Finslerian relativity theory

The possible manifestation of Finslerian metrical properties of space-time in the kinematics and dynamics of locally nontest particles is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 49–52, April, 1980.     

A Finslerian extension of general relativity

A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.     

A new approach to the theory of relativity. II. The general theory of relativity

The considerations of Part I are extended and the experimental data and hypotheses that led to the establishment of the general theory of relativity are analyzed. It is found that one of the fundamental assumptions is that light is propagated homogeneously; i.e., by using arbitrary systems of coordinates, propagation of light can be represented by a homogeneous quadratic form. This is shown to be an assumption that can be verified by experiment, at least in principle. As a result of adding a number of further assumptions to this, the usual formalism of the general theory of relativity can be established. In the above point of view, the general theory of relativity—like any other theory—cannot be built upad hoc, but is built on distinct physical hypotheses, each of which can be subjected to test by experiment.     

Rotating frames in special relativity. II. Generalized theory

The transformation theory for rotating frames presented in a previous paper (Strauss, 1974) is generalized by replacing the usual conditionr=R for Rr=Rg( _R ) so thatr is now defined for all values ofR,0R. This generalization does not affect the kinematic transformation {,T}{^(r),{^(r)}}, and the result group structure required by the theoretical constraints previously established, provided the old parameter r (=R) is now identified throughout with eitherr orR; for physical reasons it must be identified withR. The functiong, which cannot be fixed by theoretical constraints, determines the degree of geometrical anisotropy in the rotating planez=const. More specifically, sinceg enters the expression for the ratioC/D (circumference/diameter) its choice corresponds to the choice of a congruence definition for lengths in radial and tangential directions. While on this (purely geometrical) levelg remains undetermined, it can be uniquely determined experimentally on the kinematic level, e.g., by observing in the motion of a free particle. Thus the supremacy of kinematics over geometry is explicated by a further instance. At the same time, special relativity theory (SRT) is shown to belong to the class of theories with theoretically unsolvable problems.     

Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity

Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. 107 (2011) 181803] pointed out that the superluminal neutrinos reported by the OPERA would lose their energy rapidly via the Cherenkov-like process. The Cherenkov-like process for the superluminal particles would be forbidden if the principle of special relativity holds in any frame instead violated with a preferred frame. We have proposed that the Finslerian special relativity could account for the data of the neutrino superluminality (arXiv:1110.6673 [hep-ph]). The Finslerian special relativity preserves the principle of special relativity and involves a preferred direction while consists with the causality. In this Letter, we prove that the energy–momentum conservation is preserved and the energy–momentum is well defined in Finslerian special relativity. The Cherenkov-like process is forbidden in the Finslerian special relativity. Thus, the superluminal neutrinos would not lose energy in their distant propagation.     

An interaction interpretation of special relativity theory. Part II

The interaction interpretation of special relativity theory (elaborated in Part I) is discussed in relation to quantum theory. The relativistic transformations (Lorentz processes) of physical variables, on the interaction interpretation, are observation-interaction dependent, just as are the physical values (eigenvalues) of systems described by quantum-theoretic state functions; a common, basic structure of the special relativity and quantum theories can therefore be presented. The constancy of the light speed is shown to follow from interaction-transformations of frequency and wavelength variables. A parallelism is suggested between, on the one hand, the Lorentz-Clausius distinction for relativistic transformations, and, on the other, the distinction between observation-dependent and observation-independent natural processes. The empirical study of rates of macroscopic clocks can provide a critical test of the interaction interpretation and of a possible extension to gravitational time changes; the role of time as prior determinant of natural process is at issue. The Hafele-Keating observations are of general relativity effects on clocks in accelerated motion.     

Basic principles of the Finsler theory of relativity. II

The basic principles of the Finsler generalization of the theory of relativity are systematically studied. The present paper is a direct continuation of the preceding paper [1] with the same notation and a continuation of the numbering of formulas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 104–107, 1979.     

