The logic of the future in quantum theory
Abstract
According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice of future-tense propositions, with truth values in the interval , and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history.
Keywords
Cite
@article{arxiv.1409.0755,
title = {The logic of the future in quantum theory},
author = {Anthony Sudbery},
journal= {arXiv preprint arXiv:1409.0755},
year = {2017}
}
Comments
v6: Retitled and revised. All discussion of many worlds removed. 31 pages