### Investigation of the Ehrenfest paradox

#### (supervisor: Heather McCreadie)

Nature of project: **theory**, software

Available to
students on full-time physics degree schemes only.

#### Project description and methodology

When an electron beam is passed through a magnetic field the beam deflects and forms a near perfect circle. If it is assumed a perfect circle is formed, a standing wave will be set up. Using this idea as the start point the Ehrenfest paradox will be theorised. A set of equations will be formed with the constraints of the electron beam experiment and the paradox explained graphically and descriptively. The student will delve into coordinate definitions, Lorentz contractions and the resolution posted by Grøn.

*A successful project will develop beyond the above in one/some of the following directions:*

The radius is determined by the relativistic nature of the experiment. Investigate whether relativistic effects induce a pulse in the measurement of the wavelength of the standing wave.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

*This project is only available as a Y3 project.*

Please speak to **Heather McCreadie** if you consider doing this project.

*Initial literature for students:*

- Grant, I. S., and Phillips W. R., (2003) Electromagnetism, 2nd Ed. ISBN: 0 471 92711 2
- Thomson, J. J.; Phil Mag 43 (8 February 1897) 125.
- Davies, P. A.; Jennison, R. C.; J Phys A 8 (1975) 1390.
- Grøn, Ø.; Lett Nuovo Cimento 13 (1975) 441.

#### Novelty, degree of difficulty and amount of assistance required

Programming MatLab tutorials will be given (especially in 3-D mapping)

The mathematics involved is high level.

#### Project milestones and deliverables (including timescale)

milestone | to be completed by |

Description of each of the concepts involved. | end of November |

MatLaB plot of an electron beam in a magnetic field. | Christmas |

wavelengths identified | end of February |

One fully formed standing wave with two possible outcomes depending on velocity of the electron chosen graphically and descriptive wise shown. | Easter |