Equation 5 · The Clock That Comes Back Wrong by Exactly Its Mass

What does this equation mean?

\mathbf v

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

v

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.

Understand this part →

How to interpret it

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

What the article says around this equation

The first, $\mathcal L_{\rm G}$ , lives in the nonrelativistic (Galilei) symmetry group: translate the apparatus by a fixed vector $\mathbf b$ , apply a velocity boost $\mathbf v$ to the particle, translate by - $\mathbf b$ , boost by - $\mathbf v$ . As abstract group elements this composes to the identity, because ordinary spatial translations and ordinary Galilean boosts, considered as instantaneous operations with no elapsed time attached, form an abelian subgroup: order does not matter, and the net element is trivial by direct substitution.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to The Clock That Comes Back Wrong by Exactly Its Mass

See this formula across 3 published contexts →

Browse the mathematical compendium →