Equation 86 · The Clock That Comes Back Wrong by Exactly Its Mass
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol k_rm eff
m eff is part of the quantity the equation computes from the expression on the right.
Symbol pi
pi is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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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.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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What the article says around this equation
The Galilei loop admits an exact, non-simulated numerical check of the whole chain, because [] is precisely the recoil phase every stimulated-Raman atom interferometer already uses for its own calibration. Take a sodium atom, m=3.817510^{-26}\, , driven by a two-photon stimulated-Raman transition on the 589\, line, effective wavevector =2(2/589\,)=2.133510^{7}\, [ 16 ] . The associated recoil velocity is = /m=5.894\, . Hold the loop open for T=50\, , comparable to the short interrogation times of early stimulated-Raman interferometers, so the…
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The Galilei loop admits an exact, non-simulated numerical check of the whole chain, because [] is precisely the recoil phase every stimulated-Raman atom interferometer already uses for its own calibration. Take a sodium atom, m=3.817510^{-26}\, , driven by a two-photon stimulated-Raman transition on the 589\, line, effective wavevector =2(2/589\,)=2.133510^{7}\, [ 16 ] . The associated recoil velocity is = /m=5.894\, . Hold the loop open for T=50\, , comparable to the short interrogation times of early stimulated-Raman interferometers, so the translation leg is b=T=2.947\, . The loop area is b=T=1.73710^{-4}\, , and the phase debt is
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