Equation 95 · Part 3 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Phi

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

\Phi

What this part means

the single measured phase.

Its job in the formula

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

Full expressionSymbol PhiArticle meaning

Where the article explains it

A single measured phase $\Phi$ at one fixed loop area cannot, by itself, distinguish m from an unknown additive offset baked into the apparatus — any constant phase shift from an uncalibrated pulse timing, an unaccounted path-length difference, or a stray field looks identical to a rescaling of $\mathbf b$ $\cdot$ $\mathbf v$ .

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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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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