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ℏkeff2T/m≈5.9×104 rad\hbar k_{\rm eff}^2T/m\approx5.9\times10^{4}\,\mathrm{rad}

Why this formula appears here

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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keff2k_{\rm eff}^2

Symbol k_rm eff^2

krk_rm eff2f^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

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TT

Symbol T

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mm

Symbol m

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

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Published contexts (1)

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ℏkeff2T/m≈5.9×104 rad\hbar k_{\rm eff}^2T/m\approx5.9\times10^{4}\,\mathrm{rad}

Equation 127 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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