Quantization in Spacetime from Null Paths in Higher Dimensions

TL;DR

This paper explores how quantization rules in 4D spacetime can emerge from null paths in a 5D manifold, linking higher-dimensional geometry with quantum behavior of particles.

Contribution

It demonstrates that standard quantization in 4D can be derived from the canonical metric in 5D null paths, connecting higher-dimensional geometry with quantum mechanics.

Findings

Standard quantization rules can be obtained from 5D null paths.

Massive particles can exhibit wave-like properties in this framework.

Implications for 4D/5D relationships are discussed.

Abstract

Massive particles on timelike paths in spacetime can be viewed as moving on null paths in a higher-dimensional manifold. This and other consequences follow from the use of Campbell's theorem to embed 4D general relativity in non-compactified 5D Kaluza-Klein theory. We now show that it is possible in principle to obtain the standard rule for quantization in 4D from the canonical metric with null paths in 5D. Particle mass can be wavelike, as suggested originally by Dirac, and other 4D/5D consequences are outlined.