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Titlebook: Quantum Logic in Algebraic Approach; Miklós Rédei Book 1998 Springer Science+Business Media Dordrecht 1998 Hilbert space.algebra.mechanics

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Observables and states in the Hilbert space formalism of quantum mechanics,rmalism of quantum mechnics but it is not the only and not even the most “natural” one. We shall see in Chapter 6 that the so-called “algebraic” quantum mechanics is equally important. The Hilbert space formalism has a long history that goes back to the twenties and it was worked out rigorously by v
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Lattice theoretic notions,the . of a lattice (Definitions 3.5, 3.6 and 3.10). The proposition stating that a lattice on which a finite dimension function exists is necessarily modular (Proposition 3.3) will become important in the Chapter 6. The one-to-one correspondence between prime filters in a lattice and lattice homomor
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Physical theory in semantic approach,ful and empirically checkable according to a particular theory that describes the physical system. “Logical relation of propositions” means relations of propositions from the the point of view of “truth”, “falsity”, “entailment”, etc. The analysis of the logic of a physical system can, and will in t
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The problem of hidden variables,926 paper [26] that introduces the probabilistic interpretation of quantum state (see also [73]), and the hidden variable problem has revived from time to time in the past six decades. We could witness its last revival in the early eighties, and the debates about this issue have been going on ever s
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