dorsal/arxiv
View SchemaProbabilities and Quantum Reality: Are There Correlata?
| Authors | Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209116 |
| URL | https://arxiv.org/abs/quant-ph/0209116 |
| DOI | 10.1023/A:1026092212820 |
Abstract
Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or decoherent) histories solution is provided by its single framework rule, an approach that includes conventional (Copenhagen) quantum theory as a special case. Mermin's Ithaca interpretation addresses the same problem by defining probabilities which make no reference to a sample space or event algebra (``correlations without correlata''). But this leads to severe conceptual difficulties, which almost inevitably couple quantum theory to unresolved problems of human consciousness. Using histories allows a sharper quantum description than is possible with a density matrix, suggesting that the latter provides an ensemble rather than an irreducible single-system description as claimed by Mermin. The histories approach satisfies the first five of Mermin's desiderata for a good interpretation of quantum mechanics, including Einstein locality, but the Ithaca interpretation seems to have difficulty with the first (independence of observers) and the third (describing individual systems).
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"abstract": "Any attempt to introduce probabilities into quantum mechanics faces\ndifficulties due to the mathematical structure of Hilbert space, as reflected\nin Birkhoff and von Neumann\u0027s proposal for a quantum logic. The (consistent or\ndecoherent) histories solution is provided by its single framework rule, an\napproach that includes conventional (Copenhagen) quantum theory as a special\ncase. Mermin\u0027s Ithaca interpretation addresses the same problem by defining\nprobabilities which make no reference to a sample space or event algebra\n(``correlations without correlata\u0027\u0027). But this leads to severe conceptual\ndifficulties, which almost inevitably couple quantum theory to unresolved\nproblems of human consciousness. Using histories allows a sharper quantum\ndescription than is possible with a density matrix, suggesting that the latter\nprovides an ensemble rather than an irreducible single-system description as\nclaimed by Mermin. The histories approach satisfies the first five of Mermin\u0027s\ndesiderata for a good interpretation of quantum mechanics, including Einstein\nlocality, but the Ithaca interpretation seems to have difficulty with the first\n(independence of observers) and the third (describing individual systems).",
"arxiv_id": "quant-ph/0209116",
"authors": [
"Robert B. Griffiths"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/A:1026092212820",
"title": "Probabilities and Quantum Reality: Are There Correlata?",
"url": "https://arxiv.org/abs/quant-ph/0209116"
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