Quantum LogicSpringer Science & Business Media, 1 wrz 1998 - 216 Quantum Logic 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. |
Spis treści
1 Hilbert space quantum mechanics | 1 |
2 Comeasurable observables | 7 |
22 Operations and order relations among propositions | 9 |
221 Subspace operations and order relation implication | 10 |
222 Projection operations and order relation implication | 11 |
24 Spin onehalf | 13 |
25 Spin one | 15 |
26 Mutually commuting operators as functions of a single Uroperator | 19 |
75 Nonlocality | 100 |
751 PeresMermin construction | 101 |
752 GreenbergerHorneZeilingerMermin construction | 102 |
76 Physical realizability | 105 |
762 Consequences of counterfactual reasoning | 108 |
8 Quantum tautologies | 111 |
9 What price valuedefiniteness? | 123 |
91 Varieties of embeddings | 124 |
27 Dynamics | 21 |
3 Complementarity | 23 |
32 Pasting of quasiclassical logics | 26 |
34 Spin one | 29 |
35 Fastings of higher complexity | 30 |
352 Finite subalgebras of threedimensional Hilbert logic | 31 |
353 Finite subalgebras of ndimensional Hilbert logics | 36 |
354 Leaving the finite subalgebra case | 39 |
4 Hilbert lattices | 41 |
41 Review of basic definitions | 42 |
422 Nondistributivity | 43 |
423 Modularity | 44 |
425 Algebraic properties | 45 |
44 Hilbert lattice for spin one measurements | 46 |
5 Composite systems | 51 |
6 Probabilities | 59 |
61 Probabilities in blocks | 61 |
62 Probabilities in pastings | 63 |
twovalued measures and embeddings | 64 |
64 Spin onehalf | 67 |
65 Nongleason type probability measures | 70 |
66 Spin one | 72 |
67 Counterintuitive probabilities | 75 |
7 Contextuality | 79 |
72 KochenSpecker construction | 85 |
722 Nonseparating set of twovalued probability measures | 87 |
723 Nonexistence of twovalued probability measures | 89 |
73 Bell construction | 91 |
732 Nonexistent set of probability measures | 92 |
74 Peres construction | 93 |
911 Injective lattice homomorphism | 125 |
912 Injective order homomorphism preserving lattice operations among comeasurable propositions | 126 |
92 Surjective extensions | 135 |
93 Outlook | 136 |
10 Quasiclassical analogies | 139 |
101 Fireflyinabox and generalized urn models | 141 |
102 Automaton logic | 145 |
1021 Moore and Mealy automata state machines and combinatorial circuits | 147 |
1022 Machine isomorphism serial and parallel decompositions networks and universality | 148 |
1023 Construction of automaton partition logics | 150 |
1024 Varieties | 155 |
1025 Embeddings and characterization | 160 |
1026 Reversibility | 168 |
103 Elements of generalized probability theory on nonboolean prepositional structures | 178 |
1033 Examples | 180 |
1034 Counterintuitive probabilities | 181 |
A Lattice theory | 183 |
A2 Partial order relation | 184 |
A3 Lattice | 186 |
A31 Distributive lattice | 188 |
A33 Modular lattice | 189 |
A34 Orthomodular lattice | 190 |
A35 Commutator and Center of orthomodular lattice | 191 |
A37 Block pasting of orthomodular lattices | 192 |
A4 Examples | 197 |
A43 Greatest common divisor and least common multiplier | 198 |
| 201 | |
| 213 | |
Kluczowe wyrazy i wyrażenia
a₁ anor anorb arbitrary associated atoms automata automaton automaton logic automaton partition logic black box blocks Boolean algebra Boolean lattice cartesian product chapter classical Boolean comeasurable observables complement computation Concentric circles indicate corresponding counterfactual defined Definition denoted depicted in Figure dimensional Hilbert drawn in Figure elements of physical Equation example finite subalgebras Gleason's theorem Greechie diagram Hasse diagram hidden parameter Hilbert lattice Hilbert logic Hilbert space homomorphism horizontal sum identified implies input isomorphic Kalmbach Kochen and Specker Kochen-Specker Kochen-Specker theorem lattice operations linear subspace logical structure M₁ mapping matrix Mealy automaton modular noncomeasurable one-to-one order relation orthocomplemented lattice orthogonal orthomodular lattice p₁ partially ordered set particle physical reality projection operators propositional calculus propositional structure propositional systems L(x quantum logic quantum mechanics quasi-classical represented self-adjoint set of two-valued spin one-half subset tautology theorem tripod truth assignments two-valued probability measures urn model vector