Equation 40 · Part 8 · The Clock That Comes Back Wrong by Exactly Its Mass

subscript

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

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle 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

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

The article lists its research sources here.