[FOM] Question on the number line
urquhart at cs.toronto.edu
Thu Nov 17 08:30:45 EST 2005
John von Neumann suggested a resolution to these sort of
puzzles, in his paper "Operator Methods in Classical Mechanics",
Annals of Mathematics, Vol. 33 (1932), 587-642.
The idea is to define an observable in classical mechanics
in terms of a certain algebra. Operating over R^n,
we define the algebra of observables to be the family
of Borel sets, but with the identification of sets that
differ in a set of measure 0.
This takes care of the Suarez puzzle, and also gets rid of
physically meaningless questions like: "Is the length of
this metal rod a rational number?"
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