Journal of Philosophical Logic

, Volume 30, Issue 1, pp 27–50 | Cite as

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

  • Hans Halvorson


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.

Boolean algebra probability measure unsharp quantum logic 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Hans Halvorson
    • 1
  1. 1.Department of PhilosophyUniversity of PittsburghUSA

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