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It is not the case that Phase differences predicted by Weyl's theory (with the -i factor) are physically measurable, as demonstrated by interference experiments with electrons.
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Reasons For
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Reason for 1 of 2
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1.
Electron interference experiments measure relative phase differences, not the absolute gauge phase introduced by Weyl's U(1) factor.
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2.
Weyl's original 1918 theory posited spacetime-path-dependent scale changes, whereas quantum mechanical phase is a distinct mathematical structure with different physical interpretation.
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3.
The empirical success of quantum electrodynamics vindicates London's 1927 reinterpretation of Weyl's gauge idea, not Weyl's original metrical theory, making the inference from interference experiments to Weyl's specific claim underdetermined.
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Reason for 2 of 2
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1.
The Aharonov-Bohm effect, often cited as confirming gauge-phase measurability, demonstrates that physically meaningful phase differences arise from electromagnetic potentials, not from Weyl's spacetime geometry.
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2.
Conflating the empirical confirmation of U(1) quantum phase with confirmation of Weyl's geometrical gauge principle commits an equivocation between formally similar but physically distinct theoretical structures.
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Reasons Against
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Reason against
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1.
Measuring a phase difference requires an interference experiment.
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2.
Interference experiments cannot be performed with macroscopic objects like clocks.
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3.
Interference experiments can be performed with electrons.
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