Since the 1970s, the Everett-Wheeler many-worlds interpretation (MWI) of Quantum Mechanics (1955) has been much in the news. One wonders about the worlds in question, their branches, their splittings, their number. It is most often ignored that this language is not that of Everett, whom Wheeler very quickly stopped supporting. Moreover, for some interpreters, the real meaning of Everett ideas is not the coexistence of many worlds, but the existence of a single quantum one. In this context, what should we think of attempts to verify Everett thesis? What about the connexion between MWI and the cosmological multiverse? How to understand the links between the quantum world and the classical one? This article tries to answer some of these questions.
The Everett interpretation of quantum mechanics is, inter alia, an interpretation of objective probability: an account of what probability really is. Everett called his work “wave mechanics without probability” for good reason: it provides a non-chancy base level of categorical properties and relations. The objection may concern justification rather than understanding, particularly if decoherence theory is used to derive the Born rule. The branch-counting rule makes nonsense of quantum mechanics but it appears to be suggested by the picture of branching. Branch counting is hardly a rival to the branch-weight rule as an interpretation of branching structure, if it brings that branching structure crashing down. Denizens of anomalous branches, or of anomalous stretches of history in one-world theories, will be misled by the observed statistics of measurements.
We unify the ER = EPR conjecture with the Many-Worlds Interpretation (MWI) by constructing a transfinite, bijective functor between the poset of entangled Everett branches and the space of Einstein-Rosen bridges. Leveraging the fact that the branching cardinality is at least
ℶ1 (the cardinality of the continuum), we employ the axiom of choice and Cantor's transfinite recursion to define a one-to-one correspondence
Φ:B×B→Ω, where
B is the set of orthogonal branches and
Ω the set of non-traversable ER bridge geometries. The mapping preserves unitarity, respects the no-communication theorem, and yields three falsifiable predictions: (i) a geometric correction to the decoherence functional, (ii) a generalised Ryu-Takayanagi formula for branch entanglement entropy, and (iii) a topological obstruction to non-Hausdorff branch merging. This work fills a precise gap in the literature and provides a rigorous mathematical foundation for ER = EPR in the Everett multiverse.