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 is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a 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 enhances the role of the Bohm potential.
Highlights
This paper is the first step towards the unification of general relativity (GR) and quantum theory (QT) on the basis of the Dendrogramic-Holographic (DH) theory [1,2]
The bit encoding is used for hierarchic relations between events in the universe described as dendrograms
The natural question arises: Can p-adic theoretical physics be somehow coupled to real experimental data? can such coupling contribute to the development of gravitation theory? We answer these questions positively
Summary
This paper is the first step towards the unification of general relativity (GR) and quantum theory (QT) on the basis of the Dendrogramic-Holographic (DH) theory [1,2]. Following Smolin’s event-physics [5,6], we unify GR and QT on the basis of a new theory and mathematics, i.e., the p-adic number system [3] Both classical and quantum random systems are represented by ensembles of dendrograms [1,2]. P-adic theoretical physics has been intensively developed [9,10,11,12,13,14,15] consistently with the development of the string theory ([9,16,17,18,19]) and complex disordered systems
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