A Finslerian version of ‘t Hooft deterministic quantum models

Abstract

Using the Finsler structure living in the phase space associated to the tangent bundle of the configuration manifold, deterministic models at the Planck scale are obtained. The Hamiltonian function are constructed directly from the geometric data and some assumptions concerning time inversion symmetry. The existence of a maximal acceleration and speed is proved for Finslerian deterministic models. We investigate the spontaneous symmetry breaking of the orthogonal symmetry SO(6N ) of the Hamiltonian of a deterministic system. This symmetry break implies the non-validity of the argument used to obtain Bell's inequalities for spin states. It is introduced and motivated in the context of Randers spaces an example of simple 't Hooft model with interactions.

Schroedinger vs. Navier–Stokes

“…Theorem 15 Under the above assumptions of stationarity and semiclassicality, the foliation F = const is orthogonal to the two foliations S = const and I = const simultaneously.…”

“…It has long been argued that quantum mechanics must emerge from an underlying classical, deterministic theory via some coarse-graining, or information-loss mechanism [8,9,13,15,16,18,19,20]; one refers to this fact as the emergence property of quantum mechanics [5]. Many emergent physical theories admit a thermodynamical reformulation, general relativity being perhaps the best example [31,34].…”

The irreversible quantum

“…The path integral (18) is the thermodynamical analogue of (10). The corresponding thermodynamical momentum p y equals Rdy/dτ , where R plays the role of a mass, and the thermodynamical Hamiltonian H corresponding to (19) reads…”

“…There exist profound analogies between these two theories [1,8,15,19,20]. Furthermore, seeming mismatches between the two actually have a natural explanation in the context of the emergent approach to quantum theory [2,4]; closely related topics were analysed long ago in [3] and more recently in [5,7,9,10,12,14,17,21,22]. One of these mismatches concerns the irreversibility of time evolution in the thermodynamical picture, as opposed to its reversibility in the quantum-mechanical picture.…”

On the semiclassical limit of emergent quantum mechanics, as a classical thermodynamics of irreversible processes in the linear regime

“…There exist profound analogies between these two theories [4,30,64,82,83]. Furthermore, seeming mismatches between the two actually have a natural explanation in the context of the emergent approach to quantum theory [5,13]; closely related topics were analysed long ago in [12] and more recently in [15,26,32,33,34,58,63,73,90,91]. One of these mismatches concerns the irreversibility of time evolution in the thermodynamical picture, as opposed to its reversibility in the quantum-mechanical picture.…”