Interpretation of the Five Dimensional Quantum Propagation of a Spinless Massless Particle

Abstract

We consider a five dimensional (5D) space-time with a space-like fifth dimension. We implement a quantum formalism by path integrals, and postulate that all the physical information on a 5D massless particle propagation is provided by the statistics over null paths in this 5D space-time. If the 5D metric is independent of the fifth coordinate, then the propagation problem can be reduced to four dimensions by foliation along the fifth coordinate, and we obtain a formulation of 4D Quantum Mechanics. If the 5D metric is independent of time, we foliate along the time coordinate, and obtain a formulation of 4D Statistical Mechanics. If the 5D metric is independent of both time and the fifth coordinate, then Quantum and Statistical Mechanics are pictures of the same 5D reality. We also discuss the foliation of a proper space dimension, the Klein-Gordon equation, and a 5D Special Relativity, completing our interpretation of the 5D geometry.