Quantum theory without classical time: octonions, and a theoretical derivation of the fine structure constant 1/137

TL;DR

This paper proposes a pre-quantum, pre-spacetime framework using octonions that derives the standard model parameters, including the fine structure constant, and suggests gravity emerges from fermion entanglement rather than quantization.

Contribution

It introduces an octonionic, matrix-valued Lagrangian theory that reformulates quantum field theory without classical time, deriving key physical constants and predicting new bosons.

Findings

Derives the fine structure constant as 1/137 from algebraic roots.

Predicts the existence of spin one Lorentz bosons replacing gravitons.

Proposes gravity as an emergent phenomenon from fermion entanglement.

Abstract

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.