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Equation 95 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol m_rm op

mop[LG]=ℏΦ/(vrb)=mm_{\rm op}[\mathcal L_{\rm G}]=\hbar\Phi/(v_rb)=m
mopm_{\rm op}

What this part means

mrm_rm op is part of the quantity the equation computes from the expression on the right.

Its job in the formula

mrm_rm op is part of the quantity the equation computes from the expression on the right.

The passage around this formula

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 vrv_r=ℏ\hbar keffk_{\rm eff}/m by definition of a recoil kick, the same number equals ℏ\hbar keff2k_{\rm eff}^2T/m , the ordinary recoil phase used to extract ℏ\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…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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