On the Physical Principles of Gravitation

As is well known, the general theory of relativity (GTR) proceeds from the so-called equivalence principle according to which the dynamic effects of gravitation are identified with the kinematic effects of accelerated motion. In this theory, gravitation is associated with the Riemannian structure of the pseudo-Euclidean space-time (described by the metric tensor and the Riemannian connectivity and the curvature related with this tensor) specified in the four-dimensional space-time continuum. In the present work, it is first demonstrated that on the level of elementary particles (within the framework of the theory of quantized fields), the equivalence principle is violated. It is established that elementary particles with different masses (for example, electron and proton) move in the external gravitational field with different accelerations. In this connection, a new approach to the problem of gravitational interactions is suggested based on deformations of a latent dynamic system conditionally called ether that underlies elementary particle theory [2].     

On quantum field theory in gravitational background

We discuss quantum fields on Riemannian space-time. A principle of local definiteness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows us to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non-stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non-inertial motion are added.     

Electrodynamics of a continuous medium in a system with specified structure

It is shown that electrodynamics can be considered not only in Minkowski space but also in Riemannian space-time. The exact solutions for the electric field within and beyond a charged plate and a sphere and the space-time geometry are found without applying the Einstein equations. The space-time geometry of a Born-rigid noninertial frame of reference (NFR) with global linear acceleration in space-time having constant curvature is obtained on the basis of the structural equations (integrability conditions). A new Lorentz-covariant condition of stationarity for possible solutions to the Maxwell equations for the particles frozen in a Born-rigid NFR is formulated. In an inertial frame of reference this condition is equivalent to zero four-curl of the field of four-accelerations of particles. This condition provides zero relativistic generalized radiation friction force. The propagation of electromagnetic waves in this NFR and the Doppler effect are described. The limitations imposed on the energy-momentum tensor in the Einstein equations are derived.     

Solitary waves on a curved space-time

A nonlinear partial differential equation is derived which admits plane solitary waves on a conformally flat Riemannian space-time. The metric is determined by the amplitude of these waves. By interpreting these solitary waves as particles we arrive at the following picture: these particles are confined to regions exhibiting singular (very large) amplitudes in an otherwise continuous wavetrain. There is, thus, no distinction between the notion of a particle and that of a wave.     

Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.     

On the origin of cosmic rays and the value of fundamental length

It is suggested that the physical mechanism responsible for the acceleration of cosmic rays is due to the stochastic (or fluctuational) structure of space-time at small distances. A method of introducing fluctuations in a conformally flat Riemannian space-time metric due to ultrahigh energy particles is presented, from which a nonlinear dynamics of particles and equations for the electromagnetic field are obtained. The former admits the acceleration mechanism for cosmic-ray particles and the extreme energy increases during the evolution of the Universe. In our model the energy of the cosmic-ray particle and its radius (the effective Schwarzschild), the age of the universe, and the value of the fundamental length are connected with one another and are determined by a unified formula, Einstein's relation for the relativistic particle energy. It allows one to define experimentally the value of the fundamental length, which is l=1.56×10 ^–33 cm for the maximum proton energy observed in cosmic rays. The problem of the energy spectrum of the cosmic rays and the ratio of intensities of the electron component to the proton component at the same energy level are also discussed.On leave of absence from the Academy of Sciences, Mongolian People's Republic, Ulan-Bator, Mongolia.     

On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles.     

Conservation laws in General Relativity in the Vierbein formalism

Conservation laws for dynamical systems in Riemannian space-time in the Vierbein formalism are deduced from the existence of motions in the space-time. The result is applied to Dirac's equation in General Relativity. Research partially supported by the National Research Council of Canada.     

Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant

The initial value problem for Einstein's field equations with positive cosmological constant is analysed where data are prescribed at past conformal infinity. It is found that the data on past conformal infinity are given, up to arbitrary conformal rescalings, by a freely specifyble Riemannian metric and a trace-free, symmetric tensorfield of valence two, which satisfies a divergence equation. For each initial data set exists a unique (semi-global) past asymptotically simple solution of Einstein's equations. The case is discussed where in such a space-time exists a Killing vector field with a time-like trajectory which approaches a point p on conformal infinity. It is shown that in a neighbourhood of the trajectory near p the space-time is conformally flat.     

Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint

We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible—that is, as far as the projective invariance of the assumed gravitational Lagrangian will allow. The outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and tracefree nonmetricity). The vanishing of the trace of the nonmetricity is due to the remaining vector constraint. We also discuss the physical significance of the relaxation of the Riemannian constraint, the possible relaxation of the vector constraint, the notion of the hypermomentum current, and its possible relation to elementary particle physics.     

How can the neutrino interact with the electromagnetic field?

Maxwell electrodynamics in the fixed Minkowski space-time background can be described in an equivalent way in a curved Riemannian geometry that depends on the electromagnetic field and that we call the electromagnetic metric(e-metric for short). After showing such geometric equivalence we investigate the possibility that new processes dependent on the e-metric are allowed. In particular, for very high values of the field, a direct coupling of uncharged particles to the electromagnetic field may appear.     

Some remarks on nonlocal field theory and space-time quantization

From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.     

Relativistic hadronic mechanics: Nonunitary, axiom-preserving completion of relativistic quantum mechanics

The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincaré symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements.     

Weak equivalence principle and gauge theory of the tetrad gravitational field

The tetrad theory of gravitation corresponding to the Treder formulation of the weak equivalence principle is incompatible with the customary method for constructing a gauge theory for a tetrad gravitational field. In this formulation, the Lagrangian of the nongravitating mass is a direct covariant generalization of the partially relativistic expression to a Riemannian space-time V₄. This incompatibility is at odds with the resutt found in the tetrad formulation of the general theory of relativity derived from the requirement of localization of the Poincaré group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 18–21, April, 1978.     

Areal objects and the problem of the λ term in the theory of gravitation

The following areal objects are considered: an ether thread contracting two material points and a multidimensional ether fibre in the pseudo-Euclidean world of events. An ether space-time model with an arbitrarily determined Riemannian metric is constructed and the problem of the λ term in Einstein equations is discussed in this regard.     

Causal independence

Causal independence of the simultaneous positions and momenta of two distinguishable particles in nonrelativistic physics and causal independence of events in two relatively spacelike regions of space-time in relativity are analyzed and discussed. This review paper formulates causal independence in a general and operational way and summarizes the inferences drawn from it in non-relativistic quantum mechanics, classical relativistic point mechanics, quantum field theory, and classical field theory. Special attention is given to the open question of the relationship between local independence and commutativity in quantum field theory.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Two studies concerning the Michelson-Morley experiment

In the first of these two studies it is argued that the discrepancy between the predicted and actual outcome of the Michelson-Morley experiment is due to the use of Newton's velocity addition theorem in conjunction with an electromagnetic theory of light. The ether hypothesis is not directly affected at all. The second study is a case study of the removal of a clash in physics generated from the outcome of an experiment. The clash due to the Michelson-Morley experiment gave rise to a program of revision. In the process of implementation of this program Newtonian mechanics was remolded. It is argued that the Riemannian space-time in Einstein's general theory of relativity may be regarded as a successor of the classical ether.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.