Mach Principle

the assertion that the inertial properties of a body arise from the interaction of that body with infinitely distant large masses of the universe. (This is one of the simplest formulations of the Mach principle, which often differ significantly from one another.) All formulations of the Mach principle, from the “experimental principles” advanced by E. Mach in The Science of Mechanics (1883) to the current ones, develop or refine the concepts of inertia, mass, and inertial frame of reference and relate them to the properties of the universe as a whole. Mach sought to give the laws of mechanics such a form that they would be independent not only of uniform and rectilinear translational motion of the frame of reference (this had been already done by Galileo) but also of its rotation.

Rejecting Newtonian concepts of absolute space, absolute time, absolute motion, and mass as a measure of the quantity of substance, Mach made the first attempt to construct a mechanics based on the fact that only relative motions, time intervals, velocities, and accelerations are experimentally observable. Consequently, according to Mach, the motions of bodies (including accelerations) can be determined only with respect to other bodies. Mach proposed to define the accelerations of bodies with respect to the center of mass of the bodies that fill the entire universe: if it is assumed that there are large masses that are sufficiently (“infinitely”) distant from the observed body, then a fixed frame of reference (an inertial frame of reference after Newton) may be related to their center with a high degree of accuracy. The uniform and rectilinear motion of a body in such a frame means that it is possible to neglect the effect of masses located at finite distances as compared with the effect of the infinitely distant bodies.

The Mach principle played an important heuristic role in the building up of the general theory of relativity by A. Einstein. Einstein subsequently rejected the Mach principle because it did not satisfy the gravitational theory that he had developed. However, the Mach principle continues to be used extensively in theoretical works whose goal is the elucidation of the structure and properties of the universe as a whole. Here, the problem of coordinating the principle with the conclusions of cosmology, originating either in Einstein’s general theory of relativity or in other gravitational theories, encounters serious contradictions; the latter suggest that the Mach principle is either invalid or experimentally unverifiable. The most important contradictions are (1) the noncoincidence in arbitrary cosmological models of the locally inertial frame of reference with the frame of reference of the “fixed stars”; (2) the existence of nontrivial solutions of the gravitational equations in a vacuum, which signify that bodies have inertia relative to empty space; and (3) the ambiguity of the correspondence between the gravitational field (and, by virtue of the equivalence principle, the field of inertial forces) and the distribution of masses throughout the universe. One of the major contradictions between the Mach principle and observational data is the absence of anisotropy of masses on the earth, despite the asymmetric positioning of the solar system in our galaxy.