To quantum mechanics through random fluctuations at the Planck time scale

Abstract

We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the asymptotic expansion of classical statistical averages with respect to a small parameter $α.$ Therefore statistical predictions of QM are only approximative and a better precision of measurements would induce deviations of experimental averages from quantum mechanical ones. In this note we present a natural physical interpretation of $α$ as the time scaling parameter (between quantum and prequantum times). By considering the Planck time $t_P$ as the unit of the prequantum time scale we couple our prequantum model with studies on the structure of space-time on the Planck scale performed in general relativity, string theory and cosmology. In our model the Planck time $t_P$ is not at all the {\it "ultimate limit to our laws of physics"} (in the sense of laws of classical physics). We study random (Gaussian) infinite-dimensional fluctuations for prequantum times $s\leq t_P$ and show that quantum mechanical averages can be considered as an approximative description of such fluctuations.