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

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

2007-10-15

arxiv.org/abs/0710.2765v2

J. Phys. A: Math. Theor. 41 (2008) 304020

Physics

Quantum Physics

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

Scientific paper

10.1088/1751-8113/41/30/304020

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.

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