Revised Robertson's test theory of special relativity

The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson [Rev. Mod. Phys. 21, 378 (1949)] of the Lorentz transformations from the results of the experimental evidence. Some researchers would argue that the proof contains an unwarranted assumption disguised as a convention about synchronization procedures. Others would say that alternative conventions are possible. In the present paper, no convention is used, but the Lorentz transformations are still obtained using only the results of the experiments in Robertson's proof, namely the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments. Thus the revised proof is a valid test theory which is independent of any conventions, since one appeals only to the experimental evidence. The analysis of that evidence shows the directions in which efforts to test special relativity should go. Finally it is shown how the resulting test theory still has to be improved for consistency in the analysis of experiments with complicated experimental setups, how it can be simplified for expediency as to what should be tested, and how it should be completed for a missing step not considered by Robertson.     

Revised Robertson's test theory of special relativity: Supergroups and superspace

The revised Robertson's test theory of special relativity (SR) has been constructed upon a family of sets of passive coordinate transformations in flat space-time [J. G. Vargas and D. G. Torr,Found. Phys., 16, 1089 (1986)]. In the same paper, it has also been shown that the boosts depend in general on the velocities of the two frames involved and not only on their relative velocity. The only exception to this is SR, if one has previously used an appropriate constraint to remove the other relativities—like Galilean relativity—from the family.In this paper we look at these coordinate transformations in the only way there is to do so, namely as transformations in a seven-dimensional Cartan Space (Cartan first considered this in his dealings with Newtonian kinematics). In this space, the boosts only depend on the relative velocity of the frames. The passive coordinate transformations in each set are shown to have a nonlinear group structure isomorphic to that of the Poincaré group.The existence of a preferred frame, except in SR, makes the active transformations inequivalent to the passive ones. It is shown that the composite active-passive transformations act on a ten-dimensional space and that each member set of the family also has a group structure. As a result, one ends up with a family of mutually isomorphic 9-parameter (homogeneous) supergroups and a family of mutually isomorphic (9 + 4)-parameter (inhomogeneous) supergroups. The presence of extra parameters could be looked upon as internal degrees of freedom, which are, however, an offshoot of the Robertson space-time.Part of this work was done while the author was at Departmento de Física, Universidad del Zulia, Maracaibo, Venezuela, and at Department of Physics, Utah State University, Logan, Utah.     

Revised Robertson's test theory of special relativity: Space-time structure and dynamics

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant Robertson's subfamilies. It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory.Part of this work was done at the Department of Physics, Utah State University, Logan, Utah 84322.     

A test theory of special relativity: I. Simultaneity and clock synchronization

The role of convention in various definitions of clock synchronization and simultaneity is investigated. We show that two principal methods of synchronization can be considered: system internal and system external synchronization. Synchronization by the Einstein procedure and by slow clock transport turn out to be equivalent if and only if the time dilatation factor is given by the Einstein result (1–v ²)^1/2. An ether theory is constructed that maintains absolute simultaneity and is kinematically equivalent to special relativity.     

Nonlinear equations of the gravitational field in the special theory of relativity

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.     

A modified Lorentz theory as a test theory of special relativity

A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. In the framework of MLT, some explicit formulas dealing with the one-way velocity of light, slow-clock transport and the Doppler effect are derived in this paper. Several typical experiments are analyzed on this basis. The results show that the empirical equivalence between MLT and special relativity is still maintained to second order terms. We confirm recent findings of other works that predict the MLT might be distinguished from special relativity at the third order by Doppler centrifuge experiments capable of a fractional frequency detection threshold of 10^–15.     

Difference between special relativistic gravitational theory and general relativity: Weak field limit

In the case of weak fields, we compare the gravitational fields and the dynamical equation of a particle deduced from special relativistic gravitational theory with the corresponding results deduced from general relativity. Then both gravitational theories can be tested by experiments.     

Motion of a particle in a gravitational field in the special theory of relativity

The equations of motion for a particle moving in a gravitational field considered in planar spacetime are derived. A simplified form of these equations is obtained for the particular case of a centrosymmetric field subject to a simplifying assumption concerning the structure of the potential of a field with this sort of symmetry. Under this assumption the displacement of the perigee of the planets amounts to five-sixths of the value given by the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 48–52, March, 1977.     

A test theory of special relativity: III. Second-order tests

Various second-order optical tests of special relativity are discussed within the framework of the test theory developed previously. Owing to the low accuracy of the Kennedy-Thorndike experiment, the Lorentz contraction is known by direct experiments only to an accuracy of a few percent. To improve this-accuracy several experiments are suggested.     

Experimental test of special relativity by laser spectroscopy

The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation factor . An experiment on metastable ⁷Li⁺, stored at a velocity of v = 0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two different ion-velocities (v = 0.03c and v = 0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage ring (ESR) at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt. The ESR permits ⁷Li⁺ to be stored at v = 0.33c which promises an improvement of the sensitivity to deviations from γ _SR by an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment.     

