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Title: Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.

Abstract

In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken here is based on three main points: (1) There are a large number of different quantum theory representations of natural numbers, integers, and rational numbers as states of qubit strings. (2) For each representation, Cauchy sequences of rational string states give a representation of the real (and complex) numbers. A reference frame is associated to each representation. (3) Each frame contains a representation of all mathematical and physical theories that have the real and complex numbers as a scalar base for the theories. These points and other aspects of the resulting fields are then discussed and justified in some detail. Also two different methods of relating the frame field to physics are discussed.

Authors:
;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
971133
Report Number(s):
ANL/PHY/CP-57836
TRN: US201003%%585
DOE Contract Number:
DE-AC02-06CH11357
Resource Type:
Conference
Resource Relation:
Journal Name: J. Phys.: Conf. Ser.; Journal Volume: 70; Journal Issue: 2007; Conference: 3rd Feynman Festival; Aug. 25, 2006 - Aug. 29, 2006; College Park, MD
Country of Publication:
United States
Language:
ENGLISH
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GAUGE INVARIANCE; PHYSICS; QUBITS; SCALARS

Citation Formats

Benioff, P., and Physics. Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.. United States: N. p., 2007. Web. doi:10.1088/1742-6596/70/1/012003.
Benioff, P., & Physics. Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.. United States. doi:10.1088/1742-6596/70/1/012003.
Benioff, P., and Physics. Mon . "Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.". United States. doi:10.1088/1742-6596/70/1/012003.
@article{osti_971133,
title = {Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.},
author = {Benioff, P. and Physics},
abstractNote = {In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken here is based on three main points: (1) There are a large number of different quantum theory representations of natural numbers, integers, and rational numbers as states of qubit strings. (2) For each representation, Cauchy sequences of rational string states give a representation of the real (and complex) numbers. A reference frame is associated to each representation. (3) Each frame contains a representation of all mathematical and physical theories that have the real and complex numbers as a scalar base for the theories. These points and other aspects of the resulting fields are then discussed and justified in some detail. Also two different methods of relating the frame field to physics are discussed.},
doi = {10.1088/1742-6596/70/1/012003},
journal = {J. Phys.: Conf. Ser.},
number = 2007,
volume = 70,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

Conference:
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  • This work is based on the field of reference frames based on quantum representations of real and complex numbers described in other work. Here frame domains are expanded to include space and time lattices. Strings of qukits are described as hybrid systems as they are both mathematical and physical systems. As mathematical systems they represent numbers. As physical systems in each frame the strings have a discrete Schroedinger dynamics on the lattices. The frame field has an iterative structure such that the contents of a stage j frame have images in a stage j-1 (parent) frame. A discussion of parentmore » frame images includes the proposal that points of stage j frame lattices have images as hybrid systems in parent frames. The resulting association of energy with images of lattice point locations, as hybrid systems states, is discussed. Representations and images of other physical systems in the different frames are also described.« less
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