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Equation 138 · Part 2 · The Entry a Relabeling Cannot Write

Symbol H_f

UHfU†UH_fU^\dagger
HfH_f

What this part means

HfH_f 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

HfH_f 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 crank-magnet error this section exists to name lives exactly at the boundary between these two Hamiltonians: an observer who correctly computes UHfH_fU†U^\dagger — a legitimate operator identity, unchanged from the passive-relabeling case above — and then uses that operator, rather than Hc(t)H_c(t) , to predict or track the rotating frame’s own dynamics will find a discrepancy with no term in their own equations to explain it, on a clock the lab frame does not keep. The discrepancy is not missing energy. It is a dropped term whose physical origin is whatever classical control is enacting U(t) in the first place — the field ramp, the driven rotation — already doing ordinary, accountable work on…

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Sources cited in the article section

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