dorsal/arxiv
View SchemaThe mathematical basis for deterministic quantum mechanics
| Authors | Gerard 't Hooft |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604008 |
| URL | https://arxiv.org/abs/quant-ph/0604008 |
| DOI | 10.1088/1742-6596/67/1/012015 |
Abstract
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
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"abstract": "If there exists a classical, i.e. deterministic theory underlying quantum\nmechanics, an explanation must be found of the fact that the Hamiltonian, which\nis defined to be the operator that generates evolution in time, is bounded from\nbelow. The mechanism that can produce exactly such a constraint is identified\nin this paper. It is the fact that not all classical data are registered in the\nquantum description. Large sets of values of these data are assumed to be\nindistinguishable, forming equivalence classes. It is argued that this should\nbe attributed to information loss, such as what one might suspect to happen\nduring the formation and annihilation of virtual black holes.\n The nature of the equivalence classes is further elucidated, as it follows\nfrom the positivity of the Hamiltonian. Our world is assumed to consist of a\nvery large number of subsystems that may be regarded as approximately\nindependent, or weakly interacting with one another. As long as two (or more)\nsectors of our world are treated as being independent, they all must be\ndemanded to be restricted to positive energy states only. What follows from\nthese considerations is a unique definition of energy in the quantum system in\nterms of the periodicity of the limit cycles of the deterministic model.",
"arxiv_id": "quant-ph/0604008",
"authors": [
"Gerard \u0027t Hooft"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1088/1742-6596/67/1/012015",
"title": "The mathematical basis for deterministic quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0604008"
},
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