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Feb 4, 2002 · The reduction of QM to probability theory based on \(L(\mathbf{H})\) is mathematically compelling, but what does it tell us about QM—or, assuming QM to be a correct and complete physical theory, about the world? How, in other words, are we to interpret the quantum logic \(L(\mathbf{H})\)? The answer will turn on how we unpack the phrase ...
- Quantum Theory and Mathematical Rigor
A brief explanation for this shift is provided below. See...
- The Basic Theory of Ordering Relations
The Basic Theory of Ordering Relations. What follows is the...
- Bell's Theorem
Bell’s Theorem is the collective name for a family of...
- Quantum Theory and Mathematical Rigor
The most common approaches are to identify outcomes that are equi-probable in every state (as in the work of Mackey), or to identify outcomes that are certain (i.e., have probability 1) in exactly the same states (as in the work of Piron).
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Does quantum mechanics require a generalisation of probability?
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The topic of probabilty in quantum mechanics is rather vast, and in this article, we shall choose to discuss it from the perspective of whether and in what sense quantum mechanics requires a generalisation of the usual (Kolmogorovian) concept of probability.
The paper reviews quantum probability theory in terms of general von Neumann algebras, stressing the similarity of the conceptual structure of classical and noncommutative probability theories and emphasizing the correspondence between the classical and quantum concepts, though also indicating the nonclassical nature of quantum probabilistic pre...
- Miklos Redei, Stephen J. Summers
- 2006
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The topic of probability in quantum mechanics is rather vast, and in this chapter, we choose to discuss it from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability.
Using the concept of "correlation" carefully analyzed in the context of classical probability and in quantum theory, the author provides a framework to compare these approaches. He also develops an extension of probability theory to construct a local hidden variable theory.
