms, Kowalski and Sergot have introduced the Event Calculus in Logic Programming, and Baral et al. have defined the specification language L which allows to express actual and hypothetical situations in a uniform setting. The L entailment relation can formalize several forms of reasoning about actions and change. In this paper we illustrate a translation of L theories into Nested Abnormality Theories, a novel form of circumscription. The proof of soundness and completeness of the translation is the main technical result of the paper, but attention is also devoted to the features of Nested Abnormality Theories to capture commonsense reasoning in general and to clarify which assumptions a logical formalization forces upon a domain. These results also help clarifying the relationship between L and other recent circumscriptive formalization for narratives, such as Miller and Shanahan`s.
Developing Modern Niger Delta Formalism
Directory of Open Access Journals (Sweden)
Edewor Uyoyou Nelson O
2014-11-01
Full Text Available Edewor Nelson (b. 1970 is a sculptor whose works depict configurations that espouse contexts associated with inimical and exploitative tendencies of petroleum oil exploration and exploitation in the Niger Delta region. His expressions represent a new formalism that is iconic of the region’s reality in terms of environmental degradation and fundamental human rights abuses. This motivation became imperative in the seemingly failure of other artistic explorations on the subject to adequately reflect modern formal archetypes for which the region’s dilemma can be expressed. The challenge of analytic study of this effort for attaining interpretative insights into this studio practice is pertinent. To realize this, corresponding Ivri traditional art form associated with the past in the region has been studied alongside petroleum drilling–related forms. This provides the fulcrum on which this article approaches an analysis of contextual and conceptual applications attributable to the stylistic oeuvre of Edewor’s practice since 1997. It uses formalism and iconography interpretative tools for its critical discourse.
Shih, Y. H.; Sergienko, A. V.; Rubin, M. H.
1993-01-01
A pair of correlated photons generated from parametric down conversion was sent to two independent Michelson interferometers. Second order interference was studied by means of a coincidence measurement between the outputs of two interferometers. The reported experiment and analysis studied this second order interference phenomena from the point of view of Einstein-Podolsky-Rosen paradox. The experiment was done in two steps. The first step of the experiment used 50 psec and 3 nsec coincidence time windows simultaneously. The 50 psec window was able to distinguish a 1.5 cm optical path difference in the interferometers. The interference visibility was measured to be 38 percent and 21 percent for the 50 psec time window and 22 percent and 7 percent for the 3 nsec time window, when the optical path difference of the interferometers were 2 cm and 4 cm, respectively. By comparing the visibilities between these two windows, the experiment showed the non-classical effect which resulted from an E.P.R. state. The second step of the experiment used a 20 psec coincidence time window, which was able to distinguish a 6 mm optical path difference in the interferometers. The interference visibilities were measured to be 59 percent for an optical path difference of 7 mm. This is the first observation of visibility greater than 50 percent for a two interferometer E.P.R. experiment which demonstrates nonclassical correlation of space-time variables.
A new derivation of the conformally flat stationary cyclic non-circular spacetimes
Energy Technology Data Exchange (ETDEWEB)
Ayon-Beato, Eloy [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); Campuzano, Cuauhtemoc [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); GarcIa, Alberto [Department of Physics, University of California, Davis, CA 95616 (United States)
2007-11-15
We present an alternative way to derive the conformally flat stationary cyclic non-circular spacetimes. We show that there is no room for stationary axisymmetric non-circular axisymmetric spacetimes. We reproduce the well know results for this sort of spacetimes recently reported in [1].
Range, Shannon K'doah; Mullins, Jennifer
This teaching guide introduces a relativity gyroscope experiment aiming to test two unverified predictions of Albert Einstein's general theory of relativity. An introduction to the theory includes the following sections: (1) "Spacetime, Curved Spacetime, and Frame-Dragging"; (2) "'Seeing' Spacetime with Gyroscopes"; (3)…
Directory of Open Access Journals (Sweden)
Farhad Ali
2016-08-01
Full Text Available In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes along with the Noether symmetries of the corresponding Lagrangians and conservation laws.
ABC of multi-fractal spacetimes and fractional sea turtles
Calcagni, Gianluca
2016-04-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime
Kuwata, Maiko; Kenmoku, Masakatsu; Shigemoto, Kazuyasu
2008-01-01
We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues for normal modes are characterized by the principal quantum number $(0
On the enigmatic – A true constant of spacetime
Indian Academy of Sciences (India)
The situation remained ambiguous and it was left to one's taste to include it or not until the quantum vacuum fluctuations were considered which relative to flat spacetime have the same form for the stress tensor as . That is how it gets slated against the Planck length and to the annoying mismatch of 120 orders of magnitude.
Charged anisotropic star on paraboloidal space-time
Indian Academy of Sciences (India)
The charged anisotropic star on paraboloidal space-time is reported by choosing a particular form of radial pressure and electric field intensity. The non-singular solution of Einstein–Maxwell system of equation has been derived and it is shown that the model satisfies all the physical plausibility conditions. It is observed that ...
Symmetries of Particle Physics: Space-time and Local Gauge ...
Indian Academy of Sciences (India)
GENERAL I ARTICLE. Symmetries of Particle Physics: Space-time and. Local Gauge Symmetries. Sourendu Gupta works on the physics of matter under extreme conditions. He works at the Tata. Institute of Fundamental. Research, Mumbai. Figure 1. Experiment and theory feed on each other. Sourendu Gupta. Introduction.
Space-time design of the public city
Thomaier, Susanne; Könecke, Benjamin; Zedda, Roberto; Stabilini, Stefano
2013-01-01
Time has become an increasingly important topic in urban studies and urban planning. The spatial-temporal interplay is not only of relevance for the theory of urban development and urban politics, but also for urban planning and governance. The space-time approach focuses on the human being with its various habits and routines in the city. Understanding and taking those habits into account in urban planning and public policies offers a new way to improve the quality of life in our cities. Adapting the supply and accessibility of public spaces and services to the inhabitants’ space-time needs calls for an integrated approach to the physical design of urban space and to the organization of cities. In the last two decades the body of practical and theoretical work on urban space-time topics has grown substantially. The book offers a state of the art overview of the theoretical reasoning, the development of new analytical tools, and practical experience of the space-time design of public cities in major Europea...
On synchronization of clocks in general space-times
Directory of Open Access Journals (Sweden)
M. R. H Khajehpour
2005-09-01
Full Text Available Einstein and transport synchronizations of infinitesimally spaced and distant clocks are considered in a general Riemannian space-time. It is shown that infinitesimally spaced clocks can always be synchronized. In general one can not find observers for whom distant clock are Einstein synchronized but transport synchronized observers do always exit. Whenever both procedures are possible, they are equivalent.
IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
Canepa, Giovanni; Dappiaggi, Claudio; Khavkine, Igor
2018-02-01
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g 0 consists of a set of tensorial equations T[g] = 0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is locally isometric to the reference spacetime metric g 0. The same notion can be extended to also include scalar or tensor fields, where the equations T[g, φ]=0 are allowed to also depend on the extra fields ϕ. We give the first IDEAL characterization of cosmological FLRW spacetimes, with and without a dynamical scalar (inflaton) field. We restrict our attention to what we call regular geometries, which uniformly satisfy certain identities or inequalities. They roughly split into the following natural special cases: constant curvature spacetime, Einstein static universe, and flat or curved spatial slices. We also briefly comment on how the solution of this problem has implications, in general relativity and inflation theory, for the construction of local gauge invariant observables for linear cosmological perturbations and for stability analysis.
