Difference between revisions of "Quantum Logic"
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The orthocomplemented lattice of any set of quantum propositions can be embedded into a Boolean algebra, which is then amenable to classical logic.<ref>Jeffery Bub and William Demopoulos, "The Interpretation of Quantum Mechanics," in ''[https://archive.org/details/logicalepistemol0000unse Logical and Epistemological Studies in Contemporary Physics]'', Boston Studies in the Philosophy of Science 13, ed. Robert S. Cohen and Marx W. Wartofsky; D. Riedel, 1974. pp. 92-122. DOI: [http://dx.doi.org/10.1007/978-94-010-2656-7 10.1007/978-94-010-2656-7]. {{ISBN|978-94-010-2656-7}}.</ref> | The orthocomplemented lattice of any set of quantum propositions can be embedded into a Boolean algebra, which is then amenable to classical logic.<ref>Jeffery Bub and William Demopoulos, "The Interpretation of Quantum Mechanics," in ''[https://archive.org/details/logicalepistemol0000unse Logical and Epistemological Studies in Contemporary Physics]'', Boston Studies in the Philosophy of Science 13, ed. Robert S. Cohen and Marx W. Wartofsky; D. Riedel, 1974. pp. 92-122. DOI: [http://dx.doi.org/10.1007/978-94-010-2656-7 10.1007/978-94-010-2656-7]. {{ISBN|978-94-010-2656-7}}.</ref> | ||
==Problems== | ==Problems== | ||
| − | + | *"How many times must a phenomenon occure before it graduates from a coincidence to a pattern?<ref>Yannis Ioannidis, ''The 5th Paradign: AI-Driven Scientific Discovery'' '''CACM 67''' No 12 (2024-12) P8</ref> | |
Quantum logic admits no reasonable [[material conditional]]; any [[logical connective|connective]] that is [[monotonicity of entailment|monotone]] in a certain technical sense reduces the class of propositions to a [[Boolean algebra (structure)|Boolean algebra]].<ref>{{cite journal | url=https://link.springer.com/content/pdf/10.1007/BF00733278.pdf | doi=10.1007/BF00733278 | title=Quantum logic revisited | year=1991 | last1= Román| first1=L. | last2=Rumbos | first2=B. | journal=Foundations of Physics | volume=21 | issue=6 | pages=727–734 | bibcode=1991FoPh...21..727R | s2cid=123383431 }}</ref> Consequently, quantum logic struggles to represent the passage of time.<ref name=linear /> One possible workaround is the theory of [[Belavkin equation|quantum filtrations]] developed in the late 1970s and 1980s by [[Viacheslav Belavkin|Belavkin]].<ref> | Quantum logic admits no reasonable [[material conditional]]; any [[logical connective|connective]] that is [[monotonicity of entailment|monotone]] in a certain technical sense reduces the class of propositions to a [[Boolean algebra (structure)|Boolean algebra]].<ref>{{cite journal | url=https://link.springer.com/content/pdf/10.1007/BF00733278.pdf | doi=10.1007/BF00733278 | title=Quantum logic revisited | year=1991 | last1= Román| first1=L. | last2=Rumbos | first2=B. | journal=Foundations of Physics | volume=21 | issue=6 | pages=727–734 | bibcode=1991FoPh...21..727R | s2cid=123383431 }}</ref> Consequently, quantum logic struggles to represent the passage of time.<ref name=linear /> One possible workaround is the theory of [[Belavkin equation|quantum filtrations]] developed in the late 1970s and 1980s by [[Viacheslav Belavkin|Belavkin]].<ref> | ||
* {{cite journal | * {{cite journal | ||
Revision as of 17:34, 17 December 2024
Full Title or Meme
The structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure.
Context
Relationship to other logics
Quantum logic embeds into linear logic[1] and the modal logic B.{{#invoke:Footnotes|sfn}} Indeed, modern logics for the analysis of quantum computation often begin with quantum logic, and attempt to graft desirable features of an extension of classical logic thereonto; the results then necessarily embed quantum logic.{{#invoke:Footnotes|sfn}}{{#invoke:Footnotes|sfn}}
The orthocomplemented lattice of any set of quantum propositions can be embedded into a Boolean algebra, which is then amenable to classical logic.[2]
Problems
- "How many times must a phenomenon occure before it graduates from a coincidence to a pattern?[3]
Quantum logic admits no reasonable material conditional; any connective that is monotone in a certain technical sense reduces the class of propositions to a Boolean algebra.[4] Consequently, quantum logic struggles to represent the passage of time.[1] One possible workaround is the theory of quantum filtrations developed in the late 1970s and 1980s by Belavkin.[5][6] It is known, however, that System BV, a deep inference fragment of linear logic that is very close to quantum logic, can handle arbitrary discrete spacetimes.[7]
References
- Also see the wiki page on Quantum Mechanics
