Equation 113 · Part 4 · The Clock That Comes Back Wrong by Exactly Its Mass

superscript

\Delta\tau\approx1.090\times10^{-16}\,\mathrm s

superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

Full expressionsuperscriptArticle meaning

The passage around this formula

To make this concrete without simulation, take the weak-field proper-time rate d $\tau$ /dt $\approx$ 1+gz/ $c^2$ for a static height z in Earth’s field, so that holding two branches at a height difference $\Delta$ z for coordinate time T gives $\Delta$ $\tau$ $\approx$ g\, $\Delta$ z\,T/ $c^2$ . For $\Delta$ z=1\, $\mathrm m$ and T=1\, $\mathrm s$ , $\Delta$ $\tau$ $\approx$ 1.090 $\times$ 10^{-16}\, $\mathrm s$ . Pair this with a single-photon optical clock transition near 698\, $\mathrm{nm}$ , comparable to the transition used in strontium-lattice-clock proposals for this kind of experiment [ 11 , 13 ] , giving $\Delta$ $\nu$ $\approx$ 4.295 $\times$ 10^{14}\, $\mathrm{Hz}$ and $\Delta$ E=h $\Delta$ $\nu$ $\approx$ 2.846 $\times$ 10^{-19}\, $\mathrm J$ , a mass excess $\Delta$ …

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the article section

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