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Equation 118 · Part 5 · The Clock That Comes Back Wrong by Exactly Its Mass

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

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.