Mach's Principle and Higher-Dimensional Dynamics

TL;DR

This paper explores the connection between Mach's principle and higher-dimensional theories, discussing recent experimental verification of gravitomagnetism and proposing a 5D extension of Einstein's gravity to incorporate Machian ideas.

Contribution

It introduces a 5D Machian extension of general relativity, linking inertial mass to an extra dimension and embedding Einstein's theory in a Ricci-flat 5D manifold.

Findings

Recent measurement of Earth's gravitomagnetic field supports Mach's principle.

Proposes a 5D framework where mass is associated with an extra dimension.

Embeds Einstein's gravity in a Ricci-flat 5D manifold to incorporate Machian ideas.

Abstract

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci-flat 5D manifold such that the 4D energy-momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented.