A refinement of the argument of local realism versus quantum mechanics by algorithmic randomness
Abstract
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In our former works [K. Tadaki, arXiv:1804.10174], based on the toolkit of algorithmic randomness, we presented a refinement of the Born rule, called the principle of typicality, for specifying the property of results of measurements in an operational way. In this paper, we make an application of our framework to the argument of local realism versus quantum mechanics for refining it, in order to demonstrate how properly our framework works in practical problems in quantum mechanics.
Keywords
Cite
@article{arxiv.2312.13246,
title = {A refinement of the argument of local realism versus quantum mechanics by algorithmic randomness},
author = {Kohtaro Tadaki},
journal= {arXiv preprint arXiv:2312.13246},
year = {2025}
}
Comments
This is an augmented edition. This work is an application of the frameworks of arXiv:1611.06201 and arXiv:1804.10174 to a different subject than arXiv:2509.07828. The above deal with the finite outcomes. In contrast, arXiv:1909.02854 deals with the infinite outcomes