Born Rule and Logical Inference in Quantum Mechanics
arXiv:1804.10067 · doi:10.1093/ptep/ptab135
Abstract
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natural extension of the classical probability.
substantially rewritten, 18 pages, no figures. Comments are welcome
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