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Are Symmetry Principles Meta-Laws?

Shi, Shelly Yiran (2025) Are Symmetry Principles Meta-Laws? [Preprint]

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Abstract

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 (2007, 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 (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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Shi, Shelly Yiranyis007@ucsd.edu0009-0003-4496-6392
Keywords: Noether's theorem, symmetry, conservation laws, meta-laws
Subjects: Specific Sciences > Physics > Classical Physics
Depositing User: Ms. Shelly Yiran Shi
Date Deposited: 07 May 2025 12:36
Last Modified: 07 May 2025 12:36
Item ID: 25255
Subjects: Specific Sciences > Physics > Classical Physics
Date: 2025
URI: https://philsci-archive.pitt.edu/id/eprint/25255

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