Non-probabilistic typicality, with application to quantum mechanics

• URL: http://arxiv.org/abs/2209.14985v1
• Date: Thu, 29 Sep 2022 17:49:14 GMT
• Title: Non-probabilistic typicality, with application to quantum mechanics
• Abstract summary: The first hypothesis is the existence of random phenomena/experiments whose events cannot generally be assigned a definite probability. The second hypothesis is that the evolution of a quantum particle can be considered as a typicalistic phenomenon.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper develops two hypotheses. The first hypothesis is the existence of random phenomena/experiments whose events cannot generally be assigned a definite probability, but that admits nevertheless a class of nearly certain events. These experiments will be referred to as ``typicalistic'' (instead of probabilistic) experiments. As probabilistic experiments are represented by probability spaces, typicalistic experiments can be represented by typicality spaces, where a typicality space is basically a probability space in which the probability measure has been replaced by a much less structured typicality measure $T$. The condition $T(A) \approx 1$ defines the typical sets, and a typicality space is related to a typicalistic experiment by associating the typical sets of the former with the nearly certain events of the latter. Various elements of a mathematical theory of typicality, including the definition of typicality spaces, are presented in the first part of the paper. The second hypothesis is that the evolution of a quantum particle (or of a system of quantum particles) can be considered as a typicalistic phenomenon, so that it can be represented by the union of typicality theory and quantum mechanics. The result is a novel formulation of quantum mechanics that does not present the measurement problem, and that also seems to avoid some of the drawbacks of Bohmian mechanics and of the Many World Interpretation. This subject is developed in the second part of the paper.

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