Symmetries of Particle Physics: Space-time and Local Gauge ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Symmetries of Particle Physics: Space-time and Local Gauge Symmetries. Sourendu Gupta. General Article Volume 6 Issue 2 February 2001 pp 29-38. Fulltext. Click here to view fulltext PDF. Permanent link:
Noncommutative geometry, symmetries and quantum structure of space-time
Energy Technology Data Exchange (ETDEWEB)
Govindarajan, T R [Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113 (India); Gupta, Kumar S [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Harikumar, E [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Meljanac, S, E-mail: trg@imsc.res.in, E-mail: kumars.gupta@saha.ac.in, E-mail: harisp@uohyd.ernet.in, E-mail: meljanac@irb.hr [Rudjer Botkovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
2011-07-08
We discuss how space-time noncommutativity affects the symmetry groups and particle statistics. Assuming that statistics is superselected under a symmetry transformation, we argue that the corresponding flip operator must be twisted. It is argued that the twisted statistics naturally leads to a deformed oscillator algebra for scalar fields in such a background.
Paraboloidal Space-Times and Relativistic Models of Strange Stars
Jotania, Kanti; Tikekar, Ramesh
The objective of this paper is to find out the suitability of an ansatz similar to that suggested by Vaidya-Tikekar, but prescribing paraboloidal geometry for the 3-space of the interior space-time of a relativistic spherical star in describing a family of physically viable models of superdense stars like Her X-1, SAX, and X-ray brust.
Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes
Caldeira Costa, R.N.
2012-01-01
In this work we elaborate on an extension of the AdS/CFT framework to a sub-class of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
Fajman, David
2017-06-01
We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
On Spacetimes with Given Kinematical Invariants: Construction and Examples
Plaue, M.; Scherfner, M.; Sousa Jr, L. A. M. de
2008-01-01
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper time description. As an application of our method we present two generalizations of the G\\"odel spacetime that follow naturally from our approach.
Baseline-dependent neutrino oscillations in asymmetrically-warped spacetimes
Hollenberg, S; Pas, H; Weiler, J T
2010-01-01
We study the possibility to explain the LSND anomaly by means of resonant active-sterile neutrino oscillations in an asymmetrically-warped spacetime. In such extra-dimensional scenarios sterile neutrinos take shortcuts through the extra dimension, which results in new types of resonances in the oscillation probability.
Linear bosonic and fermionic quantum gauge theories on curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik
2012-05-15
We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.
Asymptotic symmetries in de Sitter and inflationary spacetimes
DEFF Research Database (Denmark)
Ferreira, Ricardo J. Z.; Sandora, McCullen; Sloth, Martin S.
2017-01-01
Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state...
New spacetime superalgebras and their Kač-Moody extension
Bergshoeff, Eric; Sezgin, Ergin
1989-01-01
We present new spacetime algebras whose existence is due to special I'-matrix identities which are also necessary for the existence of super p-branes. They contain a pth-rank antisymmetric tensor, and a (p-1)-rank antisymmetric tensor-spinor generator. Furthermore the translations do not commute
Spacetime scale-invariance and the super p-brane
Bergshoeff, E.; London, L.A.J.; Townsend, P.K.
1992-01-01
We generalize to p-dimensional extended objects and type II superstrings a recently proposed Green-Schwarz type I superstring action in which the tension T emerges as an integration constant of the equations of motion. The action is spacetime scale-invariant but its equations of motion are
Zen and the Art of Space-Time Manufacturing
Directory of Open Access Journals (Sweden)
Bertolami Orfeu
2013-09-01
Full Text Available We present a general discussion about the so-called emergent properties and discuss whether space-time and gravity can be regarded as emergent features of underlying more fundamental structures. Finally, we discuss some ideas about the multiverse, and speculate on how our universe might arise from the multiverse.
Krenn, Mario; Hochrainer, Armin; Lahiri, Mayukh; Zeilinger, Anton
2017-02-01
Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces—starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.
Noncommutative spherically symmetric spacetimes at semiclassical order
Fritz, Christopher; Majid, Shahn
2017-07-01
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\
The effect of varying path properties in path steering tasks
L. Liu (Lei); R. van Liere (Robert)
2010-01-01
textabstractPath steering is a primitive 3D interaction task that requires the user to navigate through a path of a given length and width. In a previous paper, we have conducted controlled experiments in which users operated a pen input device to steer a cursor through a 3D path subject to
Joint space-time geostatistical model for air quality surveillance
Russo, A.; Soares, A.; Pereira, M. J.
2009-04-01
Air pollution and peoples' generalized concern about air quality are, nowadays, considered to be a global problem. Although the introduction of rigid air pollution regulations has reduced pollution from industry and power stations, the growing number of cars on the road poses a new pollution problem. Considering the characteristics of the atmospheric circulation and also the residence times of certain pollutants in the atmosphere, a generalized and growing interest on air quality issues led to research intensification and publication of several articles with quite different levels of scientific depth. As most natural phenomena, air quality can be seen as a space-time process, where space-time relationships have usually quite different characteristics and levels of uncertainty. As a result, the simultaneous integration of space and time is not an easy task to perform. This problem is overcome by a variety of methodologies. The use of stochastic models and neural networks to characterize space-time dispersion of air quality is becoming a common practice. The main objective of this work is to produce an air quality model which allows forecasting critical concentration episodes of a certain pollutant by means of a hybrid approach, based on the combined use of neural network models and stochastic simulations. A stochastic simulation of the spatial component with a space-time trend model is proposed to characterize critical situations, taking into account data from the past and a space-time trend from the recent past. To identify near future critical episodes, predicted values from neural networks are used at each monitoring station. In this paper, we describe the design of a hybrid forecasting tool for ambient NO2 concentrations in Lisbon, Portugal.
PATHS groundwater hydrologic model
Energy Technology Data Exchange (ETDEWEB)
Nelson, R.W.; Schur, J.A.
1980-04-01
A preliminary evaluation capability for two-dimensional groundwater pollution problems was developed as part of the Transport Modeling Task for the Waste Isolation Safety Assessment Program (WISAP). Our approach was to use the data limitations as a guide in setting the level of modeling detail. PATHS Groundwater Hydrologic Model is the first level (simplest) idealized hybrid analytical/numerical model for two-dimensional, saturated groundwater flow and single component transport; homogeneous geology. This document consists of the description of the PATHS groundwater hydrologic model. The preliminary evaluation capability prepared for WISAP, including the enhancements that were made because of the authors' experience using the earlier capability is described. Appendixes A through D supplement the report as follows: complete derivations of the background equations are provided in Appendix A. Appendix B is a comprehensive set of instructions for users of PATHS. It is written for users who have little or no experience with computers. Appendix C is for the programmer. It contains information on how input parameters are passed between programs in the system. It also contains program listings and test case listing. Appendix D is a definition of terms.
Loup, F
2004-01-01
We present the argument that the geometrical beauty of the ADDK Manyfold Universe is enough to exclude the "exotic" forms of "Dark Matter" predicted by some physical theories but never observed experimentally.We argue that if "Dark Matter" can raise by 7 times the spinning rotation of spiral arms of Galaxies around their Nuclei then "Dark Matter" should have been detected at least in our Galaxy by a very precise instrument as the NASA Chandra Satellite.Since nothing has been found and something so massive to raise 7 times the spinning speed of spiral arms cannot evade detection by highly accurate instruments we conclude that the "exotic forms of Dark Matter" which means to say WIMPS,Axions,Neutralinos,Heavy or Strange Neutrinos or other exotic forms of "Baryonic Dark Matter" dont have physical existance and we propose the natural and geometrical beauty of the Manyfold Universe provides the physical and correct explanation for "Dark Matter". We explore the natural beauty and the consequences of the ADDK Model.
