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Equation 138 · Part 4 · The Entry a Relabeling Cannot Write

subscript

UHfU†UH_fU^\dagger
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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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Learn the underlying idea

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

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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