Prosiectau Ffiseg ar gyfer myfyrwyr bl.3 a bl.4

Train through a Tunnel in Special Relativity

(supervisor: Balázs Pintér)

Nature of project: theory, software

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

Project description and methodology

In the well-known train-tunnel (or, also called, ladder and barn) paradox, the situation is described in the two inertial reference frames in which either the train (ladder) or the tunnel (barn) is stationary. We can find that the series of events look very different in the two systems. The main question the project is to answer is: What is happening in a reference frame between the two?

Solving the Lorentz coordinate transformation equations, the times, positions, and order of events can be determined. The aim is to find these results as a function of the speed of the reference frame relative to the tunnel or the train.

A successful project will develop beyond the above in one/some of the following directions:
- The lengths of the train and tunnel do not have to be equal. What can happen if the rest-length of the train is less or more than that of the tunnel?

- Reaching and leaving the ends of the tunnel by the two ends of the train can be extended by other events, which can be monitored in the different reference frames.

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 results can be visualised by animation.

- The 1D problem can be generalised to two dimensions by letting the 'observer' move at a non-zero angle to the rails.

Please speak to Balázs Pintér (bap) if you consider doing this project.

Initial literature for students:

1. Einstein, A. On the Electrodynamics of Moving Bodies, 50 (1905)
2. W. Rindler, “Length Contraction Paradox”, Am. J. Phys. 29, 365 (1961)
3. Egon Marx, “Lorentz Contraction”, Am. J. Phys. 35, 1127 (1967)
4. R. Cacioppo, A. Gangopadhyaya, "Barn and pole paradox: revisited", Physics Education, Volume 47, Issue 5, pp. 563-567 (2012)

Novelty, degree of difficulty and amount of assistance required

This particular paradox is not widely investigated. The basic version is well known but it is hard to find any of its generalisation or extension in the literature.

Supervision and discussions can be done online, if necessary.

Project milestones and deliverables (including timescale)

milestoneto be completed by
A good understanding of the basic paradox and its resolutionend of November
Setting up a list of cases to be studied in the projectChristmas
First detailed results in an intermediate reference frameend of February
Visual presentation of the main resultsmid-March