Physical Identifications for the Algebraic Quantities of Five-Dimensional Relativity

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.