Showing papers on "Four-force published in 2013"
TL;DR: In this paper, it was shown that standard even-dimensional General Relativity may emerge as a weak coupling constant limit of a Born-Infeld theory for a certain Lie subalgebra of the algebra B. In even dimensions, the Lagrangian is a Chern-Simons form for the (A)dS group.
81 citations
TL;DR: In this paper, the unique ghost-free mass and nonlinear potential terms for general relativity are presented in a diffeomorphism and local Lorentz invariant vierbein formalism.
Abstract: The unique ghost-free mass and nonlinear potential terms for general relativity are presented in a diffeomorphism and local Lorentz invariant vierbein formalism This construction requires an additional two-index St\"uckelberg field, beyond the four scalar fields used in the metric formulation, and unveils a new local SL(4) symmetry group of the mass and potential terms, not shared by the Einstein-Hilbert term The new field is auxiliary but transforms as a vector under two different Lorentz groups, one of them the group of local Lorentz transformations, the other an additional global group This formulation enables a geometric interpretation of the mass and potential terms for gravity in terms of certain volume forms Furthermore, we find that the decoupling limit is much simpler to extract in this approach; in particular, we are able to derive expressions for the interactions of the vector modes We also note that it is possible to extend the theory by promoting the two-index auxiliary field into a Nambu-Goldstone boson nonlinearly realizing a certain spacetime symmetry, and show how it is ``eaten up'' by the antisymmetric part of the vierbein
73 citations
TL;DR: Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity as mentioned in this paper, which in some regimes can be rewritten as nonlinear Poincar\'e algebras with momentum-dependent deformations of commutators between boosts and time translations.
Abstract: Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be rewritten as nonlinear Poincar\'e algebras with momentum-dependent deformations of commutators between boosts and time translations. In contrast to deformed special relativity, the deformations are derived for generators with an unambiguous physical role, following from the relationship between canonical constraints of gravity with stress-energy components. The original deformation does not appear in momentum space and does not give rise to nonlocality issues or problems with macroscopic objects. Contact with deformed special relativity may help to test loop quantum gravity or restrict its quantization ambiguities.
66 citations
TL;DR: In this paper, a screening mechanism for conformal vector-tensor modifications of general relativity is proposed, where the conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a non-null value in low density environments.
44 citations
TL;DR: Einstein regarded as one of the triumphs of his 1915 theory of gravity -the general theory of relativity -that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of general relativity supposedly violated it as mentioned in this paper.
Abstract: Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920.
34 citations
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24 Mar 2013TL;DR: In a recent article by Lewis and Tolman as mentioned in this paper, a non-analytical method was developed for obtaining the more important conclusions which can be drawn from the principle of relativity, and it may be concluded that the unexpected nature of the results of the theory of relativity is due to something unusual in the two postulates of relativity themselves.
Abstract: In a recent article by Lewis and Tolman [1] a non-analytical method I was developed for obtaining the more important conclusions which can be drawn from the principle of relativity. Our reasoning was based only upon the first and second postulates of relativity, and those fundamental conservation laws of mass, energy and momentum which science has never in a single instance been forced to abandon. Since the method of attack avoided any use of involved mathematical analysis, restricting itself to the simplest processes of logical reasoning, and, further, made no use of the assumptions of electromagnetic theory, it may be concluded that the unexpected nature of the results of the theory of relativity is due to something unusual in the two postulates of relativity themselves.
No objections have ever been made to the first postulate of relativity, as stated in its original form by Newton, that it is impossible to measure or detect absolute translatory motion through space. In the development of the theory of relativity, this postulate has been modified to include the impossibility of detecting translatory motion through any ether or medium which might be assumed to pervade space. In support of this principle is the general fact that no "ether drift" has ever been detected, but, especially, the conclusive experiments of Michelson and Morley, and Trouton and Noble, in which, a motion through the ether, of the earth in its path around the sun would certainly have been detected. For the purposes of this article we shall consider that the first postulate of relativity needs no further proof.
It is Einstein (to whom, indeed we owe the development of relativity along its present broad lines) who first stated the second postulate of relativity in a general form, namely, that the velocity of light in free space appears the same to all observers, regardless of the relative motion of the source of light and the observer. This is the assumption which has forced the theory of relativity to its strange conclusions, and it is for its further consideration that this paper is designed.
A simple example will make the extraordinary nature of the second postulate evident.
32 citations
TL;DR: Recently, it was shown that the dynamics of General Relativity can indeed be formulated as the dynamic dynamics of shapes as discussed by the authors, and a new Shape Dynamics theory, unlike earlier proposals by Barbour and his collaborators, implements local spatial conformal invariance as a gauge symmetry that replaces refoliation invariance in general Relativity.
