Showing papers on "Four-force published in 2017"

The Problem of Time : Quantum Mechanics Versus General Relativity

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Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity

Abstract: We revisit the manifestly covariant large $c$ expansion of General Relativity, $c$ being the speed of light. Assuming the relativistic connection has no pole in $c^{-2}$, this expansion is known to reproduce Newton-Cartan gravity and a covariant version of Post-Newtonian corrections to it. We show that relaxing this assumption leads to the inclusion of twistless torsion in the effective non-relativistic theory. We argue that the resulting TTNC theory is an effective description of a non-relativistic regime of General Relativity that extends Newtonian physics by including strong gravitational time dilation.

Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes

Abstract: The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry that is locally identical to the $\ensuremath{\kappa}$-Poincar\'e dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such a Hamiltonian, we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe.

Conservation, Inertia, and Spacetime Geometry

Abstract: As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter.

Special Relativity and Coordinate Transformation

Abstract: Two inertial reference frames moving at identical velocity can be seperated if one of them is put under acceleration for a duration. The coordinates of both inertial reference frames are related by this acceleration and its duration. An immediate property of such coordinate transformation is the conservation of distance and length across reference frames. Therefore, the concept of length contraction from Special Relativity is impossible in reality and physics.

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

Abstract: Here we apply the full Will-Nordtvedt version of the Parameterized Post-Newtonian (PPN) formalism to a class of General Relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant $G$ is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the External Potential Effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales, for any of them the Solar System bounds need to be considered.

General relativity as the four-dimensional Chern-Weil theory

Abstract: A classical theory of general relativity in the four-dimensional space-time is formulated as a Chern--Simons topological theory. A Chern--Simons topological theory in four dimensional space is defined using a novel translation operator, under which a Einstein--Hilbert gravitational action is invariant up to total derivative and is constructed as a second Chern class. A canonical quantization of the system is performed in a Heisenberg picture using the Nakanishi--Kugo--Ojima formalism. A complete set of the quantum Lagrangian and BRS transformations including auxiliary and ghost fields is given in a self consistent manner. With a topological insight, an appropriate Hilbert space and physical states are introduced into the theory. As a consequence, the positivity of the physical states and the unitarity of the transition matrix are ensured by the Kugo--Ojima theorem. These results suggests that the quantum general relativity in this formalism is renormalizable, if a perturbative expansion is performed with respect to an appropriate expansion constant around an appropriate grand state in a Heisenberg picture.

Relativity without Light: A Further Suggestion

Abstract: The role of the light postulate in special relativity is reexamined. The existing theory of relativity without light shows that one can deduce Lorentz-like transformations with an undetermined invariant speed based on homogeneity of space and time, isotropy of space and the principle of relativity. However, since the transformations can be Lorentzian or Galilean, depending on the finiteness of the invariant speed, a further postulate is needed to determine the speed in order to establish a real connection between the theory and special relativity. In this paper, I argue that a certain discreteness of space-time, whose existence is strongly suggested by the combination of quantum theory and general relativity, may result in the existence of a maximum and invariant speed when combing with the principle of relativity, and thus it can determine the finiteness of the speed in the theory of relativity without light. According to this analysis, the speed constant c in special relativity is not the actual speed of light, but the ratio between the minimum length and the shortest time of discrete space-time. This suggests a more complete theory of relativity, the theory of relativity in discrete space-time, which is based on the principle of relativity and the constancy of the minimum size of discrete space-time.

The Relativity and Equivalence Principles for Self-gravitating Systems

Abstract: I criticise the view that the relativity and equivalence principles are consequences of the small-scale structure of the metric in general relativity, by arguing that these principles also apply to systems with non-trivial self-gravitation and hence non-trivial spacetime curvature (such as black holes). I provide an alternative account, incorporating aspects of the criticised view, which allows both principles to apply to systems with self-gravity.

de Sitter-invariant special relativity and the dark energy problem

Abstract: The replacement of the Poincare-invariant Einstein special relativity by a de Sitter-invariant special relativity produces concomitant changes in all relativistic theories, including general relativity. A crucial change in the latter is that both the background de Sitter curvature and the gravitational dynamical curvature turns out to be included in a single curvature tensor. This means that the cosmological term no longer explicitly appears in Einstein equation, and is consequently not restricted to be constant. In this paper, the Newtonian limit of such theory is obtained, and the ensuing Newtonian Friedmann equations are show to provide a good account of the dark energy content of the present-day universe.

