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

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 reveal...

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Published in:Synthese Vol. 169; no. 1; pp. 27 - 51
Main Author: Earman, John
Format: Article
Published: Springer Nature Jul2009
Subjects:
Online Access:View this record in EBSCOhost
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        au: Earman, John
        affil: Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260, USA
      su:
        Quantum theory
        Philosophy of science
        Mechanics (Physics)
        Field theory (Physics)
        Theory of self-knowledge
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          Quantum theory
          Philosophy of science
          Mechanics (Physics)
          Field theory (Physics)
          Theory of self-knowledge
      keyword:
        Classical–quantum correspondence
        Classical-quantum correspondence
        Determinism
        Foundations of quantum mechanics
      ab: 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.
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    language: English
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