  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.
