dorsal/arxiv
View SchemaLinear Positivity and Virtual Probability
| Authors | James B. Hartle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401108 |
| URL | https://arxiv.org/abs/quant-ph/0401108 |
| DOI | 10.1103/PhysRevA.70.022104 |
| Journal | Phys. Rev. A, 70, 02210 (2004) |
Abstract
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. A quantum theory of closed systems requires two elements; 1) a condition specifying which sets of histories may be assigned probabilities that are consistent with the rules of probability theory, and 2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time-neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0 to 1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculating real probabilities. Virtual probabilities give a simple and general way of formulating quantum theory.
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"abstract": "We investigate the quantum theory of closed systems based on the linear\npositivity decoherence condition of Goldstein and Page. A quantum theory of\nclosed systems requires two elements; 1) a condition specifying which sets of\nhistories may be assigned probabilities that are consistent with the rules of\nprobability theory, and 2) a rule for those probabilities. The linear\npositivity condition of Goldstein and Page is the weakest of the general\nconditions proposed so far. Its general properties relating to exact\nprobability sum rules, time-neutrality, and conservation laws are explored. Its\ninconsistency with the usual notion of independent subsystems in quantum\nmechanics is reviewed. Its relation to the stronger condition of medium\ndecoherence necessary for classicality is discussed. The linear positivity of\nhistories in a number of simple model systems is investigated with the aim of\nexhibiting linearly positive sets of histories that are not decoherent. The\nutility of extending the notion of probability to include values outside the\nrange of 0 to 1 is described. Alternatives with such virtual probabilities\ncannot be measured or recorded, but can be used in the intermediate steps of\ncalculating real probabilities. Virtual probabilities give a simple and general\nway of formulating quantum theory.",
"arxiv_id": "quant-ph/0401108",
"authors": [
"James B. Hartle"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevA.70.022104",
"journal_ref": "Phys. Rev. A, 70, 02210 (2004)",
"title": "Linear Positivity and Virtual Probability",
"url": "https://arxiv.org/abs/quant-ph/0401108"
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