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    Made withinDC&Austin
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The local tetrads are determined by the spacetime metric only up to local Lorentz transformations.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The gauge-theoretic underdetermination of tetrads by the metric is a formal artifact, not a physical indeterminacy, since all tetrad choices yield identical observable predictions.
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    • 2.Kretschmann's 1917 objection establishes that any theory can be reformulated with formal symmetries that do not correspond to genuine physical degrees of freedom.
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    • 3.Therefore the 'extra' local Lorentz freedom indicates redundancy in the tetrad formalism rather than genuine underdetermination of physical spacetime structure by the metric.
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    Reason for 2 of 2
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    • 1.Cartan's moving frames formalism shows that a choice of tetrad field encodes additional geometric structure—specifically, a preferred parallelism—absent from the metric alone.
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    • 2.Weitzenbock's absolute parallelism and teleparallel gravity theories exploit precisely this extra structure to define connections inequivalent to the Levi-Civita connection despite sharing the same metric.
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    • 3.If distinct tetrad fields related by local Lorentz transformations can ground physically distinct geometric structures, the metric does not merely underdetermine tetrads up to Lorentz equivalence but fails to determine the relevant physical geometry at all.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Every tetrad uniquely determines the pseudo-Riemannian spacetime metric g_ij.
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    • 2.The tetrad has 16 independent components whereas the spacetime metric g_ij has only 10 independent components.
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    • 3.The extra 6 degrees of freedom of the tetrads not determined by the metric correspond to the elements of a 6-parameter internal Lorentz group.
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    Strongest counterpoint
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