Nature of project: **theory**, software

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

The two postulates of the special theory of relativity have a wide range of consequences - most of them are highly counter-intuitive. We can get closer to understanding them by the comprehension of paradoxes of relativity.

A truly fascinating one is Bell’s spaceship paradox. The original case has two spaceships at the ends of a piece of rope. The project begins with the understanding of that version of the paradox but the main part is a visualisation of the paradox in a space-time diagram. That is an effective way of studying and understanding what is actually happening to the rope as looked from different reference systems and why the outcome only seems to be different in different frames of reference.

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

- In the original paradox, the two spaceships have their own engines, providing the same acceleration of the spaceships in the inertial reference frame in which the spaceships are at rest initially. After visualising this case, one of the engines can be replaced by a force exerted by the other spaceship through the rope.

- The space-time diagram can be converted into animation, showing the, seemingly contradicting, events in different frames of reference.

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:* - To monitor the information propagation between the spaceships in the rope, additional spaceships or carriages (with no engine) can be placed along the rope. In such a model, multiple forces (pulling and pushing) acting on spaceships from their neighbouring spaceships have to be considered, which gives extra complexity to the project.

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

*Initial literature for students:*

- Flores, F. J., “SPECIAL RELATIVITY: Bell's spaceships: a useful relativistic paradox”, 2005, Physics Education, 40, 6, 500-503
- Hsu, J.-P., Hsu, L., “Extended Lorentz Transformations for Accelerated Frames and a Resolution to the ``Two-Spaceship Paradox''”, 2006, A Broader View of Relativity. Series: Advanced Series on Theoretical Physical Science, WORLD SCIENTIFIC, 10, 319-329
- Redžić, D. V., “Note on Dewan Beran Bell's spaceship problem”, 2008, European Journal of Physics, 29, 3, N11-N19
- Franklin, J., “Lorentz contraction, Bell's spaceships and rigid body motion in special relativity”, 2010, European Journal of Physics, 31, 2, 291-298

The basic version of Bell’s spaceship paradox has been solved, but more sophisticated versions have not been considered, neither proper visualisation of the paradox can be found in the literature. Assistance will be provided by way of weekly discussions.

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

Having a good understanding of the original version of the paradox | end of November |

Solution of the original version of the paradox | end of February |

Solving an extended version of the paradox | mid-March |

Space-time diagram of the paradox | Easter |