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Published equation contexts

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

Why this formula appears here

Call Φ\Phi[LG\mathcal L_{\rm G}]=m\,b\mathbf b⋅\cdotv\mathbf v/ℏ\hbar the loop’s phase debt : what the representation charges for a loop the classical group considered free. The loop invariant b\mathbf b⋅\cdotv\mathbf v carries units of m2 s−1\mathrm{m^2\,s^{-1}} , exactly the units of ℏ\hbar/mass\text{mass} , so Φ\Phi is dimensionless as a phase must be, and mass is recoverable from it as

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

Equation 40 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Call Φ\Phi[LG\mathcal L_{\rm G}]=m\,b\mathbf b⋅\cdotv\mathbf v/ℏ\hbar the loop’s phase debt : what the representation charges for a loop the classical group considered free. The loop invariant b\mathbf b⋅\cdotv\mathbf v carries units of m2 s−1\mathrm{m^2\,s^{-1}} , exactly the units of ℏ\hbar/mass\text{mass} , so Φ\Phi is dimensionless as a phase must be, and mass is recoverable from it as

Meanings in this article

  • Φ\Phi: dimensionless as a phase must be, and mass is recoverable from it as.
  • mm: the mass.
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