I'm looking for introductory materials that presents the logic of quantum mechanics originally developed by von Neumann and Birkhoff suited to someone who took a full introductory undergraduate course in QM. Material concerning quantum logic is hardly discussed in introductory texts, so I would appreciate some recommendations for students looking to familiarise themselves with this area. So far the only suitable reference I've found is "An introduction to Hilbert Space and Quantum Logic" by David W. Cohen.
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2$\begingroup$ At the risk of projecting my own opinion, I don't think "quantum logic" is a very active way of looking at things. The usual argument that "quantum mechanics plays different rules of logic" relies on the assumption that the classical conception of particles and fields is an accurate realist depiction, which is likely fallacious. Almost all modern viewpoints reject the realism of classical (or even quantum mechanical) descriptions of the universe. $\endgroup$– jwimberleyCommented Jul 11, 2021 at 14:51
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2$\begingroup$ E.g., while "quantum logic" says "a particle can be in two places at once and thus logical propositions can have multiple values,' physicists are much more inclined nowadays to reject the assumption that a particle is something that can only exist at one place/point. So, actual books on "quantum logic" in the sense of your question may tend to be older or more philosophy/logic texts than physics texts. The spiritual equivalent within physics today are the non-realist interpretations, like QBism, etc. $\endgroup$– jwimberleyCommented Jul 11, 2021 at 14:56
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I don't think that quantum logic is any useful. But if you want to learn about what it can say, look at the little book
- ''Quantum Logic'' by Karl Svozil (Springer, New York 1998).
It deals with the foundations of quantum mechanics and, related to it, the behaviour of finite, discrete deterministic systems. The quantum logical approach is particulalry suitable for the investigation and exclusion of certain hidden parameter models of quantum mechanics. Conversely, it can be used to embed quantum universes into classical ones. It is also highly relevant for the characterization of finite automation. This book has been written with a broad readership in mind. Great care has been given to the motivation of the concepts and to the explicit and detailed discussions of examples.
A more advanced book (probably beyond what you want) is
- J. Hamhalter, Quantum measure theory, Springer, New York 2013.