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    Inverse View

    It is not the case that Energy-momentum conservation laws for general coordinate transformations and internal Lorentz transformations of tetrads can be derived as a special case of Noether's second theorem.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Noether's second theorem yields differential identities (Bianchi-type), not genuine conservation laws with locally conserved currents in curved spacetime.
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    • 2.Energy-momentum pseudo-tensors in GR depend on coordinate choice, undermining the claim that diffeomorphism invariance yields bona fide conservation laws.
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    • 3.Hilbert and Klein explicitly showed in 1917 that general covariance produces identities that trivialize energy conservation, a point Noether's theorem formalizes rather than resolves.
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    Reason for 2 of 2
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    • 1.The tetrad formalism introduces local Lorentz freedom as a gauge symmetry, but Rosenfeld's 1930 analysis showed such internal symmetries generate constraints, not independent conservation laws.
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    • 2.Conservation laws derived via Noether's second theorem for tetrad Lorentz invariance are not independent of those from diffeomorphism invariance due to the contracted Bianchi identities, making the 'special case' claim redundant rather than illuminating.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The tetrad formalism provides a framework relating local Lorentz transformations to spacetime geometry.
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    • 2.Noether's second theorem governs conservation laws arising from continuous symmetry groups.
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    • 3.General coordinate transformations and internal Lorentz transformations of tetrads constitute such continuous symmetry groups.
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