Equation 95 · Part 4 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol v_r

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

v_r

What this part means

$v_r$ is an input to the expression that computes the quantity on the left.

Its job in the formula

$v_r$ is an input to the expression that computes the quantity on the left.

Full expressionSymbol v_rArticle meaning

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 $v_r$ = $\hbar$ $k_{\rm eff}$ /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…

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Learn the underlying idea

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

[14] The Feynman Path Integral Approach to Atomic Interferometry: A Tutorial ↗

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