Barack, Leor; Sago, Norichika
2010-01-01
Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the $O(m)$ conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass $m$ moving around a Schwarzschild black hole of mass ${\\mathsf M}\\gg m$. Specifically, we study the gauge-invariant function $\\rho(x)$, where $\\rho$ is defined as the $O(m)$ part of the dimensionless ratio $(\\hat\\Omega_r/\\hat\\Omega_{\\varphi})^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $x=[Gc^{-3}({\\mathsf M}+m)\\hat\\Omega_{\\varphi}]^{2/3}$ is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function $\\rho(x)$ in the interval $0
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer...... trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...
Formal Verification at System Level
Mazzini, S.; Puri, S.; Mari, F.; Melatti, I.; Tronci, E.
2009-05-01
System Level Analysis calls for a language comprehensible to experts with different background and yet precise enough to support meaningful analyses. SysML is emerging as an effective balance between such conflicting goals. In this paper we outline some the results obtained as for SysML based system level functional formal verification by an ESA/ESTEC study, with a collaboration among INTECS and La Sapienza University of Roma. The study focuses on SysML based system level functional requirements techniques.
Leus, G.; Petré, F.; Moonen, M.
2004-01-01
In the downlink of DS-CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multiuser interference (MUI). Space-time chip equalization is an efficient tool to restore the orthogonality of the user signals and suppress the MUI. Furthermore, multiple-input
Understanding Informality and Formality in Learning.
Colley, Helen; Hodkinson, Phil; Malcolm, Janice
2003-01-01
Reviews definitions of and debates over distinctions among formal, informal, and nonformal learning. Outlines questions about four aspects of formality/informality with which to analyze learning situations: process, location/setting, purposes, and content. (SK)
Formal Inspection: A Tool for TQM
Welz, L.; Kelly, J.
1995-01-01
The goal of the Formal Inspection Program at the Jet Propulsion Laboratory (JPL) is to support projects wishing to use Formal Inspections to improve the quality of software and system level engineering products.
Modeling of tool path for the CNC sheet cutting machines
Petunin, Aleksandr A.
2015-11-01
In the paper the problem of tool path optimization for CNC (Computer Numerical Control) cutting machines is considered. The classification of the cutting techniques is offered. We also propose a new classification of toll path problems. The tasks of cost minimization and time minimization for standard cutting technique (Continuous Cutting Problem, CCP) and for one of non-standard cutting techniques (Segment Continuous Cutting Problem, SCCP) are formalized. We show that the optimization tasks can be interpreted as discrete optimization problem (generalized travel salesman problem with additional constraints, GTSP). Formalization of some constraints for these tasks is described. For the solution GTSP we offer to use mathematical model of Prof. Chentsov based on concept of a megalopolis and dynamic programming.
Shortest Paths and Vehicle Routing
DEFF Research Database (Denmark)
Petersen, Bjørn
This thesis presents how to parallelize a shortest path labeling algorithm. It is shown how to handle Chvátal-Gomory rank-1 cuts in a column generation context. A Branch-and-Cut algorithm is given for the Elementary Shortest Paths Problem with Capacity Constraint. A reformulation of the Vehicle R...... Routing Problem based on partial paths is presented. Finally, a practical application of finding shortest paths in the telecommunication industry is shown....
Formal and nonformal SETI education programs
Bhathal, Ragbir
2001-08-01
Frank Drake's experiment on the search for extraterrestrial intelligence in 1960 not only generated a new field of observational astronomy but also produced spin-offs in the fields of education and the social science. SETI education programs in formal and non-formal educational institutions provide a powerful tool for educating the public and students about humanity's most profound question: are we alone in the universe? This paper discusses SETI educational programs in both formal and non-formal settings.
Spin response formalism in circular accelerators
Energy Technology Data Exchange (ETDEWEB)
Ptitsyn, V.I. [Brookhaven National Laboratory, Upton, NY 11973 (United States)], E-mail: vadimp@bnl.gov; Shatunov, Yu.M. [Budker Institute of Nuclear Physics, Novosibirsk, 630090 (Russian Federation); Mane, S.R. [Convergent Computing Inc., P. O. Box 561, Shoreham, NY 11786 (United States)], E-mail: srmane@optonline.net
2009-09-11
We present the principal features of the so-called 'spin response formalism', which is linear response theory applied to the spin dynamics in circular accelerators. The formalism is useful for calculating the resonance strengths of several classes of first-order spin resonances in rings, including those for spin flippers. We describe some of the successful applications of the formalism to various storage rings. We include a brief comparison with other formalisms and indicate topics for future work.
Formal Proofs for Nonlinear Optimization
Directory of Open Access Journals (Sweden)
Victor Magron
2015-01-01
Full Text Available We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K.This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent.The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.
Formal Verification of Circuits and Systems
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
methods in the verification task. Today formal verification is finding increasing acceptance ... approaches that are major research issues in formal verification research today. There are four articles in this issue, which show up the different flavours in the approach to formal methods in verification. The first paper by Supratik ...
Comment: universality of formal operational thought.
Mwamwenda, T S
1992-08-01
Piaget suggested four stages of development (sensorimotor, preoperational, concrete and formal operations) may be universally observed, but only the first three have been confirmed because few people attain formal operations. Both Westerners and Africans may attain formal operations, however, given the way they reason and interact in their milieu.
Formal Testing of Correspondence Carrying Software
Bujorianu, M.C.; Bujorianu, L.M.; Maharaj, S.
2008-01-01
Nowadays formal software development is characterised by use of multitude formal specification languages. Test case generation from formal specifications depends in general on a specific language, and, moreover, there are competing methods for each language. There is a need for a generic approach to
Formal analysis of design process dynamics
Bosse, T.; Jonker, C.M.; Treur, J.
2010-01-01
This paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design
Ego Identity, Egocentrism, and Formal Operations.
Protinsky, Howard; Wilkerson, Jackie
1986-01-01
Examined the relationship between ego identity, formal operations, and egocentrism in adolescents. Results indicated significant positive correlations between ego identity and formal operations and between ego identity and grade in school. Grade in school explained 21 percent of the variance while formal operational thinking, egocentrism, and sex…
Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
Hartung, Tobias
2017-12-01
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined. In particular, it is consistent with respect to lattice formulations and Wick rotations, i.e., it can be used in Euclidean and Minkowski space-time. The path integral regularization is introduced through the generalized Kontsevich-Vishik trace, that is, the extension of the classical trace to Fourier integral operators. Physically, we are replacing the time-evolution semi-group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of C . The regularized path integral is, thus, defined through analytic continuation. This regularization can be performed by means of stationary phase approximation or computed analytically depending only on the Hamiltonian and the observable (i.e., known a priori). In either case, the computational effort to evaluate path integrals or expectations of observables reduces to the evaluation of integrals over spheres. Furthermore, computations can be performed directly in the continuum and applications (analytic computations and their implementations) to a number of models including the non-trivial cases of the massive Schwinger model and a φ4 theory.
Path integrals and Voronin's theorem on the universality of the Riemann zeta function
Bitar, Khalil M.; Khuri, N. N.; Ren, H. C.
1991-10-01
We present a new approach to the path integral in latticized quantum theories. Our method is based on Voronin's theorems on the universality of the Riemann zeta function. We obtain a formula for the partition function as a discrete sum over "paths" with each path labeled by an integer and given by a zeta function evaluated at a fixed set of points in the critical strip. These points are the image of the space-time lattice resulting from a simple linear mapping. A new measure appears in our sum, and its properties are extensively discussed and a method to calculate it is given. We carried out extensive checks of the method for Euclidean quantum mechanics, and compared the results with those obtained from well-established methods as well as exact results. The comparison confirms the validity of the zeta-function method and our calculation of the measure.
