A MODEL OF PHYSICAL SPACE-TIME AS A TRAJECTORY OF A RANDOM PROCESS IN EXTERNAL PARAMETRIC TIME

A model of physical space-time in the form of a trace from a random walk on the support of some finitely generated algebra is considered. The generating set of elements is considered as a set of initial events of the physical world, and all points generated by wandering are interpreted as their consequences. The special properties of such a model allow us to obtain interesting conclusions about the possible causes of the pseudo-Euclidean metric of our world and its 3 + 1 dimension. Such effects as the expansion of the Universe with low acceleration, gravitational deformation of the metric and the superposition of the states of quantum particles get their explanation. There is an effect of duality of the description of physical interactions as long-range or short-range interaction.