  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 $\alpha.$ 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 $\alpha$ 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.
