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

Journal of Philosophical Logic 30 (1):27-50 (2001)
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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, though, 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 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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Hans Halvorson
Princeton University

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Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.
Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
[Omnibus Review].Yiannis N. Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):471-472.
A uniqueness theorem for ‘no collapse’ interpretations of quantum mechanics.Jeffrey Bub & Rob Clifton - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (2):181-219.

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