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    Weyl's geometric theory is in conflict with quantum mecha... — Carmelics
    Home/Modality & Possibility
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    Weyl's geometric theory is in conflict with quantum mechanics in a fundamental way

    Causation
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    2 reasons for
    1 reason against

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Weyl's gauge field requires path-dependent rescaling of the metric, making rest mass a functional of worldline history rather than an intrinsic invariant.
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    • 2.Quantum field theory's renormalization group demonstrates that particle masses run with energy scale, but this running is universal and history-independent, contradicting Weyl's path-dependence.
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    • 3.Dirac's 1951 reformulation of Weyl geometry required imposing a gauge-fixing condition to recover constant masses, revealing that historical path-independence must be externally stipulated, not derived.
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    Reason for 2 of 2
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    • 1.The quantum mechanical identity of indiscernibles for fermions is encoded in the Pauli exclusion principle, which presupposes exact mass-energy degeneracy across all particles of a given kind.
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    • 2.Weyl's non-integrable length connection entails that mass differences between identically-typed particles accumulate monotonically with divergent trajectories, violating the superposition principle's basis in exact state-space degeneracy.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.In quantum theory, there is a direct relation between clock rates and the masses of particles
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    • 2.A particle with a given rest mass possesses a natural frequency determined by its rest mass, the speed of light, and Planck's constant
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    • 3.In a Weyl geometry, not only clocks but also the masses of particles would depend on their histories
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    Topics

    Modality & PossibilityCausation

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    Related

    A particle with a given rest mass possesses a natural frequency determined by it...Dirac's 1951 reformulation of Weyl geometry required imposing a gauge-fixing con...If two protons have different histories, they would have different masses in a W...In a Weyl geometry, not only clocks but also the masses of particles would depen...
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    In quantum theory, there is a direct relation between clock rates and the masses...Quantum field theory's renormalization group demonstrates that particle masses r...Quantum mechanics requires that particles of the same kind must be exactly ident...The quantum mechanical identity of indiscernibles for fermions is encoded in the...Weyl's gauge field requires path-dependent rescaling of the metric, making rest ...Weyl's non-integrable length connection entails that mass differences between id...

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    SEP: weyl
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    When quantum theory was developed a few years later it became clear that Weyl’s theory was in conflict with experience in an even more fundamental way since there is a direct relation between clock rates and masses of particles in quantum theory. A particle with a certain rest mass \(m\) possesses a natural frequency which is a function of its rest mass, the speed of light \(c\), and Planck’s constant \(h\). This means that in a Weyl geometry not only clocks would depend on their histori
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    Details

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