BV-BFV approach to General Relativity: Palatini-Cartan-Holst action

Abstract: We show that the Palatini--Cartan--Holst formulation of General Relativity in tetrad variables must be complemented with additional requirements on the fields when boundaries are taken into account for the associated BV theory to induce a compatible BFV theory on the boundary.

Dyonic configurations in nonlinear electrodynamics coupled to general relativity

Abstract: We consider static, spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu u} F^{\mu u}$. After a brief review on black hole (BH) and solitonic solutions, obtained so far with pure electric or magnetic fields, an attempt is made to obtain dyonic solutions, those with both electric and magnetic charges. A general scheme is suggested, leading to solutions in quadratures for an arbitrary Lagrangian function $L(f)$ (up to some monotonicity restrictions); such solutions are expressed in terms of $f$ as a new radial coordinate instead of the usual coordinate $r$. For the truncated Born-Infeld theory (depending on the invariant $f$ only), a general dyonic solution is obtained in terms of $r$. A feature of interest in this solution is the existence of a special case with a self-dual electromagnetic field, $f \equiv 0$ and the Reissner-Nordstrom metric.

The Pin Groups in General Relativity

Abstract: There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the space-time diffeomorphism group.

General Relativity from Causality

Abstract: We study large families of theories of interacting spin 2 particles from the point of view of causality. Although it is often stated that there is a unique Lorentz invariant effective theory of massless spin 2, namely general relativity, other theories that utilize higher derivative interactions do in fact exist. These theories are distinct from general relativity, as they permit any number of species of spin 2 particles, are described by a much larger set of parameters, and are not constrained to satisfy the equivalence principle. We consider the leading spin 2 couplings to scalars, fermions, and vectors, and systematically study signal propagation in all these other families of theories. We find that most interactions directly lead to superluminal propagation of either a spin 2 particle or a matter particle, and interactions that are subluminal generate other interactions that are superluminal. Hence, such theories of interacting multiple spin 2 species have superluminality, and by extension, acausality. This is radically different to the special case of general relativity with a single species of minimally coupled spin 2, which leads to subluminal propagation from sources satisfying the null energy condition. This pathology persists even if the spin 2 field is massive. We compare these findings to the analogous case of spin 1 theories, where higher derivative interactions can be causal. This makes the spin 2 case very special, and suggests that multiple species of spin 2 is forbidden, leading us to general relativity as essentially the unique internally consistent effective theory of spin 2.

On the Logical Inconsistency of the Special Theory of Relativity

Abstract: Einstein’s Special Theory of Relativity requires systems of clock-synchronised stationary observers and the Lorentz Transformation. Without both, the Theory of Relativity fails. A system of clock-synchronised stationary observers is proven inconsistent with the Lorentz Transformation, because it is Galilean. The Special Theory of Relativity insists that Galilean systems must transform not by the Galilean Transformation, but by the non-Galilean Lorentz Transformation. The Theory of Relativity is therefore invalid due to an intrinsic logical contradiction.

Non-coordinates basis in General Relativity and Cartan's structure equations

Abstract: The basic and fundamental aspects of General Relativity are in general analysed in mathematical level of coordinate basis or holonomic frame by several authors in the literature. However, for many purposes it is more convenient to use a general basis, often called in four dimensions, a tetrad or vierbein, very useful in a local frame with orthonormal basis or pseudo-orthonormal basis. This text presents an introduction to non-coordinate basis and the two Cartan's structure equations that are mathematical implements in Riemannian geometry that facilitate the calculation of curvature tensors. The purpose of this text is to approach the language and the notation of tetrad field or vierbein with conceptual and calculational details.

Pseudo-Complex General Relativity

Abstract: The present status of the pseudo-complex General Relativity is presented. The pcGR includes many known theories with a minimal length. Restricting to its simplest form, an energy-momentum tensor is added at the right hand side of the Einstein equations, representing a dark energy, related to vacuum fluctuations. We use a phenomenological ansatz for the density and discuss observable consequences: Quaisperiodic Oscillations (QPO), effects on accretion disks and gravitational waves.

