Mach’s Principle Revised: Is the Inertia, and also Gravitational Interaction of Bodies, Determined by Their Long-Range Gravitational Interaction with Distant Matter in the Universe?

The work analyzes the basic assumption in Mach’s principle, namely that the inertia of material bodies is determined by their gravitational interaction with distant masses in the universe. However, while Mach’s principle is based on the so-called “long-range gravitational interaction” characterized by an infinitely large propagation velocity, our study is based on a “modified” long-range principle, assuming a very large but finite propagation velocity of the gravitational interaction between local material objects and distant matter. Thus, it is postulated that there are two types of gravitational interaction—short-range gravitational interaction between local objects and long-range gravitational interaction between local objects and distant matter in the universe, which are characterized by different propagation speeds, but with the same gravitational constant. On the basis of the modified long-range principle, a model of distant matter is built in the form of a hollow spherical layer with negligible thickness. The phenomenological assumption is made that the movement with acceleration of the local reference frame (RF) is related to a change in the spherically symmetric distribution of the lines of gravitational interaction of this RF with distant matter, which is expressed in a corresponding asymmetric distribution of the effective mass density on the hollow sphere. A simplified (idealized) model of the effective change of the hollow sphere of distant matter by cutting off separate segments of the sphere is proposed. On the basis of the model, the possibility of representing the inertial effects in three simplest types of reference frames through a corresponding gravitational interaction is considered: 1) inertial RF; 2) RF moving in a straight line with constant acceleration; 3) RF rotating with constant angular velocity. Expressions were obtained for the gravitational accelerations acting on the test body located inside the hollow sphere with a corresponding change (“cutting”). It is concluded that these accelerations can in a first approximation represent the inertial accelerations of the main types noted above. It is shown that in order to obtain reasonable values of the truncation parameters of the hollow sphere, it is necessary to assume that the gravitational interaction inside this sphere is not of the Newtonian type, i.e. the same depends on the distance not according to the law $$