dorsal/arxiv
View SchemaThe Measurement Problem and the Reduction Postulate of Quantum Mechanics
| Authors | Rodolfo Gambini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9803025 |
| URL | https://arxiv.org/abs/quant-ph/9803025 |
Abstract
It is well known, that the causal Schr\"odinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schr\"odinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schr\"odinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.
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"abstract": "It is well known, that the causal Schr\\\"odinger evolution of a quantum state\nis not compatible with the reduction postulate, even when decoherence is taken\ninto account. The violation of the causal evolution, introduced by the standard\nreduction postulate distinguishes certain systems (as the measurement devices),\nwhose states are very close to statistical mixtures (as the ones resulting from\nthe process of decoherence). In these systems, this violation has not any\nobservable effect. In arbitrary quantum systems, the transition from the\ninitial density matrix to a diagonal matrix predicted by the standard reduction\npostulate, would lead to a complete breakdown of the Schr\\\"odinger evolution,\nand consequently would destroy all the predictive power of quantum mechanics.\nWhat we show here, is that there is a modified version of the postulate that\nallows to treat all the quantum mechanical systems on equal footing. The\nstandard reduction postulate may be considered as a good approximation, useful\nfor practical purposes, of this modified version which is consistent with the\nSchr\\\"odinger evolution and via decoherence with the experimental results.\nWithin this approach, the physical role played by the reduction postulate is as\na tool for the computation of relative probabilities and consequently for the\ndetermination of the probabilities of consistent histories.",
"arxiv_id": "quant-ph/9803025",
"authors": [
"Rodolfo Gambini"
],
"categories": [
"quant-ph",
"gr-qc"
],
"title": "The Measurement Problem and the Reduction Postulate of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/9803025"
},
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