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. The situation is even more exciting if there are two points of observation, like two eyes, which allow three-dimensional image reconstruction. Confidence in programming in a language, such as IDL or Python, is very handy.

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

- Moving from visualising 2D to 3D

- Results provided in form of animation

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:* The complexity of the shape of the object or its dynamics is limitless.

Please speak to **Balázs Pintér** (bap) 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 level of technology is not there yet that we could construct a stereo camera with distance between the two eyes to be measured in light-seconds. The literature on relativistic stereo observations is far from complete. Any results of the project can basically be novel.

The difficulty is not necessarily in the mathematics but the non-everyday aspects of moving at speeds close to the speed of light. Still, even simple cases are expected to have only numerical solutions. So, programming skills are valuable.

Knowledge, skills, and abilities essential for the project are:

Solid understanding of the theory of special relativity;

Good mental visualisation;

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

Fine data-organisation, presentation-, and visualisation skills

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

A list of stereo observers, objects, and motion to be analysed | end of November |

Good understanding of the methods how stereo images can be formed | Christmas |

Stereo image of at least one case | end of February |

Visual illustration of the images derived from the list of cases | mid-March |