Born rule and many-worlds interpretation of quantum mechanics: an ergodic approach towards the ontological aspects of the interpretation.

In this paper, the ontological aspects of the many-worlds interpretation (MWI) of quantum mechanics are studied by employing measure-theoretical methods of the ergodic theory. Before everything it is shown that the frequency interpretation of the Born rule is independent of the measurement postulate and hence, must be extended to the statistical ontology of the MWI. Then, based on the Birkhoff's ergodic theorem we will prove that except for a Lebesgue null set of extremely rare parallel worlds, the Born rule will be refuted in all the parallel worlds created in a long-term process of consecutive experiments in the MWI of quantum mechanics. This reduces the unlimited ontology of the MWI to an extremely confined but still uncountable set of possible parallel worlds in long-term processes and allow us to acknowledge a pseudo-deterministic mechanism of quantum mechanics in the statistical picture of the theory. Hence, we conclude that the common understanding of the unconstrained MWI ontology, even if considered valid, cannot survive in long-term consecutive observations and must soon collapse into a more constrained interpretation of quantum mechanics. [ABSTRACT FROM AUTHOR]