dorsal/arxiv
View SchemaQuantum axiomatics and a theorem of M.P. Soler
| Authors | Diederik Aerts, Bart Van Steirteghem |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105107 |
| URL | https://arxiv.org/abs/quant-ph/0105107 |
| Journal | International Journal of Theoretical Physics, 39, 2000, 497 |
Abstract
Three of the traditional quantum axioms (orthocomplementation, orthomodularity and the covering law) show incompatibilities with two products introduced by Aerts for the description of joint entities. Inspired by Soler's theorem and Holland's AUG axiom, we propose a property of 'plane transitivity', which also characterizes classical Hilbert spaces among infinite dimensional orthomodular spaces, as a possible partial substitute for the 'defective' axioms.
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"abstract": "Three of the traditional quantum axioms (orthocomplementation,\northomodularity and the covering law) show incompatibilities with two products\nintroduced by Aerts for the description of joint entities. Inspired by Soler\u0027s\ntheorem and Holland\u0027s AUG axiom, we propose a property of \u0027plane transitivity\u0027,\nwhich also characterizes classical Hilbert spaces among infinite dimensional\northomodular spaces, as a possible partial substitute for the \u0027defective\u0027\naxioms.",
"arxiv_id": "quant-ph/0105107",
"authors": [
"Diederik Aerts",
"Bart Van Steirteghem"
],
"categories": [
"quant-ph"
],
"journal_ref": "International Journal of Theoretical Physics, 39, 2000, 497",
"title": "Quantum axiomatics and a theorem of M.P. Soler",
"url": "https://arxiv.org/abs/quant-ph/0105107"
},
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