Are symmetry principles meta-laws?
Noether's first theorem demonstrates that continuous symmetries give rise to conserved quantities (under appropriate conditions). This fact tempts many to hold that symmetry principles explain conservation laws. Yet there is a puzzle: the derivation goes both ways. So why does symmetry explain conse...
| Published in: | Synthese Vol. 205; no. 6; pp. 1 - 22 |
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| Format: | Article |
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Springer Nature
Jun2025
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=185350976&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 185350976 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jun2025 vid: 205 iid: 6 pid: 237 pub: Springer Nature artinfo: ui: 185350976 10.1007/s11229-025-05064-w ppf: 1 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1.7MB tig: atl: Are symmetry principles meta-laws? aug: au: Shi, Shelly Yiran affil: https://ror.org/0168r3w48 Department of Philosophy, University of California San Diego, 9500 Gilman Dr, 92093, La Jolla, CA, USA su: Noether's theorem Philosophy of science Angular momentum (Mechanics) Conserved quantity Rotational symmetry sug: subj: Noether's theorem Philosophy of science Angular momentum (Mechanics) Conserved quantity Rotational symmetry keyword: Explanation Meta-law Philosophy and Religious Studies History and Philosophy of Specific Fields Symmetry ab: Noether's first theorem demonstrates that continuous symmetries give rise to conserved quantities (under appropriate conditions). This fact tempts many to hold that symmetry principles explain conservation laws. Yet there is a puzzle: the derivation goes both ways. So why does symmetry explain conservation when the derivation is bidirectional? Lange (Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 38(3):457–481, 2007, Laws and lawmakers: Science, metaphysics, and the laws of nature, 2009) provides an answer: symmetry principles are meta-laws, and meta-laws explain first-order laws just as first-order laws explain facts. Using a "non-standard" Lagrangian Smith (Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 39(2):325–345, 2008.) claims that conservation of angular momentum can hold without rotational symmetry, providing a counter-example to Lange. In this paper, I show that Smith's non-standard Lagrangian fails to serve as a counterexample. However, that doesn't leave Lange's account unchallenged. I argue that the debate between Lange and Smith ultimately revolves around an ambiguity which, once clarified, leads to a dilemma. Which symmetry principle explains? Is it the symmetry of the action or the symmetry of equations of motion? If the former, then the symmetry is no more stable than conservation laws. Hence, we lose the desired explanatory direction. If the latter, the symmetry lacks explanatory relevance and fails to exhibit greater stability than conservation laws. However one disambiguates 'symmetry', it remains mysterious why symmetry principles explain conservation laws. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2025. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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