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Equation 118 · Part 7 · The Clock That Comes Back Wrong by Exactly Its Mass

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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