Equation 41 · The Clock That Comes Back Wrong by Exactly Its Mass

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\mathbf b\cdot\mathbf v

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b

Symbol b

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v

Symbol v

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multiplication

Multiply the quantities on either side.

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What the article says around this equation

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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