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Switch to: References
Citations of:
On the Choice of Algebra for Quantization
Philosophy of Science 85 (1):102-125 (2018)
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Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from (...) |
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I argue that it is possible to give an interpretation of the classical ℏ→0 limit of quantum mechanics that results in a partial explanation of the success of classical mechanics. The interpretation... |
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This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive Borel probability measure on R^{2n}. It follows that one can "reduce" the state space of the Weyl algebra by altering the collection of quantum mechanical observables so that all states are ones whose classical limit is physical. |
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I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery. |
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This paper attempts to make sense of a notion of ``approximation on certain scales'' in physical theories. I use this notion to understand the classical limit of ordinary quantum mechanics as a kind of scaling limit, showing that the mathematical tools of strict quantization allow one to make the notion of approximation precise. I then compare this example with the scaling limits involved in renormalization procedures for effective field theories. I argue that one does not yet have the mathematical tools (...) |
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