dorsal/arxiv
View SchemaRepresentations of Spacetime Alternatives and Their Classical Limits
| Authors | August W. Bosse, James B. Hartle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503182 |
| URL | https://arxiv.org/abs/quant-ph/0503182 |
| DOI | 10.1103/PhysRevA.72.022105 |
| Journal | Phys.Rev. A72 (2005) 022105 |
Abstract
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example. Classical spacetime alternatives that extend over time can also be represented by different quantum operators. For example, operators representing a particular value of the time average of a dynamical variable can be constructed in two ways: First, as the projection onto the value of the time averaged Heisenberg picture operator for the dynamical variable. Second, as the class operator defined by a sum over those histories of the dynamical variable that have the specified time-averaged value. We show both by explicit example and general argument that the predictions of these different representations agree in the classical limit and that sets of histories represented by them decohere in that limit.
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"abstract": "Different quantum mechanical operators can correspond to the same classical\nquantity. Hermitian operators differing only by operator ordering of the\ncanonical coordinates and momenta at one moment of time are the most familiar\nexample. Classical spacetime alternatives that extend over time can also be\nrepresented by different quantum operators. For example, operators representing\na particular value of the time average of a dynamical variable can be\nconstructed in two ways: First, as the projection onto the value of the time\naveraged Heisenberg picture operator for the dynamical variable. Second, as the\nclass operator defined by a sum over those histories of the dynamical variable\nthat have the specified time-averaged value. We show both by explicit example\nand general argument that the predictions of these different representations\nagree in the classical limit and that sets of histories represented by them\ndecohere in that limit.",
"arxiv_id": "quant-ph/0503182",
"authors": [
"August W. Bosse",
"James B. Hartle"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevA.72.022105",
"journal_ref": "Phys.Rev. A72 (2005) 022105",
"title": "Representations of Spacetime Alternatives and Their Classical Limits",
"url": "https://arxiv.org/abs/quant-ph/0503182"
},
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