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.     

A new approach to the theory of relativity. III. Problem of the ether

The considerations of the two former articles concerning the special and general theories of relativity are extended. The question of the physical reality of the ether and the interpretation of some cosmological problems are discussed. A view is expanded according to which the metric tensor g is taken as the energy momentum tensor of the ether. The gravitational equation of Einstein is considered to represent the equations of motion of the ether. The cosmological red shift is also interpreted in such terms.The considerations in this and the previous two articles^(1,2) are extensions of ideas the elaborations of which will be found in a monograph.⁽⁵⁾     

A new approach to the problem of motion in general relativity

The dynamical meaning of the equationsT ^/j/ij =0 is derived as a consequence of the mathematical structure of Einstein's equations. A generalization of Lichnerowicz's analysis of the gravitational equations is proposed.Lavoro eseguito nel centro di Matematica e Fisica Teorica del C.N.R. presso l'Università di Genova.     

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.     

A new approach to the theory of elementary domains

It is shown that Yukawa's theory of elementary domains can be formulated in a general framework. A quantized measure space structure of a space-time manifold is introduced so as to represent faithfully the elementary-domain structure. For a realization of elementary domains, an operator valued measure is defined such that it represents the spatiotemporal distribution of elementary domains. Effects of such a quantized topology are illustrated in the expressions ofS matrices.     

A new approach to diffusion-limited reaction rate theory

A new approach to the diffusion-limited reaction rate theory is developed on the base of a similar approach to consideration of Brownian coagulation, recently proposed by the author. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only to the special case of reactions with a large reaction radius, [`(r)]<sub>A</sub> << R<sub>AB</sub> << [`(r)]_B\bar r_A \ll R_{AB} \ll \bar r_B (where [`(r)]<sub>A</sub>\bar r_A, [`(r)]_B\bar r_B are the mean interparticle distances), and becomes inappropriate to calculation of the reaction rate in the case of a relatively small reaction radius, R_AB << [`(r)]<sub>A</sub>R_{AB} \ll \bar r_A, [`(r)]_B\bar r_B. In the latter, most general case particles collisions occurmainly in the kinetic regime (rather than in the diffusion one) characterized by a homogeneous (at random) spatial distribution of particles. Homogenization of particles distribution occurs owing to particles diffusion mixing on the length scale of the mean interparticle distance with the characteristic diffusion time being small in comparison with the characteristic reaction time. The calculated reaction rate for a small reaction radius in 3D formally (and casually) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, however, notably deviates at large times from the traditional result in the plane (2D) geometry.     

The stochastic quantum mechanics approach to the unification of relativity and quantum theory

The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.Supported in part by NSERC Grant A5208.     

A new approach to the theory of electrical conductivity of solids

Since the electrical conductance of a body is a measure of the fluctuations of charge in the state of thermodynamic equilibrium (Einstein 1906), an analysis of the fluctuations gives the value of the conductivity. Results are compared with those of Drude, Lorentz and Sommerfeld, the latter being based on a solution of the Boltzmann equation of transport. Brief reference is made to the possible inadequacy of the conventional model of a conductor for a fluctuation theory.     

Gravitational potentials: A constructive approach to general relativity

Recent investigations of the initial-value problem of general relativity have shown that the initial-value constraints can be formulated in all cases as a system of elliptic equations with well-defined physical and mathematical properties. The solutions of these equations can be regarded as generalized gravitational potentials. These potentials are interrelated and depend on their sources quasilinearly. They are particularly useful in analyzing asymptotically flat solutions of Einstein's equations. We have found from these results (1) a technique for constructing physically meaningful initial data in the integration of Einstein's equations, and (2) a method for characterization and analysis of the spacelike mass, momentum, angular momemtum, and multipole moments of gravitational fields.This essay received the third award from the Gravity Research Foundation for the year 1975. (Editor.)The research for this paper was partially supported by National Science Foundation grant GP43909 awarded to the University of North Carolina, Chapel Hill, North Carolina.     

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.     

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.     

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.     

T4 gauge theory of gravity and new general relativity

We formulate a space-time translationT ₄ gauge theory of gravity on the Minkowski space-time with appropriate choice of the Lagrangian. By comparing the energy-momentum law of this theory with that of new general relativity constructed on the Weitzenböck space-time we find that in the classical limit the gauge potentials correspond to the parallel vector fields in the Weitzenböck space-time and the gauge field equation coincides with the field equation of gravity in new general relativity in the linearized version. Thus we conclude that in the classical limit theT ₄ gauge theory of gravity leads to the new general relativity.     

New approach to relativity and gravitation

A theory of gravitation, where the stress-energy tensor of the gravitational field is part of the source term of the geometric curvatures, is presented. The theory predicts correctly all the Newtonian and post-Newtonian effects of gravity currently considered as crucial. For extremely strong and nonstatic fields, such as are presumed to exist in quasars and exploding stars, new predictions differing from those of the conventional theory are implied. In the correspondence limit of special relativity the theory recovers the conservation of energy-momentum properly and seems to represent a more satisfactory extension of special theory of relativity.     

A new test of general relativity

The emission of gravitational radiation by the recently discovered binary pulsar system will cause its orbital periodP to decrease at a rate which can now be predicted to beP ^–1 dP/dt= –(3 ± 2) × 10^–9yr^–1 if the only orbital perturbations are of general-relativistic origin. It is shown that other sources of period change are probably less important. The accuracy of this prediction as well as the possibility of its verification will improve greatly over the next few years. This is the first observation that can test general relativity beyond the post-Newtonian approximation.Work supported in part by National Science Foundation under grant No. MPS 74-15524.This essay received the fifth award from the Gravity Research Foundation for 1975 (Editor).     

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.     

On a new approach to the theory of the Heisenberg ferromagnet

Summing up the infinite classes of the Feynman diagrams for the spin operators with increasing power of the high density parameter we obtained the formulas both for the magnetization and the free energy. These formulas include the gaussian fluctuations of self-consistent field as well as scattering of spin waves on these fluctuations.     

Development of the new approach to the diffusion-limited reaction rate theory

The new approach to the diffusion-limited reaction rate theory, recently proposed by the author, is further developed on the base of a similar approach to Brownian coagulation. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only in the special case of reactions with a large reaction radius, $\bar r_A \ll R_{AB} \ll \bar r_B $ (where $\bar r_A $ and $\bar r_B $ are the mean inter-particle distances), and becomes inappropriate in calculating the reaction rate in the case of a relatively small reaction radius, $R_{AB} \ll \bar r_A ,\bar r_B $ . In the latter case, most important for chemical reactions, particle collisions occur not in the diffusion regime but mainly in the kinetic regime characterized by homogeneous (random) spatial distribution of particles on the length scale of the mean inter-particle distance. The calculated reaction rate for a small reaction radius in three dimensions formally (and fortuitously) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, but notably deviates at large times from the traditional result in the planar two-dimensional geometry. In application to reactions on discrete lattice sites, new relations for the reaction rate constants are derived for both three-dimensional and two-dimensional lattices.     

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.