# 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}

}