dorsal/arxiv
View SchemaFields of Iterated Quantum Reference Frames based on Gauge Transformations of Rational String States
| Authors | Paul Benioff |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604135 |
| URL | https://arxiv.org/abs/quant-ph/0604135 |
Abstract
This work is based on a description of quantum reference frames that seems more basic than others in the literature. Here a frame is based on a set of real and of complex numbers and a space time as a 4-tuple of the real numbers. There are many isomorphic frames as there are many isomorphic sets of real numbers. Each frame is suitable for construction of all physical theories as mathematical structures over the real and complex numbers. The organization of the frames into a field of frames is based on the representations of real and complex numbers as Cauchy operators defined on complex rational states of finite qubit strings. The structure of the field is based on noting that the construction of real and complex numbers as Cauchy operators in a frame can be iterated to create new frames coming from a frame. Gauge transformations on the rational string states greatly expand the number of quantum frames as, for each gauge U, there is one frame coming from the original frame. Forward and backward iteration of the construction yields a two way infinite frame field with satisfying properties. There is no background space time and there are no real or complex numbers for the field as a whole. Instead these are relative concepts associated with each frame in the field. Extension to include qukit strings for different k bases, is described as is the problem of reconciling the frame field to the existence of just one frame with one background space time for the observable physical universe.
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"abstract": "This work is based on a description of quantum reference frames that seems\nmore basic than others in the literature. Here a frame is based on a set of\nreal and of complex numbers and a space time as a 4-tuple of the real numbers.\nThere are many isomorphic frames as there are many isomorphic sets of real\nnumbers. Each frame is suitable for construction of all physical theories as\nmathematical structures over the real and complex numbers. The organization of\nthe frames into a field of frames is based on the representations of real and\ncomplex numbers as Cauchy operators defined on complex rational states of\nfinite qubit strings. The structure of the field is based on noting that the\nconstruction of real and complex numbers as Cauchy operators in a frame can be\niterated to create new frames coming from a frame. Gauge transformations on the\nrational string states greatly expand the number of quantum frames as, for each\ngauge U, there is one frame coming from the original frame. Forward and\nbackward iteration of the construction yields a two way infinite frame field\nwith satisfying properties. There is no background space time and there are no\nreal or complex numbers for the field as a whole. Instead these are relative\nconcepts associated with each frame in the field. Extension to include qukit\nstrings for different k bases, is described as is the problem of reconciling\nthe frame field to the existence of just one frame with one background space\ntime for the observable physical universe.",
"arxiv_id": "quant-ph/0604135",
"authors": [
"Paul Benioff"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"title": "Fields of Iterated Quantum Reference Frames based on Gauge Transformations of Rational String States",
"url": "https://arxiv.org/abs/quant-ph/0604135"
},
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