Against Many Worlds

The Many Worlds interpretation (MWI) posits that the universe is described by a universal wave function evolving deterministically via the Schrödinger equation. A central challenge for this framework is the 'problem of probability': how to derive the Born rule—which assigns probabilities to measurement outcomes based on the squared modulus of wave function coefficients—from a theory that is fundamentally deterministic and lacks an inherent mechanism for stochastic outcomes.

The authors argue that any attempt to justify the Born rule within MWI must follow one of three paths, all of which are blocked by the theory's structure:

• Axiomatic: Proponents might try to add the Born rule as a fundamental axiom. However, MWI relies on the claim that macro-world branches are emergent, not fundamental. One cannot axiomatically assign probabilities to emergent structures without first deriving those structures from the underlying physical axioms.
• Deductive: One cannot derive a probabilistic conclusion from purely deterministic premises without smuggling in a notion of probability. Attempts to use decision theory or self-locating uncertainty to bridge this gap fail because they either contradict the theory's ontology or require unjustified, ad hoc assumptions.
• Inductive: Inductive reasoning requires a principle of uniformity. In MWI, because every possible outcome occurs in some branch, there is no objective basis for preferring one branch over another or for assuming that 'our' branch follows a specific statistical pattern without simply assuming the Born rule at the start.

The Born rule is the primary link between quantum theory and empirical observation. If MWI cannot provide a coherent account of why we observe outcomes with the frequencies predicted by the Born rule, it fails as an empirically adequate interpretation of quantum mechanics. By identifying these fundamental obstructions, the authors suggest that the 'problem of probability' is not merely a technical hurdle to be solved by clever math, but a deep-seated incompatibility between the MWI ontology and the nature of probabilistic law.