dorsal/arxiv
View SchemaQuantum logic. A brief outline
| Authors | Karl Svozil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9902042 |
| URL | https://arxiv.org/abs/quant-ph/9902042 |
Abstract
Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quantum logic, and some of its algebraic properties, such as nondistributivity, whereby emphasis is given to concrete experimental setups related to quantum logical entities. A probability theory based on quantum logic is fundamentally and sometimes even spectacularly different from probabilities based on classical Boolean logic. We give a brief outline of its nonclassical aspects; in particular violations of Boole-Bell type consistency constraints on joint probabilities, as well as the Kochen-Specker theorem, demonstrating in a constructive, finite way the scarcity and even nonexistence of two-valued states interpretable as classical truth assignments. A more complete introduction of the author can be found in the book "Quantum Logic" (Springer, 1998)
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"abstract": "Quantum logic has been introduced by Birkhoff and von Neumann as an attempt\nto base the logical primitives, the propositions and the relations and\noperations among them, on quantum theoretical entities, and thus on the related\nempirical evidence of the quantum world. We give a brief outline of quantum\nlogic, and some of its algebraic properties, such as nondistributivity, whereby\nemphasis is given to concrete experimental setups related to quantum logical\nentities. A probability theory based on quantum logic is fundamentally and\nsometimes even spectacularly different from probabilities based on classical\nBoolean logic. We give a brief outline of its nonclassical aspects; in\nparticular violations of Boole-Bell type consistency constraints on joint\nprobabilities, as well as the Kochen-Specker theorem, demonstrating in a\nconstructive, finite way the scarcity and even nonexistence of two-valued\nstates interpretable as classical truth assignments. A more complete\nintroduction of the author can be found in the book \"Quantum Logic\" (Springer,\n1998)",
"arxiv_id": "quant-ph/9902042",
"authors": [
"Karl Svozil"
],
"categories": [
"quant-ph",
"math-ph",
"math.LO",
"math.MP"
],
"title": "Quantum logic. A brief outline",
"url": "https://arxiv.org/abs/quant-ph/9902042"
},
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