Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow

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.

Relational information framework, causality, unification of quantum interpretations and return to realism through non-ergodicity

“…Thus, action principles might be referred trivially as a particular learning procedure [34][35][36][37][38]. In recent studies [5,6], we have already drawn attention to intriguing parallels between our approach, which yields the emergence of quantum theory from DHT, and the neural network model of the universe as described in articles [34][35][36][37][38]. Notably, we should highlight that p-adic neural networks have been investigated in conjunction with Euclidean quantum field theory, as detailed in references [37,38], thereby establishing a closer connection between our approach and the domain of ML.…”

“…Dendrogramic Holographic Theory (DHT) is a singular postulate theory of relational information, conceived through a series of studies [1][2][3][4][5][6]. This theory represents a relational-event-observational approach to physics and the broader realm of natural science [7,8].…”

Representation of the universe as dendrogramic hologram empowered with relational interpretation

“…However, in contrast with standard exploration of p-adics in physics, we work not with separate branches of the p-adic tree, p-adic numbers, but with batches of branches unified into dendrograms. This is a kind of holographic holistic imaging, and we call our model of universe and processes in it -dendrogramic holographic (DH) theory [10][11][12][13][14].…”