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There must exist a reformulation of quantum field theory which does not referto classical time. We propose a pre-quantum, pre-spacetime theory, which is amatrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions.The definition of spin in this theory leads us to an eight dimensionaloctonionic space-time. The algebra of the octonions reveals the standard model;model parameters are determined by roots of the cubic characteristic equationof the exceptional Jordan algebra. We derive the asymptotic low energy value1/137 of the fine structure constant, and predict the existence of universallyinteracting spin one Lorentz bosons, which replace the hypothesised graviton.Gravity is not to be quantized, but is an emergent four-dimensional classicalphenomenon, precipitated by the spontaneous localisation of highly entangledfermions.

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