Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Version 1 : Received: 8 October 2021 / Approved: 12 October 2021 / Online: 12 October 2021 (11:35:03 CEST)

How to cite: Khrennikov, A.; Shor, O.; Felix, B. Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe. Preprints 2021, 2021100176 (doi: 10.20944/preprints202110.0176.v1). Khrennikov, A.; Shor, O.; Felix, B. Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe. Preprints 2021, 2021100176 (doi: 10.20944/preprints202110.0176.v1).

Abstract

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics—not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero dimensional) serves as the base for the holographic image of the universe. In this way our theory relates to p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans-Dicke theory. We found surprising informational interrelation between the fundamental constants, h, c, G, and their DH-analogues, h(D), c(D), G(D). DH-theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH-nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhanced the role of the Bohm potential.

Keywords

unification of general relativity and quantum theory; dendrogram; hierarchic relations between events; p-adic numbers; holographic image; Mach’s principle; Brans-Dicke theory; Bohm quantum potential; Unified Field theory

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