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Equation 118 · Part 4 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Δτ

Δϕclock=2π Δν Δτ≈0.294 rad.\Delta\phi_{\rm clock}=2\pi\,\Delta\nu\,\Delta\tau\approx0.294\ \text{rad}.
Δτ\Delta\tau

What this part means

Δτ is an input to the expression that computes the quantity on the left.

Its job in the formula

Δτ is an input to the expression that computes the quantity on the left.

The passage around this formula

The resulting clock phase is Δϕclock=2π Δν Δτ≈0.294 rad\Delta\phi_{\rm clock}=2\pi\,\Delta\nu\,\Delta\tau\approx0.294\ \text{rad}. This, again, is an exact evaluation of a stated formula under stated idealized assumptions — a single-photon clock transition, no recoil, no laser phase, a static height difference held exactly one second — offered as illustrative, not as a report of anything measured. No such experiment has been performed at this scale; it is precisely the regime the cited proposals argue is at the edge of feasibility with current optical-clock coherence and large-scale atom-fountain technology, not a regime already demonstrated.

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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