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