Equation 35 · The Entry a Relabeling Cannot Write
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol H_c
is part of the quantity the equation computes from the expression on the right.
Symbol H_f
is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Before asking what a genuine coarse-graining exposes, the construction has to survive the case where nothing at all is discarded. Take = — no reduction in the space of states — and let the “coarse” description be nothing more than the same physics seen through a fixed, time-independent relabeling: a rotated spin basis, a renamed pair of levels, a change of which linear combination of states a lab calls “up.” Model this as := W for a fixed unitary W , and, because nothing has been thrown away, define the coarse Hamiltonian self-consistently as the same physical generator carried through that same relabeling, := W .
For background, read the article’s source list.
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