A differential geometric context in which quantization is a necessary condition for gauge invariance

Abstract

It has recently been argued that quantization can be established within classical theory as a consequence of lost information. In this view, classical mechanics is regarded as a union of quantum mechanics and what are called 'hidden variables'. Hidden variable theories were first considered some years ago and abandoned because they did not produce new physics. They have now been revived however, because they appear to provide a logically sound means of relating classical and quantum theories. It is argued here that the Heisenberg uncertainty relations constitute a necessary condition for gauge invariance in the 5-dimensional Kaluza-Klein theory, where the fifth dimension of 5-spacetime is hidden as a 5-dimensional theory of general relativity is projected onto 4-spacetime.