Weak circulation theorems as a way of distinguishing between generalized gravitation theories

We proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here we pose the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory.     

General relativity without tensors in a central field

For static and spherically symmetric gravitational fields in the general theory of relativity, it is found possible completely to avoid tensor analysis. The principle of equivalence, illustrated by Einstein's elevator, is used to obtain Schwarzschild's equation, on which the three well-known tests of the general theory are usually based. The derivation is guided, as with Einstein, by Poisson's (Laplace's, in empty space) equation, which here can be solved by simple calculus.     

The boundary of a boundary principle: A unified approach

The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily.     

Energy in a highly ordered universe

A new theory of particles proposed in an earlier paper is now applied to explain energy. Having earlier derived the Rydberg formula for atomic spectra without using the Pauli principle, the authors now derive the photoelectric effect, deflection of light by gravitation, and Planck's law for blackbody radiation without using Planck's assumption on energy quanta or Einstein's theory of general relativity.     

The Markov blanket trick: On the scope of the free energy principle and active inference

The free energy principle (FEP) has been presented as a unified brain theory, as a general principle for the self-organization of biological systems, and most recently as a principle for a theory of every thing. Additionally, active inference has been proposed as the process theory entailed by FEP that is able to model the full range of biological and cognitive events. In this paper, we challenge these two claims. We argue that FEP is not the general principle it is claimed to be, and that active inference is not the all-encompassing process theory it is purported to be either. The core aspects of our argumentation are that (i) FEP is just a way to generalize Bayesian inference to all domains by the use of a Markov blanket formalism, a generalization we call the Markov blanket trick; and that (ii) active inference presupposes successful perception and action instead of explaining them.     

A new theory of elementary matter

This is the first of a series of articles that reviews and expands upon a new theory of elementary matter. This paper presents an exposition of the philosophical approach and its general implications. The ensuing explicit form of the mathematical expression of the theory and several applications in the atomic and elementary particle domains will be developed in the succeeding parts of this series.The theory is based on three axioms: the principle of general relativity, a generalized Mach principle, and a correspondence principle. The approach is basically a deterministic, relativistic field theory which fully incorporates the idea that any realistic physical system is in facta closed system, without separable parts. It is shown that the most primitive mathematical expression of this theory, following as anecessary consequence of its axioms, is in terms of a set of coupled nonlinear spinor field equations. Nevertheless, the exact formalism is constructed to asymptotically approach the quantum mechanical formalism for a many-particle system, in the limit of sufficiently small energy-momentum transfer among the components of the considered closed system. Thus, all of the mathematical predictions of nonrelativistic quantum mechanics are contained in this theory, as a mathematical approximation. However, predictions follow from the exact form of this theory (where energy-momentum transfer can be arbitrarily large) that are not contained in the quantum theory.     

Steps Towards the Axiomatic Foundations of the Relativistic Quantum Field Theory: Spin-Statistics, Commutation Relations, and CPT Theorems

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed form the notion of basic field and system of basic fields. In comparison with others formulations, in our realistic approach fields are regarded as real things with symmetry properties. Finally, the general structure is contrasted with other formulations.     

On the inertial mass concept in special and general relativity

Inertial mass in relativity theory is discussed from a conceptual view. It is shown that though relativistic dynamics implies a particular dependence of the momentum of a free particle on its velocityin special relativity, which diverges as v approaches c, the inertial mass itself of a moving body remains constant, from any frame of observation. However, extension to general relativity does conceptually introduce variability of the inertial mass of a body, through a necessarily generally covariant field theory of inertia, when the Mach principle is incorporated into the theory of general relativity, as a theory of matter.     

Scalar-tensor theory and propagating torsion theory

We prove that scalar conformal transformations can convert the variational principle of the propagating torsion theory into the variational principle of general scalar-tensor theory, and show that scalar-tensor theory is conformally equivalent to propagating torsion theory.     

Cosmological models in general relativity and brans-dicke theories: a comparison

We review general relativistic and Brans-Dicke cosmological models of the early universe and for the present phase. Both theories render similar results, in general, as far as Mach's principle is concerned. There is some difference in the stability problem for the inflationary phase, and we point out how to test one theory against the other experimentally.     

