Equation 91 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Phi

\Phi[\mathcal L_{\rm G}]=\frac{m\,v_rb}{\hbar}\approx6.29\times10^{4}\ \text{rad}.

\Phi

What this part means

the single measured phase.

Its job in the formula

Phi is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol PhiArticle meaning

Where the article explains it

A single measured phase $\Phi$ at one fixed loop area cannot, by itself, distinguish m from an unknown additive offset baked into the apparatus — any constant phase shift from an uncalibrated pulse timing, an unaccounted path-length difference, or a stray field looks identical to a rescaling of $\mathbf b$ $\cdot$ $\mathbf v$ .

The passage around this formula

The Galilei loop admits an exact, non-simulated numerical check of the whole chain, because $\Phi$ [ $\mathcal L_{\rm G}$ ] is precisely the recoil phase every stimulated-Raman atom interferometer already uses for its own calibration. Take a sodium atom, m=3.8175 $\times$ 10^{-26}\, $\mathrm{kg}$ , driven by a two-photon stimulated-Raman transition on the 589\, $\mathrm{nm}$ line, effective wavevector $k_{\rm eff}$ =2(2 $\pi$ /589\, $\mathrm{nm}$ )=2.1335 $\times$ 10^{7}\, $\mathrm{m^{-1}}$ [ 16 ] . The associated recoil velocity is $v_r$ = $\hbar$ $k_{\rm eff}$ /m=5.894\, $\mathrm{cm\,s^{-1}}$ . Hold the loop open for T=50\, $\mathrm{ms}$ , comparable to the short interrogation times of early stimulated-Raman interferometers, so the…

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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 surrounding passage

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