Abstract: Barbour’s interpretation of Mach’s principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, “shapes.” Recently, it was shown that the dynamics of General Relativity can indeed be formulated as the dynamics of shapes. This new Shape Dynamics theory, unlike earlier proposals by Barbour and his collaborators, implements local spatial conformal invariance as a gauge symmetry that replaces refoliation invariance in General Relativity. It is the purpose of this paper to answer frequent questions about (new) Shape Dynamics, such as its relation to Poincare invariance, General Relativity, Constant Mean (extrinsic) Curvature gauge, earlier Shape Dynamics, and finally the conformal approach to the initial value problem of General Relativity. Some of these relations can be clarified by considering a simple model: free electrodynamics and its dual shift symmetric formulation. This model also serves as an example where symmetry trading is used for usual gauge theories.
30 citations
Book•
01 Jan 2013
TL;DR: The Lorentz transformation as discussed by the authors has been used for the conservation of energy-momentum and the principle of equivalence in the relation between different dimensions of spacetime. But it has not yet been applied to general relations.
Abstract: PART I: THE RELATIVISTIC WORLD 1. Basic ideas 2. The Lorentz transformation 3. Moving light sources 4. Dynamics 5. The conservation of energy-momentum 6. Further kinematics 7. Relativity and electromagnetism 8. Electromagnetic radiation PART II: AN INTRODUCTION TO GENERAL RELATIVITY 9. The Principle of Equivalence 10. Warped spacetime 11. Physics from the metric PART III: FURTHER SPECIAL RELATIVITY 12. Tensors and index notation 13. Rediscovering electromagnetism 14. Lagrangian mechanics 15. Angular momentum 16. Energy density 17. What is spacetime?
30 citations
TL;DR: A comment on the letter by M. Mansuripur, Phys.
Abstract: This editorial discusses "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation".
TL;DR: A Comment on the Letter by M. Mansuripur, Phys.
Abstract: A Comment on the Letter by M. Mansuripur, Phys. Rev. Lett. 108, 193901 (2012). The authors of the Letter offer a Reply.
TL;DR: In this article, it was shown that general relativity is the unique spatially covariant effective field theory of the transverse, traceless graviton degrees of freedom, and that the Lorentz covariance of general relativity can be interpreted as an accidental or emergent symmetry of the gravitational sector.
Abstract: We provide evidence that general relativity is the unique spatially covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector.
TL;DR: In this article, the authors reformulate the general theory of relativity in the language of Riemann-Cartan geometry, and they show that the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field.
Abstract: We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.
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TL;DR: Weyl and Cartan as mentioned in this paper revisited the space problem from the point of view of transformations operating in the infinitesimal neighbourhoods of a manifold (spacetime) and surveyed further developments in mathematics and physics of the second half of the 20th century, in which core ideas of Weyl's and/or Cartan's analysis were further investigated or incorporated into basic theories (physics).
Abstract: Starting from a short review of the "classical" space problem in the sense of the 19th century (Helmholtz -- Lie -- Klein) it is discussed how the challenges posed by special and general relativity to the classical analysis were taken up by Hermann Weyl and Elie Cartan. Both mathematicians reconsidered the space problem from the point of view of transformations operating in the infinitesimal neighbourhoods of a manifold (spacetime). In a short outlook we survey further developments in mathematics and physics of the second half of the 20th century, in which core ideas of Weyl's and/or Cartan's analysis of the space problem were further investigated (mathematics) or incorporated into basic theories (physics).
TL;DR: In this article, a detailed study examines two postulates of Special Relativity and concludes that the claim of "constant one-way speed of light" contradicts itself, which shakes the foundation of these theories.
Abstract: A constant one-way light speed is essential for the Theory of Relativity. This detailed study examines two postulates of Special Relativity and concludes that the claim of “constant one-way speed of light” contradicts itself. The equations of Special Relativity are foundations of many physics theories. The findings on controversial Relativity postulates shake the foundation of these theories. Fortunately, equations similar to Special Relativity equations can be derived, assuming that two-way light speed is constant, without the use of Special Relativity Postulates. These new equations provide a better foundation that is compatible with the correct existing physics theories. There is no threat of invalidating all existing physics theories, only incorrect ones. Instead, we can take a new look at some fundamental questions shared among physicists.
TL;DR: In this paper, the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic $D$-dimensional spacetimes are summarised.
Abstract: Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarise the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic $D$-dimensional spacetimes.
TL;DR: In this article, the authors argue that perfect inertial dragging may save the principle of relativity, and that this requires a new model of the Minkowski spacetime where the cosmic mass is represented by a massive shell with radius equal to its own Schwarzschild radius.
