dorsal/arxiv
View SchemaQuantum Mechanics from Symmetry and Statistical Modelling
| Authors | Inge S. Helland |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908075 |
| URL | https://arxiv.org/abs/quant-ph/9908075 |
Abstract
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary statistical model is defined. The parameters of the single experiments are functions of a hyperparameter, which defines the state of the system. There is a symmetry group acting on the hyperparameters, and for the induced action on the parameters of the single experiment a simple consistency property is assumed, called permissibility of the parametric function. The other assumptions needed are rather weak. The derivation relies partly on quantum logic, partly on a group representation of the hyperparameter group, where the invariant spaces are shown to be in 1-1 correspondence with the equivalence classes of permissible parametric functions. Planck's constant only plays a role connected to generators of unitary group representations.
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"abstract": "A version of quantum theory is derived from a set of plausible assumptions\nrelated to the following general setting: For a given system there is a set of\nexperiments that can be performed, and for each such experiment an ordinary\nstatistical model is defined. The parameters of the single experiments are\nfunctions of a hyperparameter, which defines the state of the system. There is\na symmetry group acting on the hyperparameters, and for the induced action on\nthe parameters of the single experiment a simple consistency property is\nassumed, called permissibility of the parametric function. The other\nassumptions needed are rather weak. The derivation relies partly on quantum\nlogic, partly on a group representation of the hyperparameter group, where the\ninvariant spaces are shown to be in 1-1 correspondence with the equivalence\nclasses of permissible parametric functions. Planck\u0027s constant only plays a\nrole connected to generators of unitary group representations.",
"arxiv_id": "quant-ph/9908075",
"authors": [
"Inge S. Helland"
],
"categories": [
"quant-ph"
],
"title": "Quantum Mechanics from Symmetry and Statistical Modelling",
"url": "https://arxiv.org/abs/quant-ph/9908075"
},
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