CONSEQUENCES OF COVARIANCE IN KALUZA-KLEIN THEORY

When the (3 + 1) Einstein equations with matter are regarded as a subs et of the (4 + 1) Kaluza-Klein equations in apparent vacuum, the recov ery of appropriate properties of matter requires in general that the ( 4 + 1) metric depend on all the coordinates including the extra one. W e display some consequences of (4 + 1) covariance through the use of e xact solutions and coordinate transformations. We conclude that 4-D ph ysics can be regarded as taking place on a hypersurface in 5-D, a math ematical condition which may be set by a physical one on the rest mass es of particles.