Node C03: Symmetry ↔ Conservation

Node C03: Symmetry ↔ Conservation

C03 — Symmetry ↔ Conservation { "id": "C03", "claim": "Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.", "domain": ["classical mechanics", "quantum field theory", "particle physics", "crystallography", "cosmology", "aesthetics"], "pattern": ["symmetry", "conservation", "Noether_correspondence", "Lie_groups"], "mechanism": "Noether's theorem: if the action S is invariant under a continuous transformation parameterized by ε, then the Noether current j^μ satisfies ∂_μ j^μ = 0, yielding a conserved charge Q = ∫ j^0 d³x. The mechanism is pure mathematics applied to physical Lagrangians.", "scale": "quantum → cosmic", "claim_tier": "T0", "sources": [ "Noether, E. (1918). 'Invariante Variationsprobleme.' Nachr. v. d. Ges. d. Wiss. zu Goettingen, 235-257.", "Weyl, H. (1928). Gruppentheorie und Quantenmechanik.", "Wigner, E. (1939). 'On Unitary Representations of the Inhomogeneous Lorentz Group.' Ann. Math., 40(1), 149-204." ], "dual": "Symmetry-breaking (C04) — the structure that voids symmetry produces the phenomenological world.", "falsifier": "For the theorem: proof error (none found in 107 years). For the mapping to physical reality: a conserved quantity in nature with no underlying symmetry of the action; or a symmetry with no corresponding conservation law.", "rival_frame": "Noether's theorem is a mathematical identity, not a physical claim. It says nothing about WHY nature has symmetries — it only tells us that IF a symmetry exists, a conservation law follows. The symmetries themselves remain unexplained.", "independence_check": "MATHEMATICAL PROOF — universally applied, not independently derived. However: the applications span classical mechanics (Noether), quantum theory (Weyl), particle physics (Wigner's classification), and cosmology — each domain found the theorem independently useful without borrowing from another domain's application.", "pattern_type": "mathematical", "maps_to_axiom": ["A1", "A3"] }

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Corpus map

• Same node, other planes: Encyclopedia C03 · Inventory invariant
• Edges touching C03: convergence edge 3 · disconfirming edge 4
• Catalogue hub: Public Article · Schema