Article Title：On the nature of continuous physical quantities in classical and quantum mechanics
Abstract：
Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, thought, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No--that the status of individual continuous quantities is very different in quantum mechanics than in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical quantum mechanics; and that it is , after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics.
Keywords: Boolean algebra; probability measure; unsharp quantum logic
DOI: 10.1023/A:1017574203443
Source：JOURNAL OF PHILOSOPHICAL LOGIC
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