dorsal/arxiv
View SchemaRemarks on an attempted axiomatisation of Quantum Mechanics, due to Lucien Hardy, and Ten Theses on Hilbert's Sixth Problem and Quantum Measurement
| Authors | Joseph F. Johnson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606038 |
| URL | https://arxiv.org/abs/quant-ph/0606038 |
Abstract
From the standpoint of Hilbert's Sixth Problem, which is the axiomatisation of Physics, the famous paper of Lucien Hardy's, Quantum Theory from Five Reasonable Axioms, is not relevant. The present paper argues that Hardy does not give a physical definition of `limit', and if we assume the usual mathematical definition of limit of a sequence, he fails to define a sequence in physical terms to which the usual definition is applicable. We argue that one should not, in fact, try to define probability in terms of the usual notion of limit of a sequence of results of a measurement because of seemingly insurmountable difficulties in axiomatising the notion of function or sequence in this context. Von Plato's and the authour's work (see http:arxiv.org/abs/quant-ph/0502124 and euclid.unh.edu/~jjohnson/axiomatics.html for larger context and further references) on the definition of physical probability needs to be used in this context. We conclude with ten theses on quantum measurement, from the standpoint of the Hilbert problem.
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"abstract": "From the standpoint of Hilbert\u0027s Sixth Problem, which is the axiomatisation\nof Physics, the famous paper of Lucien Hardy\u0027s, Quantum Theory from Five\nReasonable Axioms, is not relevant. The present paper argues that Hardy does\nnot give a physical definition of `limit\u0027, and if we assume the usual\nmathematical definition of limit of a sequence, he fails to define a sequence\nin physical terms to which the usual definition is applicable. We argue that\none should not, in fact, try to define probability in terms of the usual notion\nof limit of a sequence of results of a measurement because of seemingly\ninsurmountable difficulties in axiomatising the notion of function or sequence\nin this context. Von Plato\u0027s and the authour\u0027s work (see\nhttp:arxiv.org/abs/quant-ph/0502124 and\neuclid.unh.edu/~jjohnson/axiomatics.html for larger context and further\nreferences) on the definition of physical probability needs to be used in this\ncontext. We conclude with ten theses on quantum measurement, from the\nstandpoint of the Hilbert problem.",
"arxiv_id": "quant-ph/0606038",
"authors": [
"Joseph F. Johnson"
],
"categories": [
"quant-ph"
],
"title": "Remarks on an attempted axiomatisation of Quantum Mechanics, due to Lucien Hardy, and Ten Theses on Hilbert\u0027s Sixth Problem and Quantum Measurement",
"url": "https://arxiv.org/abs/quant-ph/0606038"
},
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