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Equation 77 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Δτ

Δτ\Delta\tau
Δτ\Delta\tau

What this part means

Δτ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

Δτ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Two degenerate limits of the proper-time form confirm the derivative is doing the right job rather than hiding a division problem. As m→\to0 , Δ\Deltaϕ\phi→\to0 at every fixed Δ\Deltaτ\tau , so the slope — and therefore mopm_{\rm op} — vanishes identically: a massless worldline is exactly the case with no proper time to speak of in the first place, and the formula correctly returns nothing to divide. And if the two branches are held at equal proper time, Δ\Deltaτ\tau=0 , then…

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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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