← Mathematical compendium

Published equation contexts

b,v\mathbf b,\mathbf v

Why this formula appears here

Because m enters only through the fixed central charge and b\mathbf b,v\mathbf v are the loop’s own declared parameters, mopm_{\rm op}[LG\mathcal L_{\rm G}] does not depend on which inertial frame is used to describe the apparatus from outside: boosting the whole laboratory changes how an external observer labels positions and velocities, but it does not change which group elements were composed in the lab, nor the central charge attached to the representation. The construction is a scalar of the loop, not an artifact of a chosen external frame. A torsion balance testing the ordinary, classical equivalence principle never needs this fact, because nothing about a suspended mass on a fiber depends on…

Read the full article-specific guide →

Read the representative guide

bb

Symbol b

b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →
vv

Symbol v

v is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Read this term in its guide →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

b,v\mathbf b,\mathbf v

Equation 47 · Evolutionary Physics

The Clock That Comes Back Wrong by Exactly Its Mass

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Because m enters only through the fixed central charge and b\mathbf b,v\mathbf v are the loop’s own declared parameters, mopm_{\rm op}[LG\mathcal L_{\rm G}] does not depend on which inertial frame is used to describe the apparatus from outside: boosting the whole laboratory changes how an external observer labels positions and velocities, but it does not change which group elements were composed in the lab, nor the central charge attached to the representation. The construction is a scalar of the loop, not an artifact of a chosen external frame. A torsion balance testing the ordinary, classical equivalence principle never needs this fact, because nothing about a suspended mass on a fiber depends on…

Equation guide → · Article →