A test theory of special relativity: II. First order tests

First-order tests of special relativity are based on a comparison of clocks synchronized with the help of slow clock transport with those synchronized by the Einstein procedure. This comparison enables the measurement of the one-way velocity of light and is equivalent to a measurement of the time dilatation factor. The accuracy of present measurements is of the order 10^–7, yielding an upper limit of 3 cm/sec for the ether drift.     

Rotational relativity theory

The constancy of the spin of the photon was recently shown to lead to a new Lorentz-type transformation that relates the energy, rotational velocity, moment of inertia, and angular momentum, where rotational invariance was the basis of the theory instead of the ordinary linear invariance of special relativity. In this paper the new group of transformations is shown to lead naturally to a special theory of relativity whose basic metric has anR×S ³ topology rather than the familiar Minkowskian metric. Predictions by the theory are shown to be highly supported by experiment.     

Five-dimensional relativity theory

The five-dimensional relativity theory proposed by Kaluza is formulated covariantly for a Riemannian space containing a Killing geodesic vector field. From this five-dimensional space a four-dimensional physical space is extracted. The field equations in empty 5-space are essentially uniquely determined and correspond to the Einstein-Maxwell equations in 4-space. In the presence of a field in 5-space the field equations involve a tensor which is associated with energy, momentum, charge and current densities in 4-space. For a 5-space containing dust the field equations lead to particle motion described by the geodesic equations. The latter correspond in 4-space to the Lorentz equations of motion for particles with arbitrary ratios of charge to mass and also for certain entities (tachyons and luminons) unobserved hitherto.     

Causal functions in general relativity. II

It is shown that important space-time structure conditions of stable causality and strong causality are characterized in terms of causal functions.     

The gauge in general relativity. II

The present paper and a companion work are intended as one possible realization of a non-customary gauge theory of general relativity-as set forth in only broad outline in an earlier work. In this first paper, it is found that both radar echo delay and the perihelion shift differ slightly from their customary expressions. Unfortunately, it is also found that the usual statement of the principle of equivalence does not hold in the present formulation. Finally, in the second paper, a single cosmological model is investigated that appears to be promising.This work forms part of a Ph.D. dissertation by L.S.     

Waves in five-dimensional relativity theory

We give an exact solution of the five-dimensional relativity equations, and interpret it using the induced-matter formalism wherein geometry in 5D gives rise to matter in 4D. The solution represents oscillations of ordinary 3D space where the associated medium has the equation of state of the classical de Sitter vacuum. We outline implications for the inflationary universe model.     

Elementary particles in bimetric general relativity. II

The possibility of an elementary particle in the framework of classical bimetric general relativity is explored further. A model is considered which is filled with a pressureless primal fluid having a fixed ratio of charge density to mass density. This ratio is assumed to be0, ± ₀ , where ₀ is a universal constant <0.5. If the particle charge is assumed to be ±1/3e, the mass is a fraction of the Planck mass, the fraction being greater than0.0285.     

Rotating steady-state configurations in general relativity. II

Space-times with timelike Killing vector field and axial Killing vector field are studied. Physical coordinates are constructed for the metric of differentially rotating matter. It is proved that, for matter flow whose streamline tangents areu = + , the matter region must be either Petrov type I orD.Partially supported by a National Research Council of Canada grant.     

Quantum relativity theory and quantum space-time

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugoveki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (elementary particles). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that quarks should be considered as quantum relativistic particles.Supported by the Hungarian Academy of Sciences.     

Electromagnetic radiation in the general theory of relativity. I

The possibilities are investigated for the joint solution of Einstein's and Maxwell's equations for an isotropic electromagnetic field. Three groups of metric forms of space are shown, in which such a solution is permissible.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 65–69, April, 1973.In conclusion the author thanks Professor V. I. Rodichev and Professor D. D. Ivanenko for an interesting discussion of the problem considered in the paper.     

Basic principles of the Finsler theory of relativity. I

Physical principles are considered from which may be developed a generalization of relativity theory based on Finsler geometry, which is a metric generalization of Riemannian geometry.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 58–62, 1978.