MP352: Special Relativity

Spring 2021 (2nd semester of 2020-2021)

Lecturer:   Masud Haque   (     Tutor is Gert Vercleyen (

Lectures & Tutorials

Lectures and tutorials are through Teams.

Lectures are scheduled for Tuesdays (12:05) and Fridays (16:05).   To attend lectures: please join the meeting on the MP352 Teams page at these times.

Tutorial times:   Wednesdays 10:05.   Please join the meeting on the MP352 Teams page at this time for tutorials.

Problem sets

Problem set 11.     Due Monday May 3rd.
Partial solutions/hints for problem set 11.

Problem set 10.     Due Monday April 26th.
Partial solutions/hints for problem set 10.

Problem set 09.     Due Monday April 19th.
Partial solutions/hints for problem set 09.

Problem set 08.     Due after the Easter break, Monday April 12th.
Partial solutions/hints for problem set 08.

Problem set 07.     Due Monday March 29th.
Partial solutions/hints for problem set 07.

Problem set 06.     Due Monday March 22nd.
For the Study Break: twice as long as the usual weekly problems.
Partial solutions/hints for problem set 06.

Problem set 05.     Due Tuesday March 8th.
Partial solutions/hints for problem set 05.

Problem set 04.     Due Monday March 1st.

Problem set 03.     Due Monday February 22th.

Problem set 02.     Due Monday February 15th.

Problem set 01.     Due Monday February 8th.

Practice Problems

Problem bank (``problem set 12'')
This is marked as `Problem set 12', but it is really a large collection of problems covering all the module material.
Should be useful for practicing material/concepts from the entire module, and for exam preparation.

Notes / handouts / Lecture notes

If you spot typos or errors in the typed notes, please let me know.

Here are typed notes on some of the introductory discussion.

Here are scanned notes on the Michelson-Morley experiment and an overview/discussion of topics to be covered.

Here are scanned notes describing the invariant interval and derivations of the Lorentz transformation.

Here are typed notes containing some derivations of the Lorentz transformaion for a standard boost.

Here are scanned notes discussing relativistic kinematics, including time dilation, length contraction, the Doppler effect, velocity addition, the twin `paradox', and spacetime (Minkowski) diagrams.

Here are scanned notes discussing dynamics (momentum and energy), and introducing 4-vectors.

Here are typed notes on dynamics: energy, momentum, force.

Here are typed notes introducting 4-vectors.

Here are typed notes listing/discussing physical examples of 4-vectors.

Here are typed notes introducting index notation, also often called tensor notation.

Here are typed notes classifying intervals (and 4-vectors) into space-like, time-like and null or light-like intervals (or 4-vectors).

Here are typed notes on the Lorentz group. The rotation group and the Poincaré group are also discussed.

Here are scanned notes discussing electromagnetism in relativistic notation and a few other topics.

Previous exams, some with example solutions   +   Sample Exams

Below are some past exams, in some cases together with sample solutions.
(The length of exams has changed since 2017.)

2020 May exam

2020 August (repeat) exam

2019 May exam

2019 August (repeat) exam

2018 August (repeat) exam, with sample solutions

2018 May exam, with sample solutions

2017 May exam, with sample solutions

2016 August (repeat) exam, with sample solutions

2016 May exam, with sample solutions

2015 May exam, with sample solutions

Below are sample exams for practice. They are in the style of previous (2017-2018) exams. Future exams may be structured slightly differently, but the material covered and the level of difficulty should be similar.

Sample exam 1

Sample exam 2

Sample exam 3

Sample exam 4

Textbooks and other sources

Special Relativity challenges our intuition and takes effort to digest; so I strongly suggest trying to read a fair bit every week.

For example, you could aim to work through two sections of Nash's notes (below) every week, or a similar amount of work from another text.

Nash notes:

lecture notes of Prof. Charles Nash, who taught MP352 some years ago
This has some overlap with the material covered now in MP352. Unfortunately, the ordering is different.


There are many textbooks covering special relativity. Our library carries a number of these textbooks.
Special relativity is also covered in many textbooks on classical mechanics or electrodynamics/electromagnetism, and often summarized in the beginning of texts on general relativity or particle physics.
I list a selection below.

(I omit publisher and publication date; should be easy enough to find.)

Material available online:

Please let me know if any of the links don't work.

The wikipedia page on Lorentz Transformations contains material very relevant to this module. Highly recommended.

The following `lecture notes' or other links are at various levels; mostly they cover the more elementary half of this module.

MP352 should make you comfortable with 4-vectors and Index notation. This is covered in many of the textbooks or notes linked above. In addition, the following links might help.

In MP352 we discuss the Lorentz group (together with the rotation group and the Poincare group); these are not covered in more elementary treatments or in Nash's notes. The following links might help.

Electromagnetism in special relativity is covered in some of the references given above. In addition:

Widely discussed basic material which are mathematically simple but cause conceptual confusions:


It will be assumed that you have met Special Relativity previously, at the level taught in the first year Mathematical Physics class (MP110) in our department.
You are strongly advised to review Special Relativity at the level of the text of Resnick-Halliday-Walker, i.e., at the level of MP110.
I strongly suggest doing this at the beginning of the semester.

Continuous Assessment and the purpose of problem sets

The plan is to assign one problem set every week. They will be posted on this webpage. The assignments will be due mondays, via the moodle page for MP352.

We will not be able to mark all the assignments. We will not announce beforehand which assignments are to be marked, so it will be to your advantage to submit every assignment.

Assignment marks (`continuous assessment') will be counted toward the final module mark only if they are to the students' advantage.
(The policy is module-dependent and varies within the Mathematical Physics department. In some modules, continuous assessment always counts toward the final module mark.)

HOWEVER: Do not think of the assignments as voluntary or optional. Without working on each assignment set, you are likely to get lost quickly, as the module will build on the assignments and assume that you have learned the material you are supposed to learn through doing the assignments.