Critical reviews and tests of the foundations of special relativity

The origin of the equilibrium paradoxes of special relativity is here analysed. We show that static forces, as defined by Hooke's law, do not transform in the same way as the usual dynamical forces, thus giving rise to the paradoxes. This inconsistency justifies the present search for alternative theories such as the modern ether theories. Some crucial tests are proposed.1. The stresses in S have to be calculated on planes which are not parallel to the x axis in S because of length contraction. Thus, the functional dependence of y' = y' (x,y) is y' = _{u x} ^-1 y, at x' = 0.2. This test is being carried out at the ULA, Mérida; see Refs. 6 and 17.     

The foundations of relativity

In a previous paper a stochastic foundation was proposed for microphysics: the nonrelativistic and relativistic domains were shown to be connected with two different approximations of diffusion theory; the relativistic features (Lorentz contraction for the coordinate standard deviation, covariant diffusion equation) were not derived from the relativistic formalism introduced at the start, but emerged from diffusion theory itself. In the present paper these results are given a new presentation, which aims at elucidating not the foundations of quantum mechanics, but those of relativity. This leads to a discussion of points still controversial in the interpretation of relativity. In particular two problems appear in a new light: the character of time and length alterations, and the privileged role of the velocityc. Besides, the question of a possible limitation of relativity (and more generally of the laws of mechanics) in the domain of particle substructure is raised and supported by exemples drawn from the hydrodynamical model of a spinned particle. Suggestions are presented for the possibility of a deeper conceptual unification of special and general relativity.     

Experiment for testing special relativity theory

An experiment aimed at testing special relativity via a comparison of the velocity of a nonmatter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay ²²Na (β+)²²Ne is proposed.

     

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.     

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.     

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 principle of relativity and the special relativity triple

Based on the principle of relativity and the postulate on universal invariant constants (c,l) as well as Einstein's isotropy conditions, three kinds of special relativity form a triple with a common Lorentz group as isotropy group under full Umov–Weyl–Fock–Lorentz transformations among inertial motions.     

A hundred years of special theory of relativity

A special theory of relativity is considered here as an episode of non-Euclidean geometry. Special attention is drawn to the fact that the replacement of the fifth Euclidean postulate by the Lobachevsky postulate of parallel straight lines in the space of velocities of a material point leads to the replacement of the postulate of the same time rate by the postulate of the same velocity of light in all inertial reference systems.     

Segal's chronometric theory as a completion of the special theory of relativity

The main ideas and conclusions of the chronometric theory of I. Segal are surveyed. This theory differs from the special theory of relativity in that it replaces Minkowski space by a modelM=R ¹ ×S ³, but without specifying in the latter a Lorentz metric. In modelM a 15-dimensional conformal group acts globally. Some successful applications of the chronometric theory to cosmology are mentioned, and a number of examples are cited to show the prospects for its use in the physics of elementary particles. The chronometric theory is briefly compared with the twistor program of Penrose.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 84–89, August, 1993.     

R×S 3 special theory of relativity

A theory of relativity, along with its appropriate group of Lorentz-type transformations, is presented. The theory is developed on a metric withR×S ³ topology as compared to ordinary relativity defined on the familiar Minkowskian metric. The proposed theory is neither the ordinary special theory of relativity (since it deals with noninertial coordinate systems) nor the general theory of relativity (since it is not a dynamical theory of gravitation). The theory predicts, among other things, that finite-mass particles in nature have maximum rotational velocities, a prediction highly supported by recent experiments on 14 nuclei, such as ¹⁵⁹ Yb that survives fission with angular velocities of up to 0.9 of the predicted value but does not reach it.Address during academic year 1985/1986: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742.     

Exposition of magnetostatics based on the special theory of relativity

We present the division Magnetostatics in the course of general physics, with the treatment based on the deductions of the special theory of relativity, the invariance of the electric charge, Coulomb's law, and the superposition principle of fields. The exposition begins with the analysis of the interaction of two point electric charges with arbitrary orientations of their velocities.Translated from Izvestiya Vysshikh Uchenbnykh Zavedenii, Fizika, No. 4, pp. 61–65, April, 1985.     

Is quantum theory compatible with special relativity?

How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.     

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.     

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.     

Formalism to deal with Reichenbach's special theory of relativity

The objective of this article is to provide a formalism to deal with the special theory of relativity (STR, in short) as riewed by Reichenbach, according to which STR involves an ineradicableconventionality of simultaneity. One of the two postulates of STR asserts that, in empty space, the one-way speed of light relative to inertial frames is constant. Experimental evidence, however, is related to the constancy of the round-trip speed of light and has no bearing on one-way speeds. Following Reichenbach's viewpoint, we relax the second postulate of STR, abandoning the constancy of the one-way speed of light to the more realistic one asserting the constancy of the round-trip speed of light. This, in turn, results in a formalism to deal with Reichenbach's special theory of relativity (RSTR, in short) in which the two one-way speeds of light in empty space, C_±, in the two senses of a round-trip are arbitrarily selected in such a way that their harmonic mean is the measurable round-trip speed of light, c. Experimentally, RSTR and STR are indistinguishable and, hence, represent the same physical theory. It is only the formalism that we use to deal with STR which is extended in RSTR to accommodate the immeasurability of one-way velocities. The usefulness of the proposed formalism to study special relativity is demonstrated.     

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.     

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.