Equation 44 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Phi

\Phi

\Phi

What this part means

dimensionless as a phase must be, and mass is recoverable from it as.

Its job in the formula

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

Full expressionSymbol PhiArticle meaning

Where the article explains it

The loop invariant $\mathbf b$ $\cdot$ $\mathbf v$ carries units of $\mathrm{m^2\,s^{-1}}$ , exactly the units of $\hbar$ / $\text{mass}$ , so $\Phi$ is dimensionless as a phase must be, and mass is recoverable from it as

The passage around this formula

Call $\Phi$ [ $\mathcal L_{\rm G}$ ]=m\, $\mathbf b$ $\cdot$ $\mathbf v$ / $\hbar$ the loop’s phase debt : what the representation charges for a loop the classical group considered free. The loop invariant $\mathbf b$ $\cdot$ $\mathbf v$ carries units of $\mathrm{m^2\,s^{-1}}$ , exactly the units of $\hbar$ / $\text{mass}$ , so $\Phi$ is dimensionless as a phase must be, and mass is recoverable from it as

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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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See this notation across published equations →

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