Quantum Logic
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
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.[3] 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.[4][5] 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.[6]
References
- Also see the wiki page on Quantum Mechanics
