Nature of project: **theory**, software

Available to students on full-time physics degree schemes or joint students.

The Lorentz transformation formulas in special relativity relate the spatial and temporal coordinates of events in frames of reference moving relative to each other at constant speeds. By those equations, maps can be transformed between such reference frames, showing in a particular frame of reference where objects can be found at given times and where and when events occur. Due to the finite speed of light, however, the world surrounding an observer looks differently than the world maps. Events seem to occur at different places, objects appear of different sizes and shapes.

Students will study this bizarre world by the means of special relativity. The mechanics and geometric properties of one-, two-, and three-dimensional objects moving relative to the observer will be analysed. Confidence in programming in a language, such as IDL or python, will be rewarding.

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

- Investigating the appearance of moderately complicated 3D objects would be a nice extension of the project

- Creating animation for visualising the results

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.

*Additional scope or challenge if taken as a Year-4 project:* - Relativistic description of rotation or rolling brings up extra challenges, which makes the problem suitable for a Y4 project

- Stereo vision of the world is an even more exciting area to be explored

Please speak to **Balázs Pintér** if you consider doing this project.

*Initial literature for students:*

- McGill, N.C., “The Apparent Shape of Rapidly Moving Objects in Special Relativity”, 1968, Contemporary Physics, 9, 33
- Suffern, K. G., “The apparent shape of a rapidly moving sphere”, 1988, American Journal of Physics, 56, 8, 729-733
- Fukue, J, “Observational Appearance of Luminous Relativistic Movers”, 2009, Publications of the Astronomical Society of Japan, 61, 4, 645-657
- Arkadiy, L., “The distortion of a body's visible shape at relativistic speeds”, 2009, Eur. J. Phys., 30, 191

The idea that a world map and a visual image of the world are different due to the speed of light is not new. Its fascinating consequences, however, are far from fully explored.

Only basic maths techniques are needed for the project as the Lorentz formulas are simple algebraic equations.

Knowledge, skills and abilities essential for the project are:

Solid understanding of the theory of special relativity;

Good mental visualization;

Readiness to move away from concepts based on our everyday experiences;

Fine data-organisation, presentation, and visualisation skills

milestone | to be completed by |
---|---|

Understanding the main concepts of the project | end of November |

Deriving distances, sizes, angles, and shapes in 2D problems | end of February |

Complete description of one particular case | mid-March |

Visualisation of the main results | Easter |