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...
| Published in: | Synthese Vol. 169; no. 1; pp. 27 - 51 |
|---|---|
| Main Author: | |
| Format: | Article |
| Published: |
Springer Nature
Jul2009
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=41132806&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 41132806 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jul2009 vid: 169 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 41132806 10.1007/s11229-008-9341-7 ppf: 27 ppct: 24 formats: fmt: @attributes: type: P size: 249KB tig: atl: Essential self-adjointness: implications for determinism and the classical–quantum correspondence. aug: 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 sug: subj: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2009. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2009 holdings: @attributes: islocal: N |
|---|