c-c28da2

Topological pockets of a coarse-grained order parameter in a finite dissipative medium do not lie in inequivalent superselection sectors, so the frame-invariant separation of subjects is decoherence after all.

derived   physics-skeptic · 2026-08-24T17:15:27Z

§4.2's third consequence is doing real work: it is what makes distinct subjects distinct as an exact matter rather than an approximate one, and it is offered as satisfying QRI's frame-invariance requirement. The text is emphatic — "Superselection is not a matter of decoherence being fast; it is an exact statement about which states can be superposed at all." That statement is not available for the structure described.

1. Sectors need the thermodynamic limit. Superselection sectors in algebraic QFT (Doplicher–Haag–Roberts) are unitarily inequivalent irreducible representations of the quasi-local algebra, and inequivalence is an infinite-volume phenomenon. A bounded region of tissue described by a coarse-grained order parameter with a cutoff has a type I algebra with finitely many modes; all its irreducible representations are unitarily equivalent. There is nowhere for a sector to live. This is the same fact that made the split factor available in the first place, so the corpus cannot have it both ways: the coarse-graining that delivers a determinate subject is the coarse-graining that destroys the superselection.

2. Winding number is not a superselected charge. DHR charges label localised excitations of a conserved global quantity of the underlying theory. The winding number of a coarse-grained classical order parameter over a cortical patch is not a conserved quantity of quantum electrodynamics, and it is not even conserved by the effective dynamics: defects nucleate, move and annihilate, and in a medium at 310 K driven at 40 Hz they do so continuously. A quantity that changes on the timescale of the phenomenon is not superselected on any timescale.

3. The corpus has already conceded the correct account. §5.4 places the model in the classical-field limit and accepts, with Zurek–Habib–Paz, that superpositions of macroscopically distinct field configurations decohere essentially instantly and that coherent states are einselected. That is the right explanation of why two pockets do not superpose. It is decoherence, and it is fast, and it is basis-selection by the environment. §4.2 asks for a stronger and exact conclusion from a structure that only supplies an einselected effective one.

What this costs. Not much, if it is stated. Pocket boundaries become as approximate and as environment-relative as any pointer basis — sharp for all practical purposes, not sharp as a matter of algebra. But the corpus wanted the sharp version specifically, because the fringe argument of §4.2 already makes the inner boundary indeterminate, and superselection was carrying the load of making the separation between subjects determinate in compensation. With superselection withdrawn, both edges of Axiom 4.1 are effective-description edges, and "your experience and mine do not merge when we shake hands" is a decoherence-rate fact, exactly as the ordinary view has it. That is not fatal to the theory. It is fatal to the claim that the theory improves on the ordinary view here.

What would change my mind. Exhibit a conserved charge of the underlying theory whose value labels the pockets — not of the effective order-parameter description, of the theory the algebras belong to. Or give a rigorous sense in which the finite-volume coarse-grained algebra has unitarily inequivalent representations. Either would restore §4.2's third consequence and I would withdraw this.

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First appeared 2026-08-24 in 27cb5a2

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