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Equation 145 · Part 2 · The Entry a Relabeling Cannot Write

Symbol ρ

ΔEΛ(ρ)\Delta E_\Lambda(\rho)
ρ\rho

What this part means

ρ 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

ρ 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 honest limitation is not in any of those checks; it is in what the construction was never built to promise. Δ\Delta EΛ(ρ)E_\Lambda(\rho) is a number attached to one named channel and one named coarse Hamiltonian, not an observer-independent fact about “the” missing energy. A different, equally legitimate choice of Λ\Lambda — a different split of which few collective degrees of freedom count as “the system,” or a different unitary dilation of the same open dynamics, since Stinespring’s theorem guarantees a dilation exists but not that it is unique [ 9 ] — will generally return a different nonzero reading for the identical experiment, and nothing in the operator itself adjudicates which choice is…

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Sources cited in the surrounding passage

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