dorsal/arxiv
View SchemaInstability, Isolation, and the Tridecompositional Uniqueness Theorem
| Authors | Matthew J. Donald |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412013 |
| URL | https://arxiv.org/abs/quant-ph/0412013 |
Abstract
The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a wavefunction in a triple tensor product Hilbert space has at most one decomposition into a sum of product wavefunctions with each set of component wavefunctions linearly independent. I demonstrate that, in many circumstances, the unique component wavefunctions and the coefficients in the expansion are both hopelessly unstable, both under small changes in global wavefunction and under small changes in global tensor product structure. In my opinion, this means that the theorem cannot underlie law-like solutions to the problems of the interpretation of quantum theory. I also provide examples of circumstances in which there are open sets of wavefunctions containing no states with various decompositions.
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"abstract": "The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a\nwavefunction in a triple tensor product Hilbert space has at most one\ndecomposition into a sum of product wavefunctions with each set of component\nwavefunctions linearly independent. I demonstrate that, in many circumstances,\nthe unique component wavefunctions and the coefficients in the expansion are\nboth hopelessly unstable, both under small changes in global wavefunction and\nunder small changes in global tensor product structure. In my opinion, this\nmeans that the theorem cannot underlie law-like solutions to the problems of\nthe interpretation of quantum theory. I also provide examples of circumstances\nin which there are open sets of wavefunctions containing no states with various\ndecompositions.",
"arxiv_id": "quant-ph/0412013",
"authors": [
"Matthew J. Donald"
],
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"quant-ph"
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"title": "Instability, Isolation, and the Tridecompositional Uniqueness Theorem",
"url": "https://arxiv.org/abs/quant-ph/0412013"
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