Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.
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Plotnitsky, A. A New Book of Numbers: On the Precise Definition of Quantum Variables and the Relationships between Mathematics and Physics in Quantum Theory. Found Phys 36, 30–60 (2006). https://doi.org/10.1007/s10701-005-9004-1
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DOI: https://doi.org/10.1007/s10701-005-9004-1