On the equivalence of nonrelativistic quantum mechanics based upon sharp and fuzzy measurements

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Abstract
Starting from the idea that physical measurements may have residual imprecisions, the possibility of replacing the nonrelativistic, three‐dimensional configuration space by a so‐called fuzzy configuration space, having an isomorphic Borel structure, is discussed. A quantization procedure with respect to such a space is developed, and the invariance of nonrelativistic quantum mechanics under such Borel isomorphisms is exploited to prove the equivalence of this quantization procedure to the usual quantization procedure on a fuzzy‐free configuration space. Further, any Galilean invariant dynamics is shown to be insensitive to such imprecisions in the measurements of position and momentum.

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