# Bounds on length scales of classical spacetime foam models

## Abstract

Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations {omega}{sup 2}={omega}{sup 2}(k-vector) are calculated, in particular, the coefficients of the quadratic and quartic terms in k-vector. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations and, thereby, on particular combinations of the fundamental length scales of the static spacetime foam models considered. Spacetime foam models with a single length scale are excluded, even models with a length scale close to the Planck length (as long as a classical spacetime remains relevant)

- Authors:

- Institute for Theoretical Physics, University of Karlsruhe (Thailand), 76128 Karlsruhe (Germany)

- Publication Date:

- OSTI Identifier:
- 21010898

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024028; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; COSMIC GAMMA BURSTS; COSMOLOGY; DISPERSION RELATIONS; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; MINKOWSKI SPACE; QUANTUM FIELD THEORY; SPACE-TIME; VECTORS; WAVE PROPAGATION

### Citation Formats

```
Bernadotte, S., and Klinkhamer, F. R..
```*Bounds on length scales of classical spacetime foam models*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.024028.

```
Bernadotte, S., & Klinkhamer, F. R..
```*Bounds on length scales of classical spacetime foam models*. United States. doi:10.1103/PHYSREVD.75.024028.

```
Bernadotte, S., and Klinkhamer, F. R.. Mon .
"Bounds on length scales of classical spacetime foam models". United States.
doi:10.1103/PHYSREVD.75.024028.
```

```
@article{osti_21010898,
```

title = {Bounds on length scales of classical spacetime foam models},

author = {Bernadotte, S. and Klinkhamer, F. R.},

abstractNote = {Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations {omega}{sup 2}={omega}{sup 2}(k-vector) are calculated, in particular, the coefficients of the quadratic and quartic terms in k-vector. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations and, thereby, on particular combinations of the fundamental length scales of the static spacetime foam models considered. Spacetime foam models with a single length scale are excluded, even models with a length scale close to the Planck length (as long as a classical spacetime remains relevant)},

doi = {10.1103/PHYSREVD.75.024028},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}