Equation 40 · Part 2 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol L_rm G

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

L_{\rm G}

What this part means

$L_r$ m G is part of the quantity the equation computes from the expression on the right.

Its job in the formula

$L_r$ m G is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol L_rm GArticle meaning

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 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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