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Equation 91 · Part 7 · The Clock That Comes Back Wrong by Exactly Its Mass

fraction

Φ[LG]=m vrbℏ≈6.29×104 rad.\Phi[\mathcal L_{\rm G}]=\frac{m\,v_rb}{\hbar}\approx6.29\times10^{4}\ \text{rad}.
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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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A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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