← All parts of this equation

Equation 104 · Part 3 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Δτ

Δϕclock=−ΔEℏ Δτ.\Delta\phi_{\rm clock}=-\frac{\Delta E}{\hbar}\,\Delta\tau.
Δτ\Delta\tau

What this part means

Δτ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

Δτ is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…the standard bookkeeping in which a system’s total rest energy Mc2c^2 includes whatever internal energy HintH_{\rm int} it holds: M=M0M_0+HintH_{\rm int}/c2c^2 . If the same object is sent along two paths that differ in proper time by Δ\Deltaτ\tau , and its internal state differs between the two paths — ground on one, excited on the other — then the two branches’ free-particle phases differ by Δϕclock=−ΔEℏ Δτ\Delta\phi_{\rm clock}=-\frac{\Delta E}{\hbar}\,\Delta\tau. The shared M0M_0c2c^2Δ\Deltaτ\tau/ℏ\hbar term, common to both arms, is an overall phase and drops out of any interference…

Read this part in the article →

Learn the underlying idea

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

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