Lecturer: Masud Haque (haque@thphys.nuim.ie)

Lectures & Tutorials

Lecture times and locations: Tuesdays, 12:05, Physics Hall; Fridays, 16:05, Hall D (Arts Block).

Tutorials: Wednesdays 10:05, Hall C (Arts Block).

The tutor is Aonghus Hunter-McCabe (Aonghus.HunterMccabe@mu.ie).

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.

Problem sets

Problem set 03. Due Monday February 24th.

Problem set 02. Due Monday February 17th.

Problem set 01. Due Monday February 10th.

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, in the drawer marked 352 near the front door of the Theoretical Physics department.

We might not be able to mark all the assignments; some assignments might go un-marked. 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.

Notes/handouts

Here are some derivations of the
Lorentz transformations for a standard boost.

If you spot any typos or errors, please let me know.

Material, 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 treats Special Relativity in detail. Great fun to read. -
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.

There are several copies of the book in the university library. -
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 an 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'. -
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*

More mathematical. -
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*

A very special and worthwhile read. 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:

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.

- Notes from DAMTP Cambridge.
- Notes from Macquarie.
- Notes from Princeton IAS.
- Notes from Virginia Tech.
- Mermin's Notes (LASSP, Cornell).
- Notes from Sussex.
- The wikipedia page on Special Relativity is quite detailed.
- There is a wikibook on Special Relativity.

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.

- Notes introducting the metric tensor and the Lorentz group.
- Notes by A.Jaffe, discussing the rotation group and the Lorentz group.
- The wikipedia page on the Lorentz group.