Conservation Laws in the Compensation Model of Gravitation

Abstract

Two methods for the derivation of the dynamical conservation laws in the compensation model of gravitation are proposed. On the basis of these two methods, the local distinction between the inertial and gravitational properties of matter is elucidated. In field theory dynamical conservation laws are obtained with the help of Noether's theorem and by extracting them from the field equations describing the interactions. These methods are not equivalent. The first makes use of extremals of a closed physical system, the second makes use of extremals of its field subsystem. We will show that these methods lead to different results in the compensation model of gravitation (CMG) (1). The importance of this fact is elucidated by noting that these methods allow one to construct independent representations in the CMG of the inertial and gravitational properties of matter. We mention some positions of this theory. Its main novelty consists in the choice of symmetry of the gravitational interaction: the operation of parallel transport along integral curves of some vector field in Minkowski space М4. It is in just this way that non-uniform T(4) translations are treated in (1). This made it possible to reveal the special transformational properties of known fields and to represent gravity as a gauge theory of a new mixed tensor field G ν μ . The CMG is constructed in analogy with Yang-Mills theory and generalizes it. The choice of the field Lagrangian here turned out to be tightly linked with symmetries in М4. This function does not contain second derivatives and satisfies all of the requirements placed on such constructions. The corresponding equations formally reproduce the tetrad representation of Einstein's equations, but the concepts of the base space and the tangent space change places. The CMG is constructed in flat М4. Here the integral conservation laws are easily formulated if their local analogs, the covariant equations of continuity, are known (2). In what follows we restrict ourselves to a derivation of precisely these local laws.