Equation 127 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol k_rm eff^2

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

k_{\rm eff}^2

What this part means

$k_r$ m ef $f^2$ is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Its job in the formula

$k_r$ m ef $f^2$ is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Full expressionSymbol k_rm eff^2Article meaning

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\, $\mathrm{nm}$ ( $k_{\rm eff}$ $\approx$ 9.00 $\times$ 10^6\, $\mathrm{m^{-1}}$ ) scales as $k_{\rm eff}$ g $T^2$ $\approx$ 8.8 $\times$ 10^{7}\, $\mathrm{rad}$ for T=1\, $\mathrm s$ . The recoil term for a strontium-mass atom ( m $\approx$ 1.443 $\times$ 10^{-25}\, $\mathrm{kg}$ ) scales as $\hbar$ $k_{\rm eff}^2$ T/m $\approx$ 5.9 $\times$ 10^{4}\, $\mathrm{rad}$ . The clock term computed above is $\approx$ 0.29\, $\mathrm{rad}$ . Both confound terms are, respectively, roughly eight and five orders of magnitude larger than the signal, which is exactly why…

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