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...

Full description

Bibliographic Details
Published in:Synthese Vol. 205; no. 6; pp. 1 - 22
Main Author: Shi, Shelly Yiran
Format: Article
Published: Springer Nature Jun2025
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=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