On the nature of continuous physical quantities in classical and quantum mechanics

Details On the nature of continuous physical quantities in classical and quantum mechanics On the nature of continuous physical quantities in classical and quantum mechanics

2000-03-17

arxiv.org/abs/quant-ph/0003074v1

Journal of Philosophical Logic 30, 27-50 (2001)

Physics

Quantum Physics

26 pages, LaTeX

Scientific paper

10.1023/A:1017574203443

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, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller (Journal of Philosophy, 1979), 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 and 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.

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