dorsal/arxiv
View SchemaOn a Time Symmetric Formulation of Quantum Mechanics
| Authors | B. Reznik, Y. Aharonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9501011 |
| URL | https://arxiv.org/abs/quant-ph/9501011 |
| DOI | 10.1103/PhysRevA.52.2538 |
| Journal | Phys. Rev. A 52, 2538 (1995). |
Abstract
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically recast the basics of quantum mechanics - dynamics, observables, and measurement theory - in terms of two-states as the elementary quantities. We find a simple and suggestive formulation, that ``unifies'' two complementary observables: probabilistic observables and non-probabilistic `weak' observables. Probabilities are relevant for measurements in the `strong coupling regime'. They are given by the absolute square of a two-amplitude (a projection of a two-state). Non-probabilistic observables are observed in sufficiently `weak' measurements, and are given by linear combinations of the two-amplitude. As a sub-class they include the `weak values' of hermitian operators. We show that in the intermediate regime, one may observe a mixing of probabilities and weak values. A consequence of the suggested formalism and measurement theory, is that the problem of non-locality and Lorentz non-covariance, of the usual prescription with a `reduction', may be eliminated. We exemplify this point for the EPR experiment and for a system under successive observations.
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"abstract": "We explore further the suggestion to describe a pre- and post-selected system\nby a two-state, which is determined by two conditions. Starting with a formal\ndefinition of a two-state Hilbert space and basic operations, we systematically\nrecast the basics of quantum mechanics - dynamics, observables, and measurement\ntheory - in terms of two-states as the elementary quantities. We find a simple\nand suggestive formulation, that ``unifies\u0027\u0027 two complementary observables:\nprobabilistic observables and non-probabilistic `weak\u0027 observables.\nProbabilities are relevant for measurements in the `strong coupling regime\u0027.\nThey are given by the absolute square of a two-amplitude (a projection of a\ntwo-state). Non-probabilistic observables are observed in sufficiently `weak\u0027\nmeasurements, and are given by linear combinations of the two-amplitude. As a\nsub-class they include the `weak values\u0027 of hermitian operators. We show that\nin the intermediate regime, one may observe a mixing of probabilities and weak\nvalues. A consequence of the suggested formalism and measurement theory, is\nthat the problem of non-locality and Lorentz non-covariance, of the usual\nprescription with a `reduction\u0027, may be eliminated. We exemplify this point for\nthe EPR experiment and for a system under successive observations.",
"arxiv_id": "quant-ph/9501011",
"authors": [
"B. Reznik",
"Y. Aharonov"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.52.2538",
"journal_ref": "Phys. Rev. A 52, 2538 (1995).",
"title": "On a Time Symmetric Formulation of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/9501011"
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