Note on the existence theorem in ``Emergent Quantum Mechanics and Emergent Symmetries''

Abstract

Recently 't Hooft demonstrated that ``For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization''. An extension is presented here which covers quantum systems that are characterized by a complete set of mutually commuting Hermitian operators (``beables''). We introduce the symmetry of beables: any complete set of beables is as good as any other one which is obtained through a real general linear group transformation. The quantum numbers of a specific set are related to symmetry breaking initial and boundary conditions in a deterministic model. The Hamiltonian, in particular, can be taken as the emergent beable which provides the best resolution of the evolution of the model universe.

10 pages; 1 reference and 1 explanatory sentence added; accepted for Journal of Physics A: Math and Theor

References in corpus (11)

• Quantum Gravity as a Dissipative Deterministic System
• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
• Dissipation and quantization
• The mathematical basis for deterministic quantum mechanics
• Quantum Theory from Quantum Gravity
• Evidence for a continuum limit in causal set dynamics
• The clock ambiguity and the emergence of physical laws
• Deterministic models of quantum fields
• 't Hooft's quantum determinism -- path integral viewpoint
• Quantum fields, cosmological constant and symmetry doubling
• Consequences of 't Hooft's Equivalence Class Theory and Symmetry by Large Coarse Graining

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• Emergent quantum mechanics of the event-universe, quantization of events via Denrographic Hologram Theory
• Fundamental Principles of Theoretical Physics and Concepts of Quasiaverages, Quantum Protectorate and Emergence
• An entropic picture of emergent quantum mechanics
• Positive curvature can mimic a quantum
• The Ricci flow on Riemann surfaces