Interaction in scalar theories of gravitation

It is shown that O. Bergmann's (1956) scalar field theory is similar to G. Nordström's (1912). The interaction term in the former's theory is equivalent to non-linearising the Nordström theory by including twice the energy density of the field as a source term in the Poisson-like equation. It is further shown that, if the interaction term (1+v) in Bergmann's theory is replaced by (1+v)², then the subsequent field equation appears more reasonable in that the energy density (not twice) appears as a source term.     

Plasma,gravitation, and force-free geometries

We show that it is possible, by a suitable choice of metrics and connections, to construct for a wide class of relativistic equations of motion a geometry wherein the interacting particles become free of nongravitational forces and move on autoparallels. Some examples prove the consistency of this extended geodesic principle.     

Relativistic gravitation

Classical dynamics, often called 'molecular dynamics' when applied to atoms and molecules, is much easier than solving the many-body Schrodinger equation for a number of reasons. In particular, correlation and rearrangement are simple in classical dynamics. Fermion molecular dynamics (FMD) is a quasi-classical method for treating quantum-mechanical systems using classical equations of motion with momentum-dependent model potentials added to the usual Hamiltonian. These model potentials constrain the motion to satisfy the Heisenberg uncertainty and the Pauli exclusion principles. We discuss the foundations of the FMD model and its applications to atomic and molecular structure, ion-atom collisions, stopping powers, formation of antiprotonic atoms, and multiple ionization of atoms in strong laser fields.     

A non-covariant theory of gravitation,I

Homogeneous isotropic models of the universe, based on the general theory of relativity, lead to the existence of a preferred frame of reference, which is similar to the absolute space of, Newton, and a preferred time coordinate, which resembles the absolute time of Newton. These concepts seem to be in contradiction to the principle of covariance on which the general relativity theory is based. A theory of gravitation is therefore proposed which uses the world picture of general relativity but is not covariant. In the three crucial tests, the proposed theory gives the same results as the general relativity theory. However, in contrast to general relativity, the present theory predicts the emission of gravitational waves by spherically symmetric systems, and gravitational waves are found, in general, to have both transverse and longitudinal components.     

A non-covariant theory of gravitation,II

This is a continuation of a previous paper, in which a theory of gravitation was developed based on the existence of a preferred frame of reference and a preferred time coordinate in the universe. The gravitational field equations are derived with the help of a variational principle containing three constants. Two relations among the constants are introduced, leaving one of them arbitrary. This constant does not affect the precession of the perihelion of Mercury but does affect the behaviour of gravitational waves. By changing one of the relations among the constants, one can account for the discrepancy in the precession of the perihelion associated with the oblateness of the sun, as found by Dicke and Goldenberg.     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Information and gravitation

An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric is proportional to a probability amplitude φ_uv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired in a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor T_μv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric and associated equations in the probability amplitudes φ_uv. The gauge condition φ _v ^uv =0 (Lorentz condition) and conservation of energy and momentum T_v ^μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φ_uv.     

Gauge gravitation theory

The particularity of the gauge gravitation theory is that Dirac fermion fields possess only Lorentz exact symmetries. It follows that different tetrad gravitational fieldsh define nonisomorphic representations _h of cotangent vectors to a space-time manifoldX ⁴ by Dirac's-matrices on fermion fields. One needs these representations in order to construct the Dirac operator defined in terms of jet spaces. As a consequence, gravitational fieldsh fail to form an affine space modeled after any vector space of deviationsh'–h of some background fieldh. They therefore fail to be quantized in accordance with the familiar quantum field theory. At the same time, deformations of representation _h describe deviations ofh such thath + is not a gravitational field. These deviations form a vector space, i.e., satisfy the superposition principle. Their Lagrangian, however, differs from familiar Lagrangians of gravitation theory. For instance, it contains masslike terms.     

Self-coupled scalar gravitation

The requirement in scalar theories of gravitation that the source of the field includes the trace of its own stress tensor is investigated in two models: (1) The geometrical Nordstr0m theory, which is the conformally flat metric analog of Einstein's theory. (2) The ostensibly non-geometrical flat space system of Freund and Nambu. Both are derived in closed form as cubic self-interacting systems and shown to be equivalent.Supported in part by U.S.A.F., O.A.R. under O.S.R. grant 70-1864.Supported by the National Research Council of Canada under grant 694.     

Entropy and gravitation

Einstein's gravitational theory is analyzed from a thermodynamic point of view. A thermodynamic potential characterizing the sources of gravitational fields is presented. By means of this potential the entropy production density is derived. Einstein's equations with dissipative terms appear as linear phenomenological laws in the sense of irreversible thermodynamics. Some thermodynamic influences on gravitational phenomena are discussed.     

Weber electrodynamics: part III. mechanics,gravitation

Weber electrodynamics predicts the Kaufmann-Bucherer experiments and the fine structure energy level splitting of the H-atom (neglecting spin) without mass change with velocity (i.e., mass ). The Weber potential for the gravitational case yields Newtonian mechanics, confirming Mach's principle. It provides a cosmological condition yielding an estimated radius of the universe of 8 × 10⁹ light years. Despite these successes, the independent evidence for Kaufmann mechanics, where mass changes with velocity (i.e., mass ) is convincing. Perhaps a slight alteration may make the Weber theory compatible with Kaufmann mechanics.     

Scale-covariant gravitation and electromagnetism

The theory of scale-covariant gravity is extended to include charged matter and electromagnetism at the classical level. The possibility of charge creation exists and the creation rate of charge differs from the creation rate of matter. A variational principle for scale-covariant gravity and electromagnetism coupled to a charged perfect fluid is given.Supported by a grant from the National Research Council of Canada.     

Reference systems and gravitation

It is shown how the formalism of the tetrad theory of gravitation used by Treder (1967a, b, 1970) follows from the more general fibre bundle formalism. This is of interest in the study of the relations between tetrad theories and the general theory of relativity. In particular, the breaking of the principle of general relativity and the interpretation of tetrad fields as reference systems are considered in greater detail.     

Many-time hamiltonian gravitation theory

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

Lorentz-Covariant theory of gravitation

A Lorentz-covariant theory of gravitation is proposed. It is based on a simple form of the Lagrangian for the gravitational field. The field equations have a simple mathematical structure where the energy-momentum tensor of matter and of gravitational field is the source of the field. The theory agrees with general relativity for the three well-known effects, i.e., red shift, deflection of light, and perihelion.     

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (Sect. 4.1). For the standard test cases (PPN scheme, Schwarz schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.     

Bi-metric theories of gravitation

The bi-metric theory recently proposed by Rosen is examined in the case of superdense static objects.     

A compensatory gravitation model

A gauge gravitation model is proposed which uses the operation of parallel transfer of bundle layers along the integral curves of the vector fields in the Minkowski space as symmetry. A modification of the Yang-Mills gauge formalism is given on the basis of the foregoing model. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 75–81, May, 2006.     

Spin strings in gravitation

Vibrating annular singular filaments in the Kerr-Schild metrics which are analogues of the strings of the dual models are considered. The spin excitation of the filament is related to the propagation of an electromagnetic wave along it. The model is described by a point source undergoing periodic motion in the complex domain.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 113–119, July, 1978.