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arXiv:quant-ph/0312179

Quantum time ordering and degeneracy. I: Time ordering in quantum mechanics

J. H. McGuire, Alexander Godunov, Kh. Kh. Shakov, Kh. Yu. Rakhimov, Athanasios Chalastaras

Published Dec 21, 2003• 0 citations
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Abstract

We examine how time ordering works in quantum mechanics and in classical mechanics.
DOI
10.48550/arxiv.quant-ph/0312179

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The classical limit problem of quantum mechanics is revisited on the basis of a scheme that enables a quantitative study of the way the quantum-classical agreement emerges while going through the intermediate mass range between the microscopic and the macroscopic domains. As a specific application of such a scheme, we investigate the classical limit of a quantum time distribution - an area of study that has remained largely unexplored. For this purpose, we focus on the arrival time distribution in order to examine the way the observable results pertaining to the quantum arrival time distribution which is defined in terms of the probability current density gradually approach the relevant classical statistical results for an ensemble that corresponds to a Gaussian wave packet evolving in a linear potential.
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The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined.