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Equation 48 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol m_rm op

mop[LG]m_{\rm op}[\mathcal L_{\rm G}]
mopm_{\rm op}

What this part means

mrm_rm op 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

mrm_rm op 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

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…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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