dorsal/arxiv
View SchemaOn the relation between quantum mechanical probabilities and event frequencies
| Authors | Charis Anastopoulos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403207 |
| URL | https://arxiv.org/abs/quant-ph/0403207 |
| DOI | 10.1016/j.aop.2004.05.002 |
| Journal | Annals of Physics 313, 368 (2004) |
Abstract
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive measurements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend explicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and propositions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives.
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"abstract": "The probability `measure\u0027 for measurements at two consecutive moments of time\nis non-additive. These probabilities, on the other hand, may be determined by\nthe limit of relative frequency of measured events, which are by nature\nadditive. We demonstrate that there are only two ways to resolve this problem.\nThe first solution places emphasis on the precise use of the concept of\nconditional probability for successive measurements. The physically correct\nconditional probabilities define additive probabilities for two-time\nmeasurements. These probabilities depend explicitly on the resolution of the\nphysical device and do not, therefore, correspond to a function of the\nassociated projection operators. It follows that quantum theory distinguishes\nbetween physical events and propositions about events, the latter are not\nrepresented by projection operators and that the outcomes of two-time\nexperiments cannot be described by quantum logic.\n The alternative explanation is rather radical: it is conceivable that the\nrelative frequencies for two-time measurements do not converge, unless a\nparticular consistency condition is satisfied. If this is true, a strong\nrevision of the quantum mechanical formalism may prove necessary. We stress\nthat it is possible to perform experiments that will distinguish the two\nalternatives.",
"arxiv_id": "quant-ph/0403207",
"authors": [
"Charis Anastopoulos"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2004.05.002",
"journal_ref": "Annals of Physics 313, 368 (2004)",
"title": "On the relation between quantum mechanical probabilities and event frequencies",
"url": "https://arxiv.org/abs/quant-ph/0403207"
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