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Equation 90 · Part 6 · The Clock That Comes Back Wrong by Exactly Its Mass

subscript

vrb=vr2T=1.737×10−4 m2 s−1v_rb=v_r^2T=1.737\times10^{-4}\,\mathrm{m^2\,s^{-1}}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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