## A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers

## Abstract

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 Schrodinger 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 parent 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.

- Authors:

- Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1198240

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Published Article

- Journal Name:
- Advances in Mathematical Physics

- Additional Journal Information:
- Journal Name: Advances in Mathematical Physics Journal Volume: 2009; Journal ID: ISSN 1687-9120

- Publisher:
- Hindawi Publishing Corporation

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

### Citation Formats

```
Benioff, Paul. A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers. Country unknown/Code not available: N. p., 2009.
Web. doi:10.1155/2009/452738.
```

```
Benioff, Paul. A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers. Country unknown/Code not available. doi:10.1155/2009/452738.
```

```
Benioff, Paul. Thu .
"A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers". Country unknown/Code not available. doi:10.1155/2009/452738.
```

```
@article{osti_1198240,
```

title = {A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers},

author = {Benioff, Paul},

abstractNote = {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 Schrodinger 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 parent 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.},

doi = {10.1155/2009/452738},

journal = {Advances in Mathematical Physics},

number = ,

volume = 2009,

place = {Country unknown/Code not available},

year = {2009},

month = {1}

}

DOI: 10.1155/2009/452738