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    Home/Original/inverse
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    Inverse View

    It is not the case that Tensor calculus is not the proper mathematical instrument for translating quantum-theoretic equations of the electron into general relativity.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Cartan's formalism of moving frames (repère mobile) allows spinors to be defined on curved manifolds via local orthonormal frames (vielbeins) without requiring affine transformation laws.
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    • 2.The vielbein formalism embeds tensor calculus within a broader framework where ψ components are defined relative to local Lorentz frames, not arbitrary coordinate systems, dissolving the incompatibility Weyl identifies.
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    • 3.Fock and Ivanenko (1929) demonstrated explicitly that Dirac's equation admits generally covariant formulation using this extended calculus, empirically refuting the claim that tensor methods are categorically improper.
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    Reason for 2 of 2
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    • 1.The claim conflates the inadequacy of a specific formulation of tensor calculus with the inadequacy of tensor-based frameworks generally, committing a fallacy of hasty generalization.
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    • 2.Élie Cartan's and later Penrose's spinor calculus shows that the representation theory of the Lorentz group, not the affine group, is the operative constraint, and this constraint is manageable within generalized differential geometry.
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    • 3.If the proper criterion for mathematical instruments is empirical adequacy rather than transformation-group universality, then any calculus yielding generally covariant Dirac equations satisfies the requirement, regardless of its affine limitations.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Vectors and tensors transform under the most general linear (affine) transformations, meaning their transformation laws extend from Cartesian to affine coordinate systems.
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    • 2.The quantity ψ belongs to a representation of the rotation group that cannot be extended to the affine group.
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    • 3.Because ψ does not transform under affine transformations, ψ components cannot be defined relative to an arbitrary coordinate system in general relativity the way electromagnetic potentials and field strengths can.
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