Integrating path dependency and path creation in a general understanding of path constitution
Meyer, Uli; Schubert, Cornelius
2007-01-01
Path dependency as it is described by Arthur and David portrays technological developments as historically embedded, emergent processes. In contrast, Garud and Karnøe's notion of path creation emphasises the role of strategic change and deliberate action for the development of new technologies. In this article, we integrate both concepts into a general understanding of path processes which accounts for emergent as well as deliberate modes of path constitution. In addition, we distinguish betw...
Two Generations of Path Dependence
DEFF Research Database (Denmark)
Madsen, Mogens Ove
Even if there is no fully articulated and generally accepted theory of Path Dependence it has eagerly been taken up across a wide range of social sciences - primarily coming from economics. Path Dependence is most of all a metaphor that offers reason to believe, that some political, social...... or economic processes have multiple possible paths of outcomes, rather than a unique path of equilibria. The selection among outcomes may depend on contingent choices or events - outcomes of path-dependent processes require a very relevant study - a perception of history....
Directory of Open Access Journals (Sweden)
David Middleton
2005-01-01
Full Text Available The hillside’s tidal waves of yellow-green Break downward into full-grown stalks of wheat In which a peasant, shouldering his hoe Passes along a snaking narrow path -- A teeming place through which his hard thighs press And where his head just barely stays above The swaying grain, drunken in abundance, Farm buildings almost floating on the swells Beyond which sea gulls gliding white in air Fly down on out of sight to salty fields, Taking the channel fish off Normandy, A surfeit fit for Eden i...
Directory of Open Access Journals (Sweden)
Jamie Waters
2014-09-01
Full Text Available This project uses Newton’s Second Law of Motion, Euler’s method, basic physics, and basic calculus to model the flight path of a rocket. From this, one can find the height and velocity at any point from launch to the maximum altitude, or apogee. This can then be compared to the actual values to see if the method of estimation is a plausible. The rocket used for this project is modeled after Bullistic-1 which was launched by the Society of Aeronautics and Rocketry at the University of South Florida.
Mehhtz, Peter
2005-01-01
JPF is an explicit state software model checker for Java bytecode. Today, JPF is a swiss army knife for all sort of runtime based verification purposes. This basically means JPF is a Java virtual machine that executes your program not just once (like a normal VM), but theoretically in all possible ways, checking for property violations like deadlocks or unhandled exceptions along all potential execution paths. If it finds an error, JPF reports the whole execution that leads to it. Unlike a normal debugger, JPF keeps track of every step how it got to the defect.
Formal Methods at Intel - An Overview
Harrison, John
2010-01-01
Since the 1990s, Intel has invested heavily in formal methods, which are now deployed in several domains: hardware, software, firmware, protocols etc. Many different formal methods tools and techniques are in active use, including symbolic trajectory evaluation, temporal logic model checking, SMT-style combined decision procedures, and interactive higher-order logic theorem proving. I will try to give a broad overview of some of the formal methods activities taking place at Intel, and describe the challenges of extending formal verification to new areas and of effectively using multiple formal techniques in combination
The pathology of command and control: a formal synthesis
Directory of Open Access Journals (Sweden)
Michael Cox
2016-09-01
Full Text Available One of the most important theories in the study of environmental governance and policy is the pathology of command and control, which describes the negative consequences of top-down, technocratic governance of social and ecological systems. However, to date, this theory has been expressed somewhat inconsistently and informally in the literature, even by the seminal works that have established its importance and popularized it. This presents a problem for the sustainability science community if it cannot be sure of the precise details of one of its most important theories. Without such precision, applications and tests of various elements of the theory cannot be conducted reliably to advance the knowledge of environmental governance. I address this problem by synthesizing several seminal works to formalize this theory. The formalization involves the identification of the individual elements of the theory and a diagrammatic description of their relationships with each other that unfold in a series of semi-independent causal paths. Ideally, with such a formalization, scholars can use this theory more reliably and more meaningfully in their future work. I conclude by discussing the implications this theory has for the governance of natural resources.
Directory of Open Access Journals (Sweden)
Jisheng Zhang
2015-06-01
Full Text Available It is essential for transportation management centers to equip and manage a network of fixed and mobile sensors in order to quickly detect traffic incidents and further monitor the related impact areas, especially for high-impact accidents with dramatic traffic congestion propagation. As emerging small Unmanned Aerial Vehicles (UAVs start to have a more flexible regulation environment, it is critically important to fully explore the potential for of using UAVs for monitoring recurring and non-recurring traffic conditions and special events on transportation networks. This paper presents a space-time network- based modeling framework for integrated fixed and mobile sensor networks, in order to provide a rapid and systematic road traffic monitoring mechanism. By constructing a discretized space-time network to characterize not only the speed for UAVs but also the time-sensitive impact areas of traffic congestion, we formulate the problem as a linear integer programming model to minimize the detection delay cost and operational cost, subject to feasible flying route constraints. A Lagrangian relaxation solution framework is developed to decompose the original complex problem into a series of computationally efficient time-dependent and least cost path finding sub-problems. Several examples are used to demonstrate the results of proposed models in UAVs’ route planning for small and medium-scale networks.
Formal modeling of virtual machines
Cremers, A. B.; Hibbard, T. N.
1978-01-01
Systematic software design can be based on the development of a 'hierarchy of virtual machines', each representing a 'level of abstraction' of the design process. The reported investigation presents the concept of 'data space' as a formal model for virtual machines. The presented model of a data space combines the notions of data type and mathematical machine to express the close interaction between data and control structures which takes place in a virtual machine. One of the main objectives of the investigation is to show that control-independent data type implementation is only of limited usefulness as an isolated tool of program development, and that the representation of data is generally dictated by the control context of a virtual machine. As a second objective, a better understanding is to be developed of virtual machine state structures than was heretofore provided by the view of the state space as a Cartesian product.
Sugiyama, Naonori S; Futamase, Toshifumi
2013-01-01
Precise understanding of non-linear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale structure of the universe. The "{\\delta}N formalism" is a popular and powerful technique for computing non-linear evolution of cosmological perturbations on large scales. In particular, it enables us to compute the curvature perturbation, {\\zeta}, on large scales without actually solving perturbed field equations. However, people often wonder why this is the case. In order for this approach to be valid, the perturbed Hamiltonian constraint and matter-field equations on large scales must, with a suitable choice of coordinates, take on the same forms as the corresponding unperturbed equations. We find that this is possible when (1) the unperturbed metric is given by a homogeneous and isotropic Friedmann-Lema\\^itre-Robertson-Walker metric; and (2) on large scales and with a suita...
Formalization in Component Based Development
DEFF Research Database (Denmark)
Holmegaard, Jens Peter; Knudsen, John; Makowski, Piotr
2006-01-01
We present a unifying conceptual framework for components, component interfaces, contracts and composition of components by focusing on the collection of properties or qualities that they must share. A specific property, such as signature, functionality behaviour or timing is an aspect. Each aspect...... may be specified in a formal language convenient for its purpose and, in principle, unrelated to languages for other aspects. Each aspect forms its own semantic domain, although a semantic domain may be parameterized by values derived from other aspects. The proposed conceptual framework is introduced...... by small examples, using UML as concrete syntax for various aspects, and is illustrated by one larger case study based on an industrial prototype of a complex component based system....
Formal analysis of electromagnetic optics
Khan-Afshar, Sanaz; Hasan, Osman; Tahar, Sofiène
2014-09-01
Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.
A Formal Calculus for Categories
DEFF Research Database (Denmark)
Cáccamo, Mario José
This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...