Matter and geometry in a unified theory

The prediction of general relativity on the gravitational collapse of matter ending in a point is viewed as an absurdity of the kind to be expected in any consistent physical theory due to ultimate conflicts of the axioms of geometry with the properties of physical objects. The necessity to introduce a probability interpretation for the solution of partial differential equations in space time for quantum theory points to similar roots. It is pointed out that quantum theory in the very small is not going to eliminate the problem, but macroscopic quantum effects in the large, modifying the properties of the horizon, may achieve it. Solutions such as wormholes allow as much empirical evidence as any science fiction. The present approach considers successive modifications of the field equations and equations of motion of gravitational theory by admixture of terms with higher derivatives. The rigorous application of a gauge principle combines Einstein's equations with the tensor analog of Maxwell's equations which are of third order for the metric. It is speculated that the natural presence of torsion in such a gauge theory is related to matter sources.     

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 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.     

Nonsingular field model of a particle

The concept of a particlelike solution of the equations for interacting fields with allowance for gravitation is discussed. An example of a nonsingular spherically symmetric solution is obtained for interacting scalar and electromagnetic fields in the general theory of relativity; the regularity of the metric is ensured by the finiteness of the matter and total energies, and by the equivalence principle. It is shown that these conditions are also satisfied with interacting fields that are singular at the center.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 69–74, November, 1978.     

An axiomatization of general relativity

An axiomatization of the general theory of relativity is proposed. The assumed philosophical background is critical realism. None of the principles commonly considered as founding the theory, such as (a) the equality of inertial and gravitational mass, (b) the principle of equivalence, (c) the principle of general covariance, (d) the geodesic postulate, and (e) Mach's principle, are taken as axioms in our system.     

Some remarks on general covariance of quantum theory

If one accepts Einstein's general principle of relativity (covariance principle) also for the sphere of microphysics (quantum mechanics, quantum field theory, theory of elementary particles), one has to ask how far the fundamental laws of traditional quantum physics fulfil this principle. The reason for presenting this short paper is to draw attention to a series of papers that have appeared during the last years, in which the author criticized the usual scheme of quantum theory (Heisenberg picture, Schrödinger picture, etc.) and presented a new foundation of the basic laws of quantum physics, obeying the principle of fundamental covariance (Einstein's covariance principle in space-time and covariance principle in Hilbert space of quantum operators and states) [1].Dedicated to Achille Papapetrou on the occasion of his retirement.     

A geometrical theory of spin motion

A discussion of the fundamental interrelation of geometry and physical laws with Lie groups leads to a reformulation and heuristic modification of the principle of inertia and the principle of equivalence, which is based on the simple de Sitter group instead of the Poincaré group. The resulting law of motion allows a unified formulation for structureless and spinning test particles. A metrical theory of gravitation is constructed with the modified principle, which is structured after the geometry of the manifold of the de Sitter group. The theory is equivalent to a particular Kaluza-Klein theory in ten dimensions with the Lorentz group as gauge group. A restricted version of this theory excludes torsion. It is shown by a reformulation of the energy momentum complex that this version is equivalent to general relativity with a cosmologic term quadratic in the curvature tensor and in which the existence of spinning particle fields is inherent from first principles. The equations of the general theory with torsion are presented and it is shown in a special case how the boundary conditions for the torsion degree of freedom have to be chosen such as to treat orbital and spin angular momenta on an equal footing. The possibility of verification of the resulting anomalous spin-spin interaction is mentioned and a model imposed by the group topology ofSO(3,2) is outlined in which the unexplained discrepancy between the magnitude of the discrete valued coupling constants and the gravitational constant in Kaluza-Klein theories is resolved by the identification of identical fermions as one orbit. The mathematical structure can be adapted to larger groups to include other degrees of freedom.     

Remarks on the relation between general relativity and quantum theory

A discussion of the diffraction and scattering of particles by a grating shows that the experiment discussed by H. Hönl and by L. Rosenfeld in 1965 and again in 1981 does not reveal any contradiction between general relativity and quantum theory. Moreover, these theories, in principle, cannot refute one another because the (weak) principle of equivalence, underlying general relativity theory, entails that gravitation does not alter the laws of microphysics.Dedicated to the memory of Prof. Helmut Hönl (1903–1981).     

Killing time

Theoretical consequences of the gravitational origin of inertial reaction forces, that is, Mach's principle, are explored. It is argued that Mach's principle leads to the conclusion that time, as we normally treat it in our common experience and physical theory, is not a part of fundamental reality; the past and future have a real, objective existence, as is already suggested by both special and general relativity theory. A laboratory scale experiment whereby Mach's principle, and thus radical timeless ness, can be established is mentioned.     

Gravitation in flat space. principle of equivalence for massive bodies of gravitational structure

It is shown that in a new nonmetrical nonlinear theory of gravitation in flat space [1, 2], satisfying the four classical effects of the general theory of relativity and the weak principle of equivalence for massive bodies of electromagnetic structure, the weak principle of equivalence is also satisfied for massive bodies of gravitational structure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 26–32, May, 1979.