Objective and Subjective Solomonoff Probabilities in Quantum Mechanics
This addresses foundational issues in quantum probability for philosophers and physicists, but appears incremental as it builds on existing algorithmic probability approaches.
The paper tackles the probability problem in quantum mechanics interpretations by generalizing algorithmic Everettianism to Bayesian and subjectivist frameworks, applying a generative probability framework to Sleeping Beauty and Replicator thought experiments.
Algorithmic probability has shown some promise in dealing with the probability problem in the Everett interpretation, since it provides an objective, single-case probability measure. Many find the Everettian cosmology to be overly extravagant, however, and algorithmic probability has also provided improved models of subjective probability and Bayesian reasoning. I attempt here to generalize algorithmic Everettianism to more Bayesian and subjectivist interpretations. I present a general framework for applying generative probability, of which algorithmic probability can be considered a special case. I apply this framework to two commonly vexing thought experiments that have immediate application to quantum probability: the Sleeping Beauty and Replicator experiments.