dorsal/arxiv
View SchemaComment on "Why quantum mechanics cannot be formulated as a Markov process"
| Authors | Piotr Garbaczewski, Robert Olkiewicz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9601016 |
| URL | https://arxiv.org/abs/quant-ph/9601016 |
| DOI | 10.1103/PhysRevA.54.1733 |
| Journal | Phys.Rev. A54 (1996) 1733-1736 |
Abstract
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.
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"abstract": "In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607,\n(1994)] claims that the theory of Markov stochastic processes cannot provide an\nadequate mathematical framework for quantum mechanics. In conjunction with the\nspecific quantum dynamics considered there, we give a general analysis of the\nassociated dichotomic jump processes. If we assume that Gillespie\u0027s\n\"measurement probabilities\" \\it are \\rm the transition probabilities of a\nstochastic process, then the process must have an invariant (time independent)\nprobability measure. Alternatively, if we demand the probability measure of the\nprocess to follow the quantally implemented (via the Born statistical\npostulate) evolution, then we arrive at the jump process which \\it can \\rm be\ninterpreted as a Markov process if restricted to a suitable duration time.\nHowever, there is no corresponding Markov process consistent with the $Z_2$\nevent space assumption, if we require its existence for all times $t\\in R_+$.",
"arxiv_id": "quant-ph/9601016",
"authors": [
"Piotr Garbaczewski",
"Robert Olkiewicz"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.54.1733",
"journal_ref": "Phys.Rev. A54 (1996) 1733-1736",
"title": "Comment on \"Why quantum mechanics cannot be formulated as a Markov process\"",
"url": "https://arxiv.org/abs/quant-ph/9601016"
},
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