CONSEQUENCES OF COVARIANCE IN KALUZA-KLEIN THEORY

When the (3 + 1) Einstein equations with matter are regarded as a subset of the (4 + 1) Kaluza-Klein equations in apparent vacuum, the recovery of appropriate properties of matter requires in general that the (4 + 1) metric depend on all the coordinates including the extra one. We display some consequences of (4 + 1) covariance through the use of exact solutions and coordinate transformations. We conclude that 4-D physics can be regarded as taking place on a hypersurface in 5-D, a mathematical condition which may be set by a physical one on the rest masses of particles.