Space Time as a Random Heap

Abstract

In this paper, we demonstrate how space-time is, rather than a differentiable manifold, a Random Heap, and how this ties up with fractal dimension 2 of a Quantum Mechanical path. In this light, we can see that there is a harmonious convergence between the stochastic approach of Nelson and the de Broglie-Bohm approach. These considerations are shown to lead to the emergence of special relativity and Quantum Mechanics.