Quantum theory without classical time: a route to quantum gravity and unification

If you are interested in the current status of the of the octonionic theory, you might find this new review article useful:

Quantum theory without classical time: a route to quantum gravity and unification

https://www.tifr.res.in/~tpsingh/Penrose90singh.pdf

152 pages, 17 figures. Invited review article submitted to the special collection "Celebrating Sir Roger Penrose's Nobel Prize"

[AVS Quantum Science (AIP Publishing and AVS), Guest Editor: Hendrik Ulbricht]

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 pre-quantum, pre-spacetime theory, which is a matrix valued Lagrangian dynamics on an octonionic spacetime. This is a deterministic but non-unitary dynamics in which evolution is described by Connes time, a feature unique to non-commutative geometry. From here, quantum field theory and its indeterminism, as well as classical space-time 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 pre-cursor 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 non-self-adjoint. 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 non-locality, while maintaining consistency with special relativity. We speculate on the possible connection of our work with twistor spaces and spinorial space-time, and with Modified Newtonian Dynamics (MOND). We point to the promising phenomenology of $E_6$, and mention possible experiments which could test the present proposal. In the end we outline further work that still remains to be done towards completion of this programme.