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Equation 3 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol L_rm G

LG\mathcal L_{\rm G}
LGL_{\rm G}

What this part means

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

Its job in the formula

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

The passage around this formula

The first, LG\mathcal L_{\rm G} , lives in the nonrelativistic (Galilei) symmetry group: translate the apparatus by a fixed vector b\mathbf b , apply a velocity boost v\mathbf v to the particle, translate by -b\mathbf b , boost by -v\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.

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Sources cited in the article section

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