Superselection: realities that do not talk to each other

Most talk of many worlds reaches for the Everett picture: one state, many branches, all of them happening. There is an older, stiffer, and in some ways better way to get many realities, and it is already in the textbooks: superselection. This post explains it, and why this programme treats it as the strongest existing physics for multiple realities without new postulates.

What superselection is

A superselection rule forbids certain superpositions. Not dynamically, not approximately: the Hilbert space of the theory splits into sectors, and no physical operation, however clever, maps one sector into another or produces interference between them. Electric charge is the classic example: no physical process creates a superposition of charge 5 and charge 7, and no interference experiment can make one visible. The sectors are each fully quantum mechanical. Between them there is silence.

That silence is the point. Each sector is a complete, consistent world in the operational sense: a copy of quantum mechanics with its own state space, its own measurements, no operational access to the others. A theory with N sectors is, to any observer confined to one sector, N distinct realities of which they experience one. Nobody inside a sector can tell how many sectors the theory has.

Where the sectors come from

The best-understood sources are real physics. Charge sectors, from gauge invariance. Theta-vacua in Yang-Mills theory: a family of unitarily inequivalent vacua labelled by an angle, each a perfectly good quantum theory, with no tunnelling between them once the theory is settled; our universe lives in one theta sector and cannot probe the others. Infrared sectors in gauge theories and gravity, where different soft-photon and soft-graviton configurations define inequivalent representations of the field algebra; a state with one total charge-memory content and a state with another are different superselection worlds in a rigorous sense. And in de Sitter space, the alpha-vacua: a discrete family of vacua related by squeezing, each indistinguishable from a thermal state to any single observer, with the two-mode structure from the squeezed-states post in this series, and no local operation that moves you from one to another.

That last sentence is the strongest. It is not speculation about quantum gravity. It is the standard structure of the theory of de Sitter space, verified to the level the squeezed-state algebra can be verified: each sector thermal at the Gibbons-Hawking temperature, exactly, with correlations between sectors carried by the global state, invisible locally.

What this buys a multiverse programme

The Everett route to many realities needs a decision rule for which decompositions of the state count as worlds, and that rule has been contested for sixty years. The superselection route needs nothing of the sort. Sectors are not a decomposition choice; they are fixed by the theory’s algebra. The question how many worlds becomes how many sectors, which is a mathematical question with a definite answer for any given theory.

That is why the framework’s branch story is built on sectors rather than on Everett branches: it wants the count to be a structural fact, not an interpretive one. The cost is honesty about what is assumed. Standard superselection rules come from conserved charges; the framework’s branch sectors are not charges, and proposing a new superselection structure is a real theoretical commitment, not a free ride on the textbook cases. The programme’s models of this, the theta-vacua and alpha-vacua analogies, are labelled as analogies with mechanism, and the kill criterion is stated: if the proposed sector structure cannot be written as an algebraic fact about the substrate theory, the analogy is dead and the multiverse claim reverts to the contested Everett version.

With the walkthroughs done, the next series walks the papers themselves, from the dimensionality argument to the newest computational work, each carrying the status labels from the method series that follows the papers. The two exclusions met here and in the previous posts, no classical local substrate, no nonlinear multiverse, are the fence the whole programme is built inside.