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    Made withinDC&Austin
    In general relativity the gauge factor necessarily become... — Carmelics
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    Home/Modality & Possibility
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    In general relativity the gauge factor necessarily becomes an arbitrary function of spacetime position.

    Causation
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.In general relativity every spacetime point has its own local tetrad.
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    • 2.The gauge freedom in the spinor transformation is tied to each tetrad independently.
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    • 3.The rigid connection between tetrads at different points is removed in general relativity.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Global gauge symmetry in special relativity already permits arbitrary constant phase transformations without position-dependence, showing gauge freedom precedes GR.
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    • 2.Weyl's own 1918 unified field theory introduced local gauge invariance as an independent postulate, not as a consequence derived from GR's tetrad structure.
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    • 3.The necessity claim conflates a sufficient condition (curved spacetime with local tetrads) with a necessary one, since local gauge freedom can be stipulated in flat spacetime.
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    Reason against 2 of 2
    ?
    • 1.Norton's hole argument analysis shows that general covariance in GR underdetermines the physical interpretation of spacetime-dependent transformations.
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    • 2.The inference from 'each point has an independent tetrad' to 'gauge factor must be position-dependent' suppresses the conventionalist alternative that global gauges remain physically admissible by stipulation.
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    Related

    Global gauge symmetry in special relativity already permits arbitrary constant p...In general relativity every spacetime point has its own local tetrad.Norton's hole argument analysis shows that general covariance in GR underdetermi...The gauge freedom in the spinor transformation is tied to each tetrad independen...
    +4 moreShow less
    The inference from 'each point has an independent tetrad' to 'gauge factor must ...The necessity claim conflates a sufficient condition (curved spacetime with loca...The rigid connection between tetrads at different points is removed in general r...Weyl's own 1918 unified field theory introduced local gauge invariance as an ind...

    Similar

    The gauge factor must be treated as a constant in special relativity.85%The spacetime geometry is itself a dynamical variable in general relat...77%In general relativity, the gravitational field is accounted for by the...76%Canonical formulations of general relativity face constraints on their...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: weyl
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    We come now to the critical part of the theory. In my view the origin and the necessity for the electromagnetic field lie in the following justification. The components \(\psi_{1},\psi_{2}\) are, in fact, not uniquely determined by the tetrad but only to the extent that they can still be multiplied by an arbitrary “gauge-factor” \(e^{i\lambda}\) of absolute value 1. The transformation of the \(\psi\) induced by a rotation of the tetrad is determined only up to such a factor. In the special
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit