Quantum theory without classical time: Octonions, and a theoretical derivation of the fine structure constant 1/137
Abstract
There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a prequantum, prespacetime theory, which is a matrixvalued Lagrangian dynamics for gravity, YangMills fields, and fermions. The definition of spin in this theory leads us to an eightdimensional octonionic spacetime. 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 lowenergy 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 fourdimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 October 2021
 DOI:
 10.1142/S0218271821420104
 arXiv:
 arXiv:2110.07548
 Bibcode:
 2021IJMPD..3042010S
 Keywords:

 Trace dynamics;
 quantum foundations;
 noncommutative geometry;
 division algebras;
 octonions;
 standard model;
 fine structure constant;
 mass ratios;
 quantum gravity;
 Physics  General Physics
 EPrint:
 9 pages, honorable mention in Gravity Research Foundation Essay Contest 2021, v2: references updated. arXiv admin note: substantial text overlap with arXiv:2110.02062