Many Retrocausal Worlds: A Foundation for Quantum Probability
Michael Ridley
TL;DR
This paper addresses the core problem of probability in the Many-Worlds Interpretation by proposing a time-symmetric, all-at-once framework called the Fixed Point Formulation (FPF). It grounds quantum probability in the structure of time-extended histories through the measure of existence and the Vaidman rule, rather than postulating the Born rule a priori. By combining event symmetry with a Keldysh contour description, the approach yields a Born-like weighting from local temporal constraints and retrocausal branching, reconciled within an Everettian ontology. The work argues that many retrocausal world-tubes collectively realize probability as relative reality across histories, offering a conceptually coherent, relativistically compatible foundation for quantum statistics with potential links to decoherence and quantum thermodynamics.
Abstract
Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the incoherence and quantitative problems. After discussing various theories of probability, I discuss the incoherence problem and argue that self-locating probabilities centered in time-extended worlds can solve it. I then discuss and refute various solutions to the quantitative problem. I argue that the only tenable way to ground these self-locating probabilities is to identify the mathematical form of the Born rule as a generic pattern in a time-extended wavefunction, and to distribute degrees of belief over the region of wavefunction occupied by this pattern. I then outline a time-symmetric version of quantum mechanics - the Fixed Point Formulation - which, interpreted within a time-symmetric Everettian framework, can provide the foundation for a theory of quantum probability.