Abstract
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process.
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Duvenhage, R. The Nature of Information in Quantum Mechanics. Foundations of Physics 32, 1399–1417 (2002). https://doi.org/10.1023/A:1020359806696
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DOI: https://doi.org/10.1023/A:1020359806696