Physical Identifications for the Algebraic Quantities of Five-Dimensional Relativity

TL;DR

This paper explores how five-dimensional relativity can interpret spacetime quantities as geometric properties of an extra dimension, assigning physical meanings to additional equations beyond Einstein's, and suggests tests for these identifications.

Contribution

It introduces a novel interpretation of five-dimensional relativity equations, assigning physical meanings to all involved equations, including conservation laws and scalar fields.

Findings

Scalar field acts like gravity but relates to inertial mass.

Four conservation equations correspond to 4D dynamics with variable cosmological 'constant'.

Proposes methods to test these geometric-physical identifications.

Abstract

When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become widespread to view the ten Einstein equations and the source terms of the energy-momentum tensor in this way. We now assign physical meanings to the other five equations involved. The scalar field acts like gravity, but concerns inertial as opposed to gravitational mass. The other four equations are conservation laws for 4D dynamics, but where the mass of a test particle is related to a local value of the cosmological 'constant'. Ways of testing these identifications are suggested.