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Equation 129 · Part 2 · The Clock That Comes Back Wrong by Exactly Its Mass

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Δϕclock\Delta\phi_{\rm clock}
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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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