The Distribution Postulate in Algorithmic Bohmian Mechanics

Abstract:In order to make the right empirical predictions Bohmian mechanics requires a special statistical boundary condition -- the distribution postulate -- but it is unclear how best to understand this condition. We show how one might use the theory of algorithmic randomness to formulate the distribution postulate as an objective constraining law. The framework requires us to say something about admissible quantum-mechanical states and measurements. In return, algorithmic Bohmian mechanics (aBM) guarantees the standard Born statistics for a collection of canonical quantum experiments in the limit, not just with high probability. The algorithmic distribution postulate provides a sharp typicality condition, clarifies the status of quantum probabilities in the deterministic theory, and provides a concrete example of how notions provided by the theory of algorithmic randomness can aid in specifying the content of a physical law.

Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)

arXiv:2606.16165 [quant-ph]

(or arXiv:2606.16165v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.16165 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.