dorsal/arxiv
View SchemaQuantum Dynamics without the Wave Function
| Authors | Rafael D. Sorkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610204 |
| URL | https://arxiv.org/abs/quant-ph/0610204 |
| DOI | 10.1088/1751-8113/40/12/S20 |
| Journal | J.Phys.A40:3207-3222,2007 |
Abstract
When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the path-integral-as-propagator to a {\it quantal measure} $\mu$ on the space $\Omega$ of all ``conceivable worlds'', and this generalized measure expresses the dynamics or law of motion of the theory, much as Wiener measure expresses the dynamics of Brownian motion. Within such ``histories-based'' schemes new, and more ``realistic'' possibilities open up for resolving the philosophical problems of the state-vector formalism. In particular, one can dispense with the need for external agents by locating the predictive content of $\mu$ in its sets of measure zero: such sets are to be ``precluded''. But unrestricted application of this rule engenders contradictions. One possible response would remove the contradictions by circumscribing the application of the preclusion concept. Another response, more in the tradition of ``quantum logic'', would accommodate the contradictions by dualizing $\Omega$ to a space of ``co-events'' and effectively identifying reality with an element of this dual space.
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"abstract": "When suitably generalized and interpreted, the path-integral offers an\nalternative to the more familiar quantal formalism based on state-vectors,\nselfadjoint operators, and external observers. Mathematically one generalizes\nthe path-integral-as-propagator to a {\\it quantal measure} $\\mu$ on the space\n$\\Omega$ of all ``conceivable worlds\u0027\u0027, and this generalized measure expresses\nthe dynamics or law of motion of the theory, much as Wiener measure expresses\nthe dynamics of Brownian motion. Within such ``histories-based\u0027\u0027 schemes new,\nand more ``realistic\u0027\u0027 possibilities open up for resolving the philosophical\nproblems of the state-vector formalism. In particular, one can dispense with\nthe need for external agents by locating the predictive content of $\\mu$ in its\nsets of measure zero: such sets are to be ``precluded\u0027\u0027. But unrestricted\napplication of this rule engenders contradictions. One possible response would\nremove the contradictions by circumscribing the application of the preclusion\nconcept. Another response, more in the tradition of ``quantum logic\u0027\u0027, would\naccommodate the contradictions by dualizing $\\Omega$ to a space of\n``co-events\u0027\u0027 and effectively identifying reality with an element of this dual\nspace.",
"arxiv_id": "quant-ph/0610204",
"authors": [
"Rafael D. Sorkin"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th",
"math.LO"
],
"doi": "10.1088/1751-8113/40/12/S20",
"journal_ref": "J.Phys.A40:3207-3222,2007",
"title": "Quantum Dynamics without the Wave Function",
"url": "https://arxiv.org/abs/quant-ph/0610204"
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