Discreteness and the origin of probability in quantum mechanics

TL;DR

This paper explores how the inherent discreteness of quantum state space can help derive the Born rule in quantum mechanics, especially for systems with finite degrees of freedom, addressing limitations of existing interpretations.

Contribution

It proposes that quantum state space discreteness can restore the derivation of the Born rule in finite systems within the Many Worlds interpretation.

Findings

Discreteness of quantum state space may validate the Born rule for finite systems.

Existing derivations struggle with finite degrees of freedom, but discreteness offers a solution.

The approach potentially reconciles the Many Worlds interpretation with observed probabilities.

Abstract

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.