Quantum mechanics as demanded by the special theory of relativity

We present a new approach on the interpretation of the quantum mechanism. The derivation is phenomenological and incorporates an energetic vacuum which interacts with elementary particles. We consider a classical ensemble average for the square of 4-velocities of identical elementary particles with the same initial conditions in Minkowski space. The relativistic extension of a result in Brownian motion allows the variance to be identified with Bohm's quantum potential. A simple relation between 4-velocities and 4-momenta at a specific 4-position with given proper time leads to one of two statistical equations that constitute our quantum theory, the other being the continuity equation. The Klein-Gordon equation is a consequence of these two statistical equations.     

Non-standard clock synchronization in special relativity and the hypothetical ether frame

Assuming an Einsteinian world, formulae are given for achieving non-standard clock synchronization by various methods. It is shown that synchronization in one inertial frame simultaneously gives the same synchronization relative to all other frames. Absolute synchronization is not unique, and considerations of synchronization cannot distinguish an ether frame. In any world, synchronization with tachyons would produce the same results as other methods.     

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.     

Phenomenon of gravitational repulsion in the general theory of relativity

Einstein's generalization of Newton's theory of gravitation in the general theory of relativity led not only to small quantitative differences between gravitational effects in the relativistic theory and the Newtonian theory, but also to essentially new phenomena and effects peculiar to the relativistic theory and absent in the Newtonian theory. This difference is so large that the gravitational interaction in Einstein's theory even altered the attraction-only property, characteristic of Newton's theory, the law of universal gravitation, and became both attractive and repulsive. It is notable that the nature of the repulsion in gravitational interaction already appears in the simplest case of a spherically symmetric isolated body. Einstein's equations admit for a spherical body a solution whose physical interpretation uniquely indicates the repulsive nature of a gravitational field inside the body, if the number of particles that make up the body is sufficiently large. The structure of such a body, density distribution of the number of particles, mass, and pressure, is determined in the equilibrium state by the pressure of the substance, the gravitational attraction of peripheral layers toward the center, and the gravitational repulsion of inner layers of matter away from the center. As a result of the gravitational repulsion of matter away from the center inside the body there appears a cavity, free of the matter making up the body and its electromagnetic radiation. If the body is cold, then the volume of the world tube of the cavity can differ from zero. In the opposite case, the world tube of the cavity reduces to the world line of the center, which is inaccessible to particles of matter and to electromagnetic radiation. Gravitational repulsion, on the other hand, is a result of the existence of a field singularity at the center of the body, whose world line is time-like.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 61–67, April, 1981.     

Tetrad analysis of rotational and vibrational motion in the special theory of relativity

The formalism of orthogonal reference frames described by Eisenhart [1] is used to analyze a rotating continuum, the circular motion of a mass point, and a relativistic oscillator from the standpoint of comoving tetrads. It is found that the velocity of the rotating object or of the mass point does not exceed the speed of light in vacuum at any distances from the rotation axis.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 74–80, November, 1970.In conclusion the author thanks Professor V. I. Rodichev for suggesting this topic and for useful comments.     

On linearity in the special theory of relativity

In deductions of Lorentz transformations of the special theory of relativity, linearity of transformation is always postulated. There are only a few discussions about this linearity in which it is deduced from some basic physical facts. Here, it is shown to be almost a mathematical consequence of the principle of relativity.     

Has the relativity principle in the special theory of relativity been fully verified by experiments?

Up to now all experiments used to verify the special theory of relativity have been done with the earth as the reference system. A suggested new Michelson-Morley experiment in Space Lab will be the first to examine the relativity principle in an inertial system other than the earth.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.     

The axiomatic foundations of the theory of special relativity

In this paper it is shown that (1) linear transformations more general than the Lorentz transformation—containing the Palacios and the Lorentz transformation as special cases—(2) and the principle of the constancy of the velocity of light (taken originally by Einstein together with the supposition of the linearity of transformation as fundamental hypotheses of the theory of special relativity)—can be deduced from Maxwell's equations for the electromagnetic fieldin vacuo (A ₁), the principle of relativity (A ₂) and the two following axioms (which do not contain explicitly the hypothesis of the isotropy of space!): (A ₃) to every event in the Galilean reference systemS there corresponds one and only one event in the systemS so that these two systems are connected by reversible single-valued functions, continuously differentiable as their inverse transformations, (A ₄) the constant relative velocitiesv _ss andv _ss betweenS andS are each other equal in magnitude and opposite in signv _ss =–v _ss To obtain uniquely the Lorentz transformation the following axiom has to be added: (A ₅) the distanceD of any two points at rest inS, situated in a plane orthogonal to the relative velocity betweenS andS is measuredS as independent of the sense of the velocity, i.e. if one changesv _ss into –v _ss the distanceD does not vary for an observer inS. Results of our theory are the ideas that (a) the fact that the Lorentz transformation is not the unique transformation leaving Maxwell's equations for the electromagnetic field in all Galilean systems of reference invariant but that there exists a more general transformation (containing these two transformations as special cases) leaving Maxwell's equations invariant; (b) that the Michelson-Morley as well as the Fizeau experiment does not represent an experimental proof in favour of the theory of special relativity. At the end of the paper the mutual relations between the principle of relativity (the axiomA ₁ together with the axiomA ₂), the axiomA ₅ and the possibility of the discernibility as well as the indiscernibility of right and left at the macrocosmic level is discussed.