Matrix formalism of synchrobetatron coupling
Directory of Open Access Journals (Sweden)
Xiaobiao Huang
2007-01-01
Full Text Available In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.
Formal Aspects of Grid Brokering
Directory of Open Access Journals (Sweden)
Attila Kertész
2009-12-01
Full Text Available Coordination in distributed environments, like Grids, involves selecting the most appropriate services, resources or compositions to carry out the planned activities. Such functionalities appear at various levels of the infrastructure and in various means forming a blurry domain, where it is hard to see how the participating components are related and what their relevant properties are. In this paper we focus on a subset of these problems: resource brokering in Grid middleware. This paper aims at establishing a semantical model for brokering and related activities by defining brokering agents at three levels of the Grid middleware for resource, host and broker selection. The main contribution of this paper is the definition and decomposition of different brokering components in Grids by providing a formal model using Abstract State Machines.
Internet's critical path horizon
Valverde, S.; Solé, R. V.
2004-03-01
Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be minimized by choosing appropriate routing strategies. But what are the requirements of routing depth in order to optimize the traffic flow? In this paper we analyse the behavior of Internet traffic with a topologically realistic spatial structure as described in a previous study [S.-H. Yook et al., Proc. Natl Acad. Sci. USA 99, 13382 (2002)]. The model involves self-regulation of packet generation and different levels of routing depth. It is shown that it reproduces the relevant key, statistical features of Internet's traffic. Moreover, we also report the existence of a critical path horizon defining a transition from low-efficient traffic to highly efficient flow. This transition is actually a direct consequence of the web's small world architecture exploited by the routing algorithm. Once routing tables reach the network diameter, the traffic experiences a sudden transition from a low-efficient to a highly-efficient behavior. It is conjectured that routing policies might have spontaneously reached such a compromise in a distributed manner. Internet would thus be operating close to such critical path horizon.
Emergence of Space-Time from Topologically Homogeneous Causal Networks
D'Ariano, Giacomo Mauro
2011-01-01
In this paper we study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity---including space-time---be defined through precise measurement procedures. Topological homogeneity is a requirement for having space-time metric emergent from the pure topology of causal connections, whereas physically corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimension. Coordinate systems are established via an Einsteinian protocol, and lead to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can also be regarded as the synchronization with a global clock of the calls to independent subroutines (corresponding to the causally independent events) in a parallel distributed computation, ...
Hamiltonian Dynamics of Doubly-Foliable Space-Times
Directory of Open Access Journals (Sweden)
Cecília Gergely
2018-01-01
Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.
Relativistic tidal effects in non standard Kerr space-time
Maselli, Andrea; Laguna, Pablo
2016-01-01
Astrophysical phenomena involving massive black holes (BHs) in close binaries are expected to leave detectable signatures in the electromagnetic and gravitational-wave spectrum. Such imprints may provide precious information to probe the space-time around rotating BHs, and to reveal new insights on the nature of gravity in the strong-field regime. To support this observational window it is crucial to develop suitable tests to verify the predictions of General Relativity (GR). In this framework, the metric recently proposed by Johannsen and Psaltis parametrises strong field deviations from a Kerr space-time in a theory-independent way. In the following, we make use of this approach to describe the tidal field produced by spinning BHs. We compute the gravito-magnetic and gravito-electric tidal tensors for particles moving on equatorial circular geodesics, comparing our results with those obtained in the standard GR scenario. Our calculations show significant differences even for distances far form the last stab...
Observables and dispersion relations in κ-Minkowski spacetime
Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna
2017-10-01
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.
Curvatronics with bilayer graphene in an effective $4D$ spacetime
Cariglia, M; Perali, A
2016-01-01
We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant L\\'evy-Leblond spin $\\frac{1}{2}$ particles near the Dirac points. We find that changing the intrinsic curvature of the bilayer sheet induces a change in the energy level of the electronic bands, switching from a conducting regime for negative curvature to an insulating one when curvature is positive. In particular, curving graphene bilayers allows opening or closing the energy gap between conduction and valence bands, a key effect for electronic devices. Thus using curvature as a tunable parameter opens the way for t...
Emergent Space-Time via a Geometric Renormalization Method
Rastgoo, Saeed
2016-01-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...
Unsupervised Action Classification Using Space-Time Link Analysis
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Feris Rogerio
2010-01-01
Full Text Available We address the problem of unsupervised discovery of action classes in video data. Different from all existing methods thus far proposed for this task, we present a space-time link analysis approach which consistently matches or exceeds the performance of traditional unsupervised action categorization methods in various datasets. Our method is inspired by the recent success of link analysis techniques in the image domain. By applying these techniques in the space-time domain, we are able to naturally take into account the spatiotemporal relationships between the video features, while leveraging the power of graph matching for action classification. We present a comprehensive set of experiments demonstrating that our approach is capable of handling cluttered backgrounds, activities with subtle movements, and video data from moving cameras. State-of-the-art results are reported on standard datasets. We also demonstrate our method in a compelling surveillance application with the goal of avoiding fraud in retail stores.
Unsupervised action classification using space-time link analysis
DEFF Research Database (Denmark)
Liu, Haowei; Feris, Rogerio; Krüger, Volker
2010-01-01
In this paper we address the problem of unsupervised discovery of action classes in video data. Different from all existing methods thus far proposed for this task, we present a space-time link analysis approach which matches the performance of traditional unsupervised action categorization methods...... in a standard dataset. Our method is inspired by the recent success of link analysis techniques in the image domain. By applying these techniques in the space-time domain, we are able to naturally take into account the spatio-temporal relationships between the video features, while leveraging the power of graph...... matching for action classification. We present an experiment to demonstrate that our approach is capable of handling cluttered backgrounds, activities with subtle movements, and video data from moving cameras....
Space-Time Foam may Violate the Principle of Equivalence
Ellis, Jonathan Richard; Nanopoulos, Dimitri V; Sakharov, Alexander S; Ellis, John
2004-01-01
The interactions of different particle species with the foamy space-time fluctuations expected in quantum gravity theories may not be universal, in which case different types of energetic particles may violate Lorentz invariance by varying amounts, violating the equivalence principle. We illustrate this possibility in two different models of space-time foam based on D-particle fluctuations in either flat Minkowski space or a stack of intersecting D-branes. Both models suggest that Lorentz invariance could be violated for energetic particles that do not carry conserved charges, such as photons, whereas charged particles such electrons would propagate in a Lorentz-inavariant way. The D-brane model further suggests that gluon propagation might violate Lorentz invariance, but not neutrinos. We argue that these conclusions hold at both the tree (lowest-genus) and loop (higher-genus) levels, and discuss their implications for the phenomenology of quantum gravity.
Spacetime foam induced collective bundling of intense fields
Oniga, Teodora
2016-01-01
The influence of spacetime foam on a broad class of bosonic fields with arbitrary numbers of particles in the low energy regime is investigated. Based on recently formulated general description of open quantum gravitational systems, we analyse the propagation of scalar, electromagnetic, and gravitational waves on both long and short time scales with respect to their mean frequencies. For the long time propagation, the Markov approximation is employed that neglects the effects of initial conditions of these waves. In this case, despite intuitively expected decoherence and dissipation from the noisy spacetime, we show that such phenomena turn out to be completely suppressed for scalar bosons, photons, and gravitons, which are coupled to gravity but otherwise free. The short time effects are then recovered through the transient non-Markovian evolution. Focusing on scalar bosons in initially incoherent states, we find that the resulting quantum dissipation depend strongly on the distribution of the particle momen...
