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Equation 124 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol k_rm eff

keffgT2≈8.8×107 radk_{\rm eff}gT^2\approx8.8\times10^{7}\,\mathrm{rad}
keffk_{\rm eff}

What this part means

krk_rm eff is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

krk_rm eff is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The scale of what needs to be canceled is worth stating plainly, using the same illustrative parameters as the previous section. The laser/center-of-mass term for a single-photon transition near 698\,nm\mathrm{nm} ( keffk_{\rm eff}≈\approx9.00×\times10^6\,m−1\mathrm{m^{-1}} ) scales as keffk_{\rm eff}gT2T^2≈\approx8.8×\times10^{7}\,rad\mathrm{rad} for T=1\,s\mathrm s . The recoil term for a strontium-mass atom ( m≈\approx1.443×\times10^{-25}\,kg\mathrm{kg} ) scales as ℏ\hbar keff2k_{\rm eff}^2T/m≈\approx5.9×\times10^{4}\,rad\mathrm{rad} . The clock term computed above is ≈\approx0.29\,rad\mathrm{rad} . Both confound terms are, respectively, roughly eight and five orders of magnitude larger than the signal, which is exactly why…

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