Version 1
: Received: 20 April 2022 / Approved: 21 April 2022 / Online: 21 April 2022 (07:56:21 CEST)
How to cite:
Shor, O.; Benninger, F.; Khrennikov, A. Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow. Preprints2022, 2022040193. https://doi.org/10.20944/preprints202204.0193.v1
Shor, O.; Benninger, F.; Khrennikov, A. Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow. Preprints 2022, 2022040193. https://doi.org/10.20944/preprints202204.0193.v1
Shor, O.; Benninger, F.; Khrennikov, A. Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow. Preprints2022, 2022040193. https://doi.org/10.20944/preprints202204.0193.v1
APA Style
Shor, O., Benninger, F., & Khrennikov, A. (2022). Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow. Preprints. https://doi.org/10.20944/preprints202204.0193.v1
Chicago/Turabian Style
Shor, O., Felix Benninger and Andrei Khrennikov. 2022 "Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow" Preprints. https://doi.org/10.20944/preprints202204.0193.v1
Abstract
Recently we started the development of Holographic Dendrogramic Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of (Smolin, Barbour, Rovelli). Elementary events are represented by branches of dendrograms, finite trees, which are generated from data with clustering algorithms. In this note we study 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 of this universe. Its events are coupled via the hierarchic relational structure which is relatively stable with respect even random generation of new events. We also observe the regularity patterns in location of new events on dendrograms. In the curse of evolution, the dendrogram’s complexity increases and determine the arrow of time the event universe. We use the complexity measure from particle shape dynamics which was shown to be increase in both direction 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 relays on Mach’s principle and Leibniz’s relationalism and his principles. By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of time arrow from the p-adic zero-dimensional field, where space and time are absent.
Keywords
event-universe; dendrograms; hierarchic relational representation; dendrogramic dynamics; shape dynamics; stability of event-universe; arrow of time
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
