Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Quantum Theory Without Classical Time: Octonions, and a Theoretical Derivation of the Fine Structure Constant 1/137

Version 1 : Received: 14 May 2021 / Approved: 17 May 2021 / Online: 17 May 2021 (07:56:36 CEST)

A peer-reviewed article of this Preprint also exists.

Journal reference: International Journal of Modern Physics D 2021
DOI: 10.1142/S0218271821420104


There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The definition of spin in this theory leads us to an eight dimensional octonionic space-time. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.


Quantum theory; Octonions; Fine structure constant; Trace dynamics; Standard model; Non-commutative geometry



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