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.
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The first, , lives in the nonrelativistic (Galilei) symmetry group: translate the apparatus by a fixed vector , apply a velocity boost to the particle, translate by - , boost by - . 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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Equation 6 · 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.
The first, , lives in the nonrelativistic (Galilei) symmetry group: translate the apparatus by a fixed vector , apply a velocity boost to the particle, translate by - , boost by - . 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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