Nature of project: **theory**, software

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

The Doppler effect is probably the most widely used and exploited phenomenon in natural sciences research and observation. The wavelength of any type of wave are shifted when the relative motion between the wave source and the observer changes.

It is known from special relativity that the wave properties also vary if space-time - in which the wave, its source, and the receiver exist - itself is altered.

Students will evaluate the qualitative and quantitative similarities and differences between classical (non-relativistic) Doppler effects and those that can be derived from the special theory of relativity.

During the planning phase of the project, students make a list of cases (such as linear motion with constant acceleration, circular motion with constant speed, etc.) for which the Doppler effects will be derived.

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

- The analysis can include clarification of some widely believed misconceptions.

- A concise enumeration of the scientific fields (medicine, astronomy, etc.) and engineering techniques where the phenomenon is used could also add value to the report.

- The project can be extended to a comparative study of the various (such as e.g. classical, optical, thermal, transverse, relativistic, gravitational, cosmological) forms of the Doppler effect.

- Detailed description and resolution of paradoxes related to the relativistic Doppler effect can also be considered.

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:* - In a Y4 project, a more comprehensive comparative study will be required. For example, the Doppler effect associated with orbital motion can be investigated.

- Another option for a fourth-year project is analysing Doppler effects on a general signal, instead of a periodic one, where the characteristic time of the signal is comparable with the time needed for the signal to get from its source to the receiver.

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

*Initial literature for students:*

- Rawat, B. L. , “Doppler effect in special relativity theory”, 1977, American Journal of Physics, 45, 12, 1211-1212
- Prokhovnik, S. J., “The operation of the relativistic Doppler effect”, 1980, Foundations of Physics, 10, 3-4, 197-208
- Klinaku, S., “The Doppler effect and the three most famous experiments for special relativity”, 2016, Results in Physics, 6, 235-237
- Ramaccia, D., Sounas, D. L., Alù, A., Toscano, A., Bilotti, F., “Doppler cloak restores invisibility to objects in relativistic motion”, 2017, Physical Review B, 95, 7, 075113

Only the simplest version of the Doppler effects (source receding from or approaching the observer at constant speed) can be found in physics textbooks: the rest requires enduring literature research and assiduous calculations and imaginative thinking. No serious mathematical complexity is required for the project but clear thinking and readiness to read the related literature. The important abilities are:

- solid understanding of the basic Doppler effect (from modules such as PH38310 or PH38510) and the theory of special relativity (PH14310)

- Good visualisation skills

- Data analysis and interpretation of visual results

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

- Fine presentation and visualisation skills

- Supervision and discussions can be done online.

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

A firm understanding of the various versions of the Doppler effect | end of October |

Looking for applications of the Doppler effect in science and technology | Christmas |

Deriving the Doppler formula for a non-trivial case | end of February |

Visualising the Doppler effect for the list of cases | Easter |