Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Representation of the universe as a dendrogramic hologram endowed with relational interpretation

Abstract : A 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Andrei Khrennikov <>
Submitted on : Monday, March 29, 2021 - 11:05:05 AM
Last modification on : Tuesday, April 13, 2021 - 3:43:08 PM


Files produced by the author(s)


  • HAL Id : hal-03184051, version 1



Oded Shor, Felix Benninger, Andrei Khrennikov. Representation of the universe as a dendrogramic hologram endowed with relational interpretation. 2021. ⟨hal-03184051⟩



Record views


Files downloads