Interference Cancellation Using Space-Time Processing and Precoding Design
Li, Feng
2013-01-01
Interference Cancellation Using Space-Time Processing and Precoding Design introduces original design methods to achieve interference cancellation, low-complexity decoding and full diversity for a series of multi-user systems. In multi-user environments, co-channel interference will diminish the performance of wireless communications systems. In this book, we investigate how to design robust space-time codes and pre-coders to suppress the co-channel interference when multiple antennas are available. This book offers a valuable reference work for graduate students, academic researchers and engineers who are interested in interference cancellation in wireless communications. Rigorous performance analysis and various simulation illustrations are included for each design method. Dr. Feng Li is a scientific researcher at Cornell University.
A nonlinear dynamics for the scalar field in Randers spacetime
Energy Technology Data Exchange (ETDEWEB)
Silva, J.E.G. [Universidade Federal do Cariri (UFCA), Instituto de formação de professores, Rua Olegário Emídio de Araújo, Brejo Santo, CE, 63.260.000 (Brazil); Maluf, R.V. [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760 (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760 (Brazil)
2017-03-10
We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.
Equivalence Principles, Spacetime Structure and the Cosmic Connection
Ni, Wei-Tou
2015-01-01
After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the equivalence principle for the photon (no birefringence, no polarization rotation and no amplification/attenuation in propagation) in the framework of linear electrodynamics using cosmic connections/observations as empirical support. The cosmic nonbirefringent propagation of photons independent of energy and polarization verifies the Galileo Equivalence Principle [Universality of Propagation] for photons/electromagnetic wave packets in spacetime. This nonbirefringence constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Thus comes the metric with axion and dilation. Constraints on axion and dilaton from astrophysical/cosmic propagation are reviewed. E\\"otv\\"os-type experiments, Hughes-Drever-type experiments, redshift experiments ...
Intertial Frame Dragging in an Acoustic Analogue spacetime
Chakraborty, Chandrachur; Majumdar, Parthasarathi
2015-01-01
We report an incipient exploration of the Lense-Thirring precession effect in a rotating {\\it acoustic analogue black hole} spacetime. An exact formula is deduced for the precession frequency of a gyroscope due to inertial frame dragging, close to the ergosphere of a `Draining Bathtub' acoustic spacetime which has been studied extensively for acoustic Hawking radiation of phonons and also for `superresonance'. The formula is verified by embedding the two dimensional spatial (acoustic) geometry into a three dimensional one where the similarity with standard Lense-Thirring precession results within a strong gravity framework is well known. Prospects of experimental detection of this new `fixed-metric' effect in acoustic geometries, are briefly discussed.
Convexity and the Euclidean Metric of Space-Time
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Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
Asymptotically Lifshitz spacetimes with universal horizons in (1 +2 ) dimensions
Basu, Sayandeb; Bhattacharyya, Jishnu; Mattingly, David; Roberson, Matthew
2016-03-01
Hořava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two-derivative Hořava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z =2 in 1 +2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti-de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.
Pre-Big Bang, space-time structure, asymptotic Universe
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Gonzalez-Mestres Luis
2014-04-01
Full Text Available Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95, while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2 spinor and the Lundmark-Lemaître-Hubble (LLH expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of
Jarzynski equality in the context of maximum path entropy
González, Diego; Davis, Sergio
2017-06-01
In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy - also known as Maximum Caliber principle -, this work proposes an alternative derivation of the well-known Jarzynski equality, a nonequilibrium identity of great importance today due to its applications to irreversible processes: biological systems (protein folding), mechanical systems, among others. This equality relates the free energy differences between two equilibrium thermodynamic states with the work performed when going between those states, through an average over a path ensemble. In this work the analysis of Jarzynski's equality will be performed using the formalism of inference over path space. This derivation highlights the wide generality of Jarzynski's original result, which could even be used in non-thermodynamical settings such as social systems, financial and ecological systems.
On fractal space-time and fractional calculus
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Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
Space-time Vector Supersymmetry and Massive Spinning Particle
Casalbuoni, Roberto; Kamimura, Kiyoshi; Longhi, Giorgio
2008-01-01
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\\'e group. For particular values of the parameters appearing in the lagrangian the model has a gauge world-line supersymmetry.{As a consequence of this local symmetry there are BPS solutions in the model preserving 1/5 of the supersymmetries.} A supersymmetric invariant quantization produces two decoupled 4d Dirac equations.
Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime
Sharif, M
2010-01-01
We study the final outcome of gravitational collapse resulting from the plane symmetric charged Vaidya spacetime. Using the field equations, we show that the weak energy condition is always satisfied by collapsing fluid. It is found that the singularity formed is naked. The strength of singularity is also investigated by using Nolan's method. This turns out to be a strong curvature singularity in Tipler's sense and hence provides a counter example to the cosmic censorship hypothesis.
Thermodynamics in Higher Dimensional Vaidya Space-Time
Debnath, Ujjal
2012-01-01
In this work, we have considered the Vaidya spacetime in null radiating fluid with perfect fluid in higher dimension and have found the solution for barotropic fluid. We have shown that the Einstein's field equations can be obtained from Unified first law i.e., field equations and unified first law are equivalent. The first law of thermodynamics has also been constructed by Unified first law. From this, the variation of entropy function has been derived on the horizon. The variation of entrop...
Supersymmetric Rotating Black Hole in a Compactified Spacetime
Maeda, Kei-ichi; Ohta, Nobuyoshi; Tanabe, Makoto
2006-01-01
We construct a supersymmetric rotating black hole with asymptotically flat four-dimensional spacetime times a circle, by superposing an infinite number of BMPV black hole solutions at the same distance in one direction. The near horizon structure is the same as that of the five-dimensional BMPV black hole. The rotation of this black hole can exceed the Kerr bound in general relativity ($q\\equiv a/G_4 M=1$), if the size is small.
Mass Formulae for Broken Supersymmetry in Curved Space-Time
Ferrara, Sergio
2016-01-01
We derive the mass formulae for ${\\cal N}=1$, $D=4$ matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to de Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing.
Quantum physics, relativity and complex spacetime towards a new synthesis
Kaiser, Gerald
1990-01-01
A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Ram K. Saxena; Zivorad Tomovski; Trifce Sandev
2015-01-01
In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find ...
Spinning gauged boson stars in anti-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Kichakova, Olga; Kunz, Jutta; Radu, Eugen
2014-01-20
We study axially symmetric solutions of the Einstein–Maxwell–Klein–Gordon equations describing spinning gauged boson stars in a (3+1)-dimensional asymptotically AdS spacetime. These smooth horizonless solutions possess an electric charge and a magnetic dipole moment, their angular momentum being proportional to the electric charge. A special class of solutions with a self-interacting scalar field, corresponding to static axially symmetric solitons with a nonzero magnetic dipole moment, is also investigated.
