  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.
