Rao-Fisher information geometry and dynamics of the event-universe views distributions

Abstract

We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between events. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic numbers. We call this kind of event mechanics Dendrogramic Holographic theory (DHT). It can be considered as a fundamental theory generating both GR and QM. In this paper we endower DHT with Rao-Cramer's information geometry. Following Smolin's derivation of QM from the event-universe, we introduce views from one event to others and by using their probability distributions we invent stochastic geometry. The important mathematical result is that all such views' distributions can be parametrized by four real parameters that are a part of the shape complexity measure introduced by Barbour in his particle shape dynamics theory – adapted to DHT. Hence, within DHT all possible event-universes can be embedded in four-dimensional real space. Asin GR, we introduce proper time. This “proper time” depends only on the change between one distribution of an observer to the other. The linkage of time to change is highlighted in the ideology of Rovelli and Barbour's shape dynamics.