Physical constraints on causality-violating spacetimes in general relativity
Janca, Andrew Joseph
The theoretical possibility of global causality violation has long been a problem within general relativity, for there exists a large number of model spacetimes known to admit closed time-like curves, trajectories allowing a timelike observer to return to some point in her own past. However, nearly all such known models have some unphysical feature. These physicality issues rendered causality-violation to the status of an interesting but safely theoretical problem until twenty years ago, when the appearance of a new type of causality-violating model spacetime and the subsequent proliferation of new models admitting closed timelike curves forced the attention of the community to the issue, and made causality violation and its possible physical consequences an active area of research within general relativity. This paper focuses on some of the older causality-violating spacetimes which model matter sources with cylindrical symmetry. By describing how cylindrically-symmetric solutions can be embedded within a spatially bounded and physically realistic body which outwardly has the symmetry of a torus or ring, it is shown that the chief problem of physical plausibility which these older solutions possess can be resolved. The intention is to make these models active candidates for consideration in future experiments to test general relativity's prediction that causality violation is a phenomenon that could be observed in the real world. Attending chapters describe physical systems other than rotating objects that can alter a local observer's experience of time to a substantial extent, including an electrically-charged massive shell slowing time in its interior (though not affecting causality) and a class of trajectories in the Reissner-Nordstrom background that could in principle allow a timelike observer to reverse her personal arrow of time relative to other observers in the spacetime as a whole. The paper concludes with a discussion of one of the plausibility problems
Vaidya spacetime for Galileon gravity's rainbow
Energy Technology Data Exchange (ETDEWEB)
Rudra, Prabir, E-mail: prudra.math@gmail.com [Department of Mathematics, Asutosh College, Kolkata, 700 026 (India); Faizal, Mir, E-mail: mirfaizalmir@gmail.com [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Ali, Ahmed Farag, E-mail: ahmed.ali@fsc.bu.edu.eg [Department of Physics, Faculty of Science, Benha University, Benha, 13518 (Egypt)
2016-08-15
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and noncommutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
The matter-antimatter interpretation of Kerr spacetime
Villata, M.
2014-01-01
Repulsive gravity is not very popular in physics. However, one comes across it in at least two main occurrences in general relativity: in the negative-$r$ region of Kerr spacetime, and as the result of the gravitational interaction between matter and antimatter, when the latter is assumed to be CPT-transformed matter. Here we show how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the above Kerr negative-$r$ regi...
Semianalytic Solution of Space-Time Fractional Diffusion Equation
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A. Elsaid
2016-01-01
Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.
Constrained field theories on spherically symmetric spacetimes with horizons
Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman
2017-02-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.
Karma or Immortality: Can Religion Influence Space-Time Mappings?
Li, Heng; Cao, Yu
2018-01-09
People implicitly associate the "past" and "future" with "front" and "back" in their minds according to their cultural attitudes toward time. As the temporal focus hypothesis (TFH) proposes, future-oriented people tend to think about time according to the future-in-front mapping, whereas past-oriented people tend to think about time according to the past-in-front mapping (de la Fuente, Santiago, Román, Dumitrache, & Casasanto, 2014). Whereas previous studies have demonstrated that culture exerts an important influence on people's implicit spatializations of time, we focus specifically on religion, a prominent layer of culture, as potential additional influence on space-time mappings. In Experiment 1 and 2, we observed a difference between the two religious groups, with Buddhists being more past-focused and more frequently conceptualizing the past as ahead of them and the future as behind them, and Taoists more future-focused and exhibiting the opposite space-time mapping. In Experiment 3, we administered a religion prime, in which Buddhists were randomly assigned to visualize the picture of the Buddhas of the Past (Buddha Dipamkara) or the Future (Buddha Maitreya). Results showed that the pictorial icon of Dipamkara increased participants' tendency to conceptualize the past as in front of them. In contrast, the pictorial icon of Maitreya caused a dramatic increase in the rate of future-in-front responses. In Experiment 4, the causal effect of religion on implicit space-time mappings was replicated in atheists. Taken together, these findings provide converging evidence for the hypothesized causal role of religion for temporal focus in determining space-time mappings. Copyright © 2018 Cognitive Science Society, Inc.
Quantum Field Theory in Curved Spacetime
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
pathChirp: Efficient Available Bandwidth Estimation for Network Paths
Energy Technology Data Exchange (ETDEWEB)
Cottrell, Les
2003-04-30
This paper presents pathChirp, a new active probing tool for estimating the available bandwidth on a communication network path. Based on the concept of ''self-induced congestion,'' pathChirp features an exponential flight pattern of probes we call a chirp. Packet chips offer several significant advantages over current probing schemes based on packet pairs or packet trains. By rapidly increasing the probing rate within each chirp, pathChirp obtains a rich set of information from which to dynamically estimate the available bandwidth. Since it uses only packet interarrival times for estimation, pathChirp does not require synchronous nor highly stable clocks at the sender and receiver. We test pathChirp with simulations and Internet experiments and find that it provides good estimates of the available bandwidth while using only a fraction of the number of probe bytes that current state-of-the-art techniques use.
Experimental Constraints of the Exotic Shearing of Space-Time
Energy Technology Data Exchange (ETDEWEB)
Richardson, Jonathan William [Univ. of Chicago, IL (United States)
2016-08-01
The Holometer program is a search for rst experimental evidence that space-time has quantum structure. The detector consists of a pair of co-located 40-m power-recycled interferometers whose outputs are read out synchronously at 50 MHz, achieving sensitivity to spatiallycorrelated uctuations in dierential position on time scales shorter than the light-crossing time of the instruments. Unlike gravitational wave interferometers, which time-resolve transient geometrical disturbances in the spatial background, the Holometer is searching for a universal, stationary quantization noise of the background itself. This dissertation presents the nal results of the Holometer Phase I search, an experiment congured for sensitivity to exotic coherent shearing uctuations of space-time. Measurements of high-frequency cross-spectra of the interferometer signals obtain sensitivity to spatially-correlated eects far exceeding any previous measurement, in a broad frequency band extending to 7.6 MHz, twice the inverse light-crossing time of the apparatus. This measurement is the statistical aggregation of 2.1 petabytes of 2-byte dierential position measurements obtained over a month-long exposure time. At 3 signicance, it places an upper limit on the coherence scale of spatial shear two orders of magnitude below the Planck length. The result demonstrates the viability of this novel spatially-correlated interferometric detection technique to reach unprecedented sensitivity to coherent deviations of space-time from classicality, opening the door for direct experimental tests of theories of relational quantum gravity.
Relativistic Positioning System in Perturbed Space-time
Kostić, Uroš; Gomboc, Andreja
2015-01-01
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild space-time. We find that positioning in a perturbed space-time is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient -- on a laptop it takes 0.04 s to determine the user's spatial and time coordinates with a relative accuracy of $10^{-28}-10^{-26}$ and $10^{-32}-10^{-30}$, respectively.
Review of software for space-time disease surveillance.
Robertson, Colin; Nelson, Trisalyn A
2010-03-12
Disease surveillance makes use of information technology at almost every stage of the process, from data collection and collation, through to analysis and dissemination. Automated data collection systems enable near-real time analysis of incoming data. This context places a heavy burden on software used for space-time surveillance. In this paper, we review software programs capable of space-time disease surveillance analysis, and outline some of their salient features, shortcomings, and usability. Programs with space-time methods were selected for inclusion, limiting our review to ClusterSeer, SaTScan, GeoSurveillance and the Surveillance package for R. We structure the review around stages of analysis: preprocessing, analysis, technical issues, and output. Simulated data were used to review each of the software packages. SaTScan was found to be the best equipped package for use in an automated surveillance system. ClusterSeer is more suited to data exploration, and learning about the different methods of statistical surveillance.