The Theory of Virtual Particles as an Alternative to Special Relativity

Abstract: Special relativity (SR) made it possible to explain a number of physical phenomena, which shows that its postulates: the principle of constancy of the speed of light and the principle of relativity (the latter suggests the invariance of physical laws with respect to Lorentz’ transformations reflecting the dependence of mass and size of moving bodies on their speed) are based on the properties of a physical process. It is shown in this paper that such a process is the creation in the physical vacuum of a virtual particles pair by the quantum entity that is a singularity in electric and/or magnetic fields and such properties are properties of this virtual particles pair, in particular, the dependence of its mass and size on the speed of the entity creating the pair. Based on the properties of virtual particles we may assume that theory of virtual particles may be an alternative to SR, it may describe the physical phenomena without using the four-dimensional kinematic formalism, remaining in the framework of the model of three-dimensional space and independent time. A substantiation of this assumption is that the equations describing the physical phenomena derived in SR can be derived as well by taking into account the creation of virtual particles pairs by quantum entities while using the Galilean addition of velocities.

Constructing balanced equations of motion for particles in general relativity: the harmonic gauge case

Abstract: We present a convenient null gauge for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connexion between the field equation and the balanced equations of motion. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, $G^2$ and $G^3$. We indicate how this approach can be extended to higher orders.

The Harmonic Oscillator in the Framework of Scale Relativity

Abstract: The dynamical law obeyed by the one-dimensional physical systems in the scale relativity approach is reduced to a Riccati nonlinear differential equation Applied to the harmonic oscillator potential, we show that such an approach permits the calculation of the solutions of the scale relativity problem in terms of the well known solutions of the Schroedinger equation for the harmonic oscillator

Extended Theory of Harmonic Maps Connects General Relativity to Chaos and Quantum Mechanism.

Abstract: General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrodinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory of physics.

Special Relativity in Complex Space-Time. Part 1. a Choice of the Domain and Transformation Preserving the Invariance of Wave Equation.

Abstract: The article shows that based on the obvious postulates, using the existing mathematical tools, an alternative theory of special relativity can be build. The results were obtained studying the invariance of a four-dimensional wave equation by the paravector calculus. As a field domain the complex space-time was selected. Its meaningfulness and implicit naturalness is shown on simple examples. The aim of the publication is to show that the physical space-time may be viewed from a different perspective, not known so far.

de Sitter invariant special relativity and galaxy rotation curves

Abstract: Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincare invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is used to study the circular velocity of stars around the galactic center. It is shown that the de Sitter modified Newtonian force---which includes corrections coming from the underlying local kinematics---could possibly explain the rotation curve of galaxies without the necessity of supposing the existence of a dark matter halo.

Gravity Beyond General Relativity

Abstract: At the core of this thesis is the question of modifying general relativity. In the previous chapter, we introduced general relativity and its cosmological solutions, culminating in a discussion of two key aspects of the cosmological standard model: \(\Lambda \)CDM at late times and inflation at early times. In this chapter, we extend that discussion to theories of gravity beyond general relativity, and in particular the theories which will receive our attention in this thesis: massive gravity, massive bigravity, and Einstein-aether theory.

Time and Spacetime in General Relativity (GR)

Abstract: This chapter begins consideration of foundations for general relativity. This is both a relativistic theory of gravitation and a freeing from absolute or background structures (as Chaps. 8 to 10 explain further). The latter perspective emphasizes Background Independence, a notion widely used in Quantum Gravity programs as well. Given the substantial conceptual and technical differences incurred by Background Independence, we further motivate the first—and only observationally established—seat of this—general relativity—by firstly briefly surveying observational evidence for general relativity. Secondly, by outlining useful features of some of its simpler cosmological and black hole solutions.

Special Relativity (Lorentz Transformation) Follows from the Definition of Inertial Frames

Abstract: Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit In this article, we point out that the existence of a finite speed limit can be readily inferred from the nature of allowed inertial frames We also show that the principle of relativity can be obtained from the defining space-time symmetries of every inertial frame Therefore, if the conventional definition of inertial frames is augmented properly, the special theory of relativity (Lorentz transformation) would follow from the definition of inertial frames

Black hole electromagnetic observations as tests of general relativity: quadratic gravity

Abstract: We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even parity sector, exemplified by Einstein-dilaton-GaussBonnet gravity, and the odd parity sector, exemplified by dynamical Chern-Simons gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on sphericallysymmetric and axially-symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes’ direction relative to the background geometry, just as in dynamical Chern-Simons gravity.

The Reasons Suggesting a Close Link between Thermodynamics and Relativity

Abstract: Since the advent of relativity, it is widely accepted that the law of conservation of energy must include the energy created by disintegration of matter, or converted into matter. The aim of the present paper deals with the insertion of this concept into the basic equations of thermodynamics.