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

### Revisiting the Twin Paradox of Special Relativity

#### (supervisor: Balázs Pintér)

Nature of project: theory, theory

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

#### Project description and methodology

A successful project will develop beyond the above in one/some of the following directions:
- Various cases of a triple can be investigated.

- The launch of the travelling twin can start at zero speed, and the acceleration can be constant, or the force on the rocket can be constant – they are different in relativity.

- A case study can be followed by a parameter study to find out which aspects of a journey contribute more to the different ageing of the twins.

- An effective way of visualisation could be the animation of the journey and the ageing of the twins as seen in different reference frames.

- The inverse problem can be solved: what dynamics of the rocket would reduce an age gap between two, or more, people to zero.

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: 2D and/or 3D motions add complexity to the problem, where even new paradoxes can be discovered and explored.

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

Initial literature for students:

1. Arunasalam, V., “Some remarks on the twin paradox in relativity”, 2008, Physics Essays, vol. 21, issue 1, pp. 6-8
2. Grandou, T., Rubin, J. L., “On the Ingredients of the Twin Paradox”, 2009, International Journal of Theoretical Physics, 48, 1, 101-114
3. Murphy, T. W. , “Confronting Twin Paradox Acceleration”, 2016, The Physics Teacher, 54, 5, 272-276
4. de Wolf, D. A., “Aging and communication in the twin paradox”, 2016, European Journal of Physics, 37, 6, 065604

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

Although several versions of the twin paradox have been already considered, the relative mathematical complexity of the solutions makes it hard to pass the knowledge on to others, and the solutions are generally not available. The student(s) will build up a journey profile (speed versus time) and derive the answers to all the paradoxical questions for that case. Then, the results will have to be made publicly understandable by visualisation, which is a new objective. The Lorentz formulas are simple algebraic equations, but finding out the ways how to apply them to different paradoxical situations will make the project challenging. Difficulty also arises from the objective that the answers and explanations should be made understandable to others by visualisation.

Supervision and discussions can be done online.

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

milestoneto be completed by
Understanding the original twin paradoxend of October
Designing a journey for one of the twinsend of November
Representation of the journey in a suitable space-time diagramend of February
Creating clear, colourful, perhaps animated, illustrations of the journey and aging of the twinsmid-March