Geodesic flows in a charged black hole spacetime with quintessence
Energy Technology Data Exchange (ETDEWEB)
Nandan, Hemwati [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Uniyal, Rashmi [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Government Degree College, Department of Physics, Tehri Garhwal, Uttarakhand (India)
2017-08-15
We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)
Classification of non-Riemannian doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)
2017-10-15
Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)
Renormalized spacetime is two-dimensional at the Planck scale
Padmanabhan, T; Kothawala, Dawood
2015-01-01
Quantum field theory distinguishes between the bare variables -- which we introduce in the Lagrangian -- and the renormalized variables which incorporate the effects of interactions. This suggests that the renormalized, physical, metric tensor of spacetime (and all the geometrical quantities derived from it) will also be different from the bare, classical, metric tensor in terms of which the bare gravitational Lagrangian is expressed. We provide a physical ansatz to relate the renormalized metric tensor to the bare metric tensor such that the spacetime acquires a zero-point-length $\\ell _{0}$ of the order of the Planck length $L_{P}$. This prescription leads to several remarkable consequences. In particular, the Euclidean volume $V_D(\\ell,\\ell _{0})$ in a $D$-dimensional spacetime of a region of size $\\ell $ scales as $V_D(\\ell, \\ell_{0}) \\propto \\ell _{0}^{D-2} \\ell^2$ when $\\ell \\sim \\ell _{0}$, while it reduces to the standard result $V_D(\\ell,\\ell _{0}) \\propto \\ell^D$ at large scales ($\\ell \\gg \\ell _{0}...
Testing the local spacetime dynamics by heliospheric radiocommunication methods
Directory of Open Access Journals (Sweden)
H.-J. Fahr
2008-05-01
Full Text Available According to general relativistic theories, cosmological spacetime is dynamic. This prediction is in excellent agreement with the huge majority of astronomical observations on large cosmic scales, especially the observations of cosmological redshifts of distant galaxies. However, on scales of heliospheric distances, verifications of general relativistic effects are based on Schwarzschild metric tests or kinetical corrections, such as the perihelion motion of Mercury, photon deflection at the Sun and gravitational photon redshifts in central gravity fields. As we will show in this paper, there is, however, a chance to detect new cosmologically relevant features on heliospheric scales by careful study of photon propagations in the local spacetime metrics, based on red- or blueshifts as a clear, but up to now overlooked, signature of the local spacetime dynamics. Thus, we propose the challenging possibility of carrying out experiments of cosmological relevance by simply using high-precision radio tracking of heliospheric spaceprobes, as already practised in cases like Pioneer-10/11, Galileo and Ulysses.
Asymptotically simple spacetimes and mass loss due to gravitational waves
Saw, Vee-Liem
The cosmological constant Λ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of Λ or Λ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on Λ: null infinity ℐ is a spacelike, null, or timelike hypersurface, if Λ > 0, Λ = 0, or Λ 0 in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of ℐ, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with Λ > 0 has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.
Landau quantization in the spinning cosmic string spacetime
Energy Technology Data Exchange (ETDEWEB)
Muniz, C.R., E-mail: celiomuniz@yahoo.com [Grupo de Física Teórica (GFT), Universidade Estadual do Ceará, UECE-FECLI, Iguatu-CE (Brazil); Bezerra, V.B. [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, CEP 58051-970, João Pessoa-PB (Brazil); Cunha, M.S. [Grupo de Física Teórica (GFT), Universidade Estadual do Ceará-UECE, CEP 60740-000, Fortaleza-CE (Brazil)
2014-11-15
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having a finite width and uniformly filled with both material and vacuum energies. - Highlights: • Solution of the wave equation characterizing the problem. • Energy levels of the particle in spacetime of the structureless string. • Expression for an analogous of the quadratic Zeeman effect. • Energy levels of the particle in spacetime of the string with internal structure. • Evidence of the string structure by the internal existence of the vacuum energy.
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying
2016-01-28
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
Cosmic microwave background and inflation in multi-fractional spacetimes
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Calcagni, Gianluca [Instituto de Estructura de la Materia,CSIC, Serrano 121, 28006 Madrid (Spain); Kuroyanagi, Sachiko [Department of Physics, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Institute for Advanced Research, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science,1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2016-08-18
We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.
Spacetime Causal Structure and Dimension from Horismotic Relation
Directory of Open Access Journals (Sweden)
O. C. Stoica
2016-01-01
Full Text Available A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated events (the horismos relation, we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works with both continuous and discrete spacetimes. The dimensionality is obtained also in the discrete case, so this approach can be suited to prove the fundamental conjecture of causal sets. Other simple conditions lead to a differentiable manifold with a conformal structure (the metric up to a scaling factor as in Lorentzian manifolds. This structure provides a simple and general reconstruction of the spacetime in relativistic theories of gravity, which normally requires topological structure, differential structure, and geometric structure (which decomposes in the conformal structure, giving the causal relations and the volume element. Motivations for such a reconstruction come from relativistic theories of gravity, where the conformal structure is important, from the problem of singularities, and from Quantum Gravity, where various discretization methods are pursued, particularly in the causal sets approach.
Pseudo-Finslerian Space-Times and Multirefringence
Skákala, Jozef; Visser, Matt
Ongoing searches for a quantum theory of gravity have repeatedly led to the suggestion that space-time might ultimately be anisotropic (Finsler-like) and/or exhibit multirefringence (multiple signal cones). Multiple (and even anisotropic) signal cones can be easily dealt with in a unified manner, by writing down a single Fresnel equation to simultaneously encode all signal cones in an even-handed manner. Once one gets off the signal cone and attempts to construct a full multirefringent space-time metric the situation becomes more problematic. In the multirefringent case we shall report a significant no-go result: in multirefringent models there is no simple or compelling way to construct any unifying notion of pseudo-Finsler space-time metric, different from a monorefringenent model, where the signal cone structure plus a conformal factor completely specifies the full pseudo-Riemannian metric. To throw some light on this situation we use an analog model where both anisotropy and multirefringence occur simultaneously: biaxial birefringent crystal. But the significance of our results extends beyond the optical framework in which (purely for pedagogical reasons) we are working, and has implications for any attempt at introducing multirefringence and intrinsic anisotropies to any model of quantum gravity that has a low energy manifold-like limit.
Momentum density of spacetime and the gravitational dynamics
Padmanabhan, T.
2016-01-01
I introduce a covariant four-vector G^a[v], which can be interpreted as the momentum density attributed to the spacetime geometry by an observer with velocity v^a, and describe its properties: (a) Demanding that the total momentum of matter plus geometry is conserved for all observers, leads to the gravitational field equations. Thus, how matter curves spacetime is entirely determined by this principle of momentum conservation. (b) The G^a[v] can be related to the gravitational Lagrangian in a manner similar to the usual definition of Hamiltonian in, say, classical mechanics. (c) Geodesic observers in a spacetime will find that the conserved total momentum vanishes on-shell. (d) The on-shell, conserved, total energy in a region of space, as measured by comoving observers, will be equal to the total heat energy of the boundary surface. (e) The off-shell gravitational energy in a region will be the sum of the ADM energy in the bulk plus the thermal energy of the boundary. These results suggest that G^a[v] can be a useful physical quantity to probe the gravitational theories.
On the performance of diagonal lattice space-time codes
Abediseid, Walid
2013-11-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria [1]-[9]. In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding. © 2013 IEEE.
On the theory of Killing orbits in spacetime
Energy Technology Data Exchange (ETDEWEB)
Hall, G S [Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, Scotland (United Kingdom)
2003-09-21
This paper gives a theoretical discussion of the orbits and isotropies which arise in a spacetime which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a spacetime in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of 'stable' orbits and the possible misbehaviour of the 'unstable' ones is pointed out and, in particular, the fact that independent Killing vector fields in spacetime may not induce independent Killing vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.
Steered transition path sampling.
Guttenberg, Nicholas; Dinner, Aaron R; Weare, Jonathan
2012-06-21
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying the dynamics based on that probability, and then reweighting to calculate averages. Because the progress constraint can be formulated in terms of occurrences of events within time intervals, the method is particularly well suited for controlling the sampling of currents of dynamic events. We demonstrate the method for calculating transition probabilities in barrier crossing problems and survival probabilities in strongly diffusive systems with absorbing states, which are difficult to treat by shooting. We discuss the relation of the algorithm to other methods.