Equation 40 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol Phi

\Phi[\mathcal L_{\rm G}]=m\,\mathbf b\cdot\mathbf v/\hbar

\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 part of the quantity the equation computes from the expression on the right.

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

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 →

The article lists its research sources here.