Equation 121 · The Clock That Comes Back Wrong by Exactly Its Mass
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Symbol L_rm P
going to mean anything operationally, it cannot live in the part of an interferometer phase that the weak equivalence principle already forbids from carrying mass information.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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This objection is not merely an engineering difficulty to be improved away. It is close to a theorem. The weak equivalence principle — the universality of free fall, tested to extraordinary precision using exactly this kind of dual-species interferometry [ 12 ] — guarantees that the center-of-mass trajectory of a falling object cannot depend on its mass or internal composition. Since the dominant term in the standard gravimeter phase is built from that trajectory and from the laser field alone, mass is required to cancel from it; a claimed mass-dependence surviving in the leading term would itself be evidence against the weak equivalence principle, not evidence for a working mass gauge. If…
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This objection is not merely an engineering difficulty to be improved away. It is close to a theorem. The weak equivalence principle — the universality of free fall, tested to extraordinary precision using exactly this kind of dual-species interferometry [ 12 ] — guarantees that the center-of-mass trajectory of a falling object cannot depend on its mass or internal composition. Since the dominant term in the standard gravimeter phase is built from that trajectory and from the laser field alone, mass is required to cancel from it; a claimed mass-dependence surviving in the leading term would itself be evidence against the weak equivalence principle, not evidence for a working mass gauge. If the phase debt of is going to mean anything operationally, it cannot live in the part of an interferometer phase that the weak equivalence principle already forbids from carrying mass information.
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