$$m_{\rm op}[\mathcal L_{\rm G}]=\hbar\Phi/(v_rb)=m$$

Equation 95 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

This is an exact analytic evaluation of the formula derived above for stated, idealized parameters — not a simulation, not a measurement, and not the output of any code run for this article. It is offered as illustrative, and it carries a built-in consistency check: because $v_r$=$\hbar$ $k_{\rm eff}$/m by definition of a recoil kick, the same number equals $\hbar$ $k_{\rm eff}^2$T/m , the ordinary recoil phase used to extract $\hbar$/m in precision atom-interferometry measurements through the general path-integral formalism for atomic interferometry [ 14 ] . The two expressions are algebraically identical, so this is a check that the loop construction reproduces a quantity the field already measures by…

Meanings in this article

• $\Phi$: the single measured phase.

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