Quantum theory without classical time: a route to quantum gravity and unification
Abstract
There must exist a reformulation of quantum field theory which does not employ classical time to describe evolution, even at low energies. To achieve this goal, we have proposed a prequantum, prespacetime theory, which is a matrix valued Lagrangian dynamics on an octonionic spacetime. This is a deterministic but nonunitary dynamics in which evolution is described by Connes time, a feature unique to noncommutative geometry. From here, quantum field theory and its indeterminism, as well as classical spacetime geometry, are emergent under suitable approximations. In the underlying theory, the algebra of the octonions reveals evidence for the standard model of particle physics, and for its unification with a precursor of gravitation, through extension to the Left Right symmetric model and the symmetry group $E_6$. When elementary particles are described by spinors made from a Clifford algebra, the exceptional Jordan algebra yields a theoretical derivation of the low energy fine structure constant, and of the observed mass ratios for charged fermions. We identify the Left Right symmetry breaking with electroweak symmetry breaking, which also results in separation of emergent four dimensional Minkowski spacetime from the internal symmetries which describe the standard model. This compactification without compactification is achieved through the Ghirardi Rimini Weber mechanism of dynamical wave function collapse, which arises naturally in our theory, because the underlying fundamental Hamiltonian is necessarily nonselfadjoint. Only classical systems live in four dimensions; quantum systems always live in eight octonionic (equivalently ten Minkowski) dimensions. We explain how our theory overcomes the puzzle of quantum nonlocality, while maintaining consistency with special relativity.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2110.02062
 Bibcode:
 2021arXiv211002062S
 Keywords:

 Physics  General Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 152 pages, 17 figures, Invited review article submitted to the special collection "Celebrating Sir Roger Penrose's Nobel Prize" [special issue of AVS Quantum Science (AIP Publishing and AVS), Guest Editor: Hendrik Ulbricht]