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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
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    Perspectives
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Noether's second theorem yields differential identities (Bianchi-type), not genuine conservation laws with locally conserved currents in curved spacetime.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Differential identities ARE conservation laws: they express continuity equations relating energy-momentum flow to curvature, physically meaningful locally.
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    • 2.Quasilocal currents (e.g., Komar integral) rigorously define conserved quantities in curved spacetime without requiring global symmetries, contradicting the claim.
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    • 3.Noether's second theorem generates the Bianchi identities precisely because they govern actual physical conservation of energy-momentum in general relativity.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Noether's second theorem applies to gauge theories with off-shell symmetries, yielding identities among equations of motion, not independent conservation laws.
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    • 2.In curved spacetime, the covariant divergence of the stress-energy tensor vanishes identically (Bianchi identity), making it a constraint rather than a conservation law.
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    • 3.Genuine local conservation requires a globally defined current density; curved spacetime lacks global symmetries needed for Noether's first theorem to apply.
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