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Published equation contexts

ℏkeff2T/m\hbar k_{\rm eff}^2T/m

Why this formula appears here

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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keff2k_{\rm eff}^2

Symbol k_rm eff^2

krk_rm eff2f^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

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TT

Symbol T

T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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mm

Symbol m

m is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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ℏkeff2T/m\hbar k_{\rm eff}^2T/m

Equation 93 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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