dorsal/arxiv
View SchemaAn Epistemological Derivation of Quantum Logic
| Authors | John Foy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001074 |
| URL | https://arxiv.org/abs/quant-ph/0001074 |
Abstract
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and modular lattices respectively. We then derive these descriptions from what we claim are basic properties of any physical theory - i.e. the notion that a quantity in such a theory may be analysed into parts and that the results of this analysis may be treated in languages with an underlying boolean structure. We shall see that in the course of constructing a model of a theory with these properties different indistinguishable possibilities will arise for how the elements of the model may be named, that is to say different possibilities arise for how they can be associated with points from Set. Taking a particular collection of possibilities gives the usual boolean lattice of the propositions of classical physics. Taking all possibilities - in a sense, the set of all things that may be described by physical theories - gives the lattice of quantum mechanical propositions. This gives an interpretation of quantum mechanics as the complete set of such possible descriptions, the complete physical description of the world.
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"abstract": "This paper deals with the foundations of quantum mechanics. We start by\noutlining the characterisation, due to Birkhoff and Von Neumann, of the logical\nstructures of the theories of classical physics and quantum mechanics, as\nboolean and modular lattices respectively. We then derive these descriptions\nfrom what we claim are basic properties of any physical theory - i.e. the\nnotion that a quantity in such a theory may be analysed into parts and that the\nresults of this analysis may be treated in languages with an underlying boolean\nstructure. We shall see that in the course of constructing a model of a theory\nwith these properties different indistinguishable possibilities will arise for\nhow the elements of the model may be named, that is to say different\npossibilities arise for how they can be associated with points from Set. Taking\na particular collection of possibilities gives the usual boolean lattice of the\npropositions of classical physics. Taking all possibilities - in a sense, the\nset of all things that may be described by physical theories - gives the\nlattice of quantum mechanical propositions. This gives an interpretation of\nquantum mechanics as the complete set of such possible descriptions, the\ncomplete physical description of the world.",
"arxiv_id": "quant-ph/0001074",
"authors": [
"John Foy"
],
"categories": [
"quant-ph"
],
"title": "An Epistemological Derivation of Quantum Logic",
"url": "https://arxiv.org/abs/quant-ph/0001074"
},
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