Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Representation of the Universe as a Dendrogramic Hologram Endowed With Relational Interpretation

Version 1 : Received: 31 March 2021 / Approved: 1 April 2021 / Online: 1 April 2021 (14:50:38 CEST)

How to cite: Khrennikov, A.; Shor, O.; Benninger, F. Representation of the Universe as a Dendrogramic Hologram Endowed With Relational Interpretation. Preprints 2021, 2021040029 (doi: 10.20944/preprints202104.0029.v1). Khrennikov, A.; Shor, O.; Benninger, F. Representation of the Universe as a Dendrogramic Hologram Endowed With Relational Interpretation. Preprints 2021, 2021040029 (doi: 10.20944/preprints202104.0029.v1).

Abstract

proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibnitz principle of the Identity of Indiscernible. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Ideologically, our theory is very close to Smolin’s dynamics of difference and Rovelli’s relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.

Subject Areas

fundamental physical theory; classical and quantum physics; p-adic numbers; disordered field; zero dimensional space; hologram; dendrogram; Planck conatnt; light velocity; Berll correlations

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