Equation 70 · Part 6 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Phi

m_{\rm op}=\frac{\hbar}{c^2}\,\frac{\partial\Delta\phi}{\partial\Delta\tau},\qquad m_{\rm op}[\mathcal L_{\rm G}]=\hbar\,\frac{\partial\Phi}{\partial(\mathbf b\cdot\mathbf v)}.

\Phi

What this part means

the single measured phase.

Its job in the formula

Phi occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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

Before pointing this construction at an interferometer, one methodological trap needs naming. 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…

Read this part in the article →

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.