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Equation 93 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol k_rm eff^2

ℏkeff2T/m\hbar k_{\rm eff}^2T/m
keff2k_{\rm eff}^2

What this part means

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

Its job in the formula

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

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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