On the Emergence of Spacetime Dimensions from Kolmogorov Entropy

Abstract

This short pedagogical report is based on a couple of premises. First, it was recently shown that the long run of non-equilibrium Renormalization Group flows is prone to end up on strange attractors. As a result, multifractals are likely to provide the proper framework for the characterization of effective field theories. Secondly, it is known that multifractal analysis uses the Kolmogorov entropy (K-entropy) to quantify the degree of disorder in chaotic systems and turbulent flows. Building on these premises, the report details the remarkable connection between K-entropy, multifractal sets and spacetime dimensions. It also supports the proposal that near and above the Fermi scale, spacetime is defined by continuous and arbitrarily small deviations from four-dimensions.