Abstract: The twin paradox is intimately related to the principle of relativity. Two twins A and B meet, travel away from each other and meet again. From the point of view of A, B is the traveller. Thus, A predicts B to be younger than A herself, and vice versa. Both cannot be correct. The special relativistic solution is to say that if one of the twins, say A, was inertial during the separation, she will be the older one. Since the principle of relativity is not valid for accelerated motion according to the special theory of relativity B cannot consider herself as at rest permanently because she must accelerate in order to return to her sister. A general relativistic solution is to say that due to the principle of equivalence B can consider herself as at rest, but she must invoke the gravitational change of time in order to predict correctly the age of A during their separation. However one may argue that the fact that B is younger than A shows that B was accelerated, not A, and hence the principle of relativity is not valid for accelerated motion in the general theory of relativity either. I here argue that perfect inertial dragging may save the principle of relativity, and that this requires a new model of the Minkowski spacetime where the cosmic mass is represented by a massive shell with radius equal to its own Schwarzschild radius.
TL;DR: In this paper, it was shown that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers, and that such a system is suitable for special relativity.
Abstract: We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of special relativity. We show that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers.
TL;DR: In this paper, a new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat.
Abstract: The Einstein–Boltzmann (EB) system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the EB system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the EB system so as to include scattering kernels which are physically well-motivated.
TL;DR: In this paper, the authors proposed generalized Bondi-Sachs equations for Cauchy-characteristic matching (CCM) to solve the problem of the inner caustics in the inner near zone.
Abstract: The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.
TL;DR: In this paper, it was shown that starting only from universal postulates such as homogeneity of space and time and Principle of Relativity, one can obtain transformations characterized by an invariant speed generally different than.
Abstract: In Special Theory of Relativity time is considered to be the 4th dimension of space – time as a consequence of Lorentz invariance and Minkowski metric, in turn based on the invariance of light speed . In this paper we’ll show that, starting only from universal postulates as homogeneity of space and time and Principle of Relativity, we can obtain space and time transformations (as the Lorentz and Tangherlini – Selleri ones) characterized by an invariant speed generally different than . These results determine crucial difficulties in the assumption of Minkowski metric and consequently in the interpretation of physical time as the 4th component of space – time, also introducing a “relativity” feature in the velocity of light in vacuum being no longer considerable as a necessarily universal invariant quantity and depending on the physical properties of space which originate from quantum vacuum. A novel interpretation of time, coherent with these results, defined as duration of material change in space, i.e. motion, is finally proposed.
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TL;DR: For a spacelike 2-surface in spacetime, the authors proposed a new definition of quasi-local angular momentum and center of mass as an element in the dual space of the Lie algebra of the Lorentz group.
Abstract: For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined quasi-local energy-momentum, this completes the definition of conserved quantities in general relativity at the quasi-local level. We justify this definition by showing the consistency with the theory of special relativity and expectations on an axially symmetric spacetime. The limits at spatial infinity provide new definitions for total conserved quantities of an isolated system, which do not depend on any asymptotically flat coordinate system or asymptotic Killing field. The new proposal is free of ambiguities found in existing definitions and presents the first definition that precisely describes the dynamics of the Einstein equation.
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TL;DR: In this paper, an attempt has been taken to elucidate t he Minkowski geometry in some details with easier mathematical calculations and diagrams where necessary, and some related definitions and related discussions are given before explaining the Minkowsky geometry.
Abstract: Space-time manifold plays an important role to expr ess the concepts of Relativity properly. Causality and space-time topology make easier the geometrical explanation of Minkowski space-time manifold. The Minkowski metric is the simplest empty space- time manifold in General Relativity, and is in fact the space-time of the Special Relativity. Hence it is the entrance of the General Relativity and Relativistic Cosmology. No material particle can travel faster than light. So that null space is the boundary of the space-time manifold. Einstein equation plays an imp ortant role in Relativity. Some related definitions and related discussions are given before explaining the Minkowski geometry. In this paper an attempt has been taken to elucidate t he Minkowski geometry in some details with easier mathematical calculations and diagrams where necessary.
TL;DR: In this article, the authors present two models combining some aspects of the Galilei and the Special relativities that lead to a unified view of both relativities, which is based on a reinterpretation of the absolute time of the relativities.
Abstract: We present two models combining some aspects of the Galilei and the Special relativities that lead to a
unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity
plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a second model that leads to a generalization of the Lorentz transformation, which includes, as particular cases, the standard Lorentz transformation and transformations that apply to the case of superluminal frames.
TL;DR: In this article, the authors discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem and in the context of the recently launched LAser RElativity Satellite (LARES).
Abstract: According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem, and in the context of the recently launched LAser RElativity Satellite (LARES). Being possibly the highest mean density orbiting body in the Solar system, this satellite provides the best realization of a test particle ever reached experimentally and provides a unique possibility for testing the predictions of General Relativity.
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TL;DR: In this article, the authors introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds having the corresponding smoothness properties.
Abstract: We introduce several axiom systems for general relativity and show that they are complete with respect to the standard models of general relativity, i.e., to Lorentzian manifolds having the corresponding smoothness properties.