Dendrographic Hologram Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow

Abstract

Recently we started the development of Dendrographic Hologram Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of Smolin et al.). Elementary events are represented by branches of dendrograms, finite trees that are generated from data with clustering algorithms. In this context, we studied the dynamics of the event universe generated by the appearance of a new event. Generally, each new event can generate the complete reconstruction of the whole dendrogramic universe. However, we found (via numerical simulation) unexpected stability in this universe. Its events are coupled via the hierarchic relational structure, which is relatively stable even with respect to the random generation of new events. We also observed the regularity patterns in the location of new events on dendrograms. In the course of evolution, the dendrogram’s complexity increases and determines the arrow of time in the event universe. We used the complexity measure from particle shape dynamics, which was shown to increase in both directions away from a Janus point and thus determine the arrow of time in symmetrical manner away from a Janus point. The particle shape dynamics theory is a relational theory with close ideological resemblance to DH-theory, as both rely on Mach’s principle and Leibniz’s relationalism and principles. By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of a time arrow from the p-adic zero-dimensional field, where space and time are absent.