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Equation 84 · Part 3 · The Clock That Comes Back Wrong by Exactly Its Mass

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m=3.8175×10−26 kgm=3.8175\times10^{-26}\,\mathrm{kg}
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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.

The passage around this formula

The Galilei loop admits an exact, non-simulated numerical check of the whole chain, because Φ\Phi[LG\mathcal L_{\rm G}] is precisely the recoil phase every stimulated-Raman atom interferometer already uses for its own calibration. Take a sodium atom, m=3.8175×\times10^{-26}\,kg\mathrm{kg} , driven by a two-photon stimulated-Raman transition on the 589\,nm\mathrm{nm} line, effective wavevector keffk_{\rm eff}=2(2π\pi/589\,nm\mathrm{nm})=2.1335×\times10^{7}\,m−1\mathrm{m^{-1}} [ 16 ] . The associated recoil velocity is vrv_r=ℏ\hbar keffk_{\rm eff}/m=5.894\,cm s−1\mathrm{cm\,s^{-1}} . Hold the loop open for T=50\,ms\mathrm{ms} , comparable to the short interrogation times of early stimulated-Raman interferometers, so the…

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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.

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Sources cited in the surrounding passage

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