A Conjecture on Deducing General Relativity and the Standard Model with Its Fundamental Constants from Rational Tangles of Strands

Abstract

Possibly the first argument for the origin of the three observed gauge groups and thus for the origin of the three non-gravitational interactions is presented. The argument is based on a proposal for the final theory that models nature at Planck scales as a collection of featureless strands that fluctuate in three dimensions. This approach models vacuum as untangled strands, particles as tangles of strands, and Planck units as crossing switches. Modelling vacuum as untangled strands implies the field equations of general relativity, when applying an argument from 1995 to the thermodynamics of such strands. Modelling fermions as tangles of two or more strands allows to define wave functions as time-averages of oriented strand crossing density. Using an argument from 1980, this allows to deduce the Dirac equation. When fermions are modelled as tangled strands, gauge interactions appear naturally as deformation of tangle cores. The three possible types of observable core deformations are given by the three Reidemeister moves. They naturally lead to a U(1), a broken and parity-violating SU(2), and a SU(3) gauge group. The corresponding Lagrangians also appear naturally. The strand model is unique, is unmodifiable, is consistent with all known data, and makes numerous testable predictions, including the absence of other interactions, of grand unification, of supersymmetry and of higher dimensions. A method for calculating coupling constants seems to appear naturally.