Recovering Statistical Mechanical Probabilities from Wavefunction Fractions

Demonstrate whether defining quantum probability as the fraction of the universal wavefunction occupied by a history (the Vaidman-rule fraction within the Fixed Point Formulation) reproduces standard statistical mechanical probabilities under appropriate conditions, such as those governing thermalization and generalized Gibbs ensembles in many-body systems.

Background

The paper proposes grounding quantum probabilities in the proportion of wavefunction occupied by time-extended histories and derives the Born rule within the Fixed Point Formulation (FPF), a time-symmetric, retrocausal framework on the Keldysh contour. In this approach, probabilities are measures of existence of histories, equated to fractions of wavefunction.

Having provided a foundation for quantum probabilities in this framework, the author asks whether these wavefunction-fraction probabilities can also recover the probabilities used in statistical mechanics, especially in regimes where thermalization and generalized Gibbs ensembles describe many-body systems.

References

I am optimistic that the ideas contained in this work can be connected to many open research questions, some of which I sketch here: Can the concept of quantum probability as wavefunction fractions be shown to reproduce statistical mechanical probabilities under the appropriate conditions?

— Many Retrocausal Worlds: A Foundation for Quantum Probability  (2510.02505 - Ridley, 2 Oct 2025) in Conclusions, final paragraph (Open research questions list)