Essential self-adjointness: Implications for determinism and the classical–quantum correspondence

Synthese 169 (1):27 - 50 (2009)
It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science.
Keywords Foundations of quantum mechanics  Determinism  Classical–quantum correspondence
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References found in this work BETA
Jeffrey Bub (1998). Interpreting the Quantum World. British Journal for the Philosophy of Science 49 (4):637-641.
John D. Norton (2007). Causation as Folk Science. In Huw Price & Richard Corry (eds.), Philosophers' Imprint. Oxford University Press

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