## MP352: Special Relativity

### Spring 2021 (2nd semester of 2020-2021)

Lecturer:   Masud Haque   (haque@thphys.nuim.ie)     Tutor is Gert Vercleyen (vercleyen.gert.2021@mumail.ie)

2021 May Exam

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

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

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.)

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.

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.

Textbooks:

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.)

• Zee, Einstein Gravity in a Nutshell
This book targets General Relativity, but on the way (in Part III) treats Special Relativity in detail.

• Chapters 11 -- 13 of:     Morin, Introduction to Classical Mechanics
Very thorough treatment. Excellent problems and exercises. Covers the more basic half or so of what we will do in this module.

• The chapter on relativity in:     Griffiths, Introduction to Electrodynamics
Very clear and physical treatment.
(Relativity is in Chapter 10 in the old edition I own; chapter number varies with edition.)

• Chapters 12 -- 14 of:     Kleppner & Kolenkow, Introduction to Mechanics, 2nd ed.
Very pedagogical. Covers maybe the more basic one-third or so of what we do in this module. The level is intermediate between the Resnick-Halliday level and the level of this module.

• Chapters 15 -- 17 of:     The Feynman Lectures on Physics, Volume I
A classic. Free to read online, on this website.
Somewhat outdated terminology/convention, but should still be worthwhile to read. Covers the more basic one-third or so of what we do in this module.

• Cheng, Relativity, gravitation, and cosmology
Special relativity is reviewed as a prerequisite to General Relativity. Very clear treatment.
Special Relativity is treated in Chapter 2 in the 1st edition, but broken up into chapters 2 and 3 in the 2nd edition.

• Chapter 1 of:     Landau & Lifshitz, The Classical Theory of Fields
This is Volume 2 of the famous Course of Theoretical Physics'. This series is generally considered challenging.

• Chapter 7 of:     Goldstein, Classical Mechanics
Concise treatment of some of the more advanced aspects.

• Chapters 1 -- 4 (and bits of chapters 5,6) of:     Woodhouse, Special Relativity
Maybe slightly more mathematical than our treatment.

• Chapters 1 -- 5 of:     Rindler, Relativity: Special, General, and Cosmological

• Chapters 29 -- 34 of:     Greiner, Classical Mechanics: Point Particles and Relativity

• Bais, Very Special Relativity: An Illustrated Guide
Avoids formalism and teaches through pictures (through carefully analyzed spacetime diagrams).

• Steane, Relativity Made Relatively Easy
This textbook covers most of the material to be covered in this module.

• The chapter on relativity in:     Jackson, Classical Electrodynamics
Concise treatment of some of the more advanced aspects.

Material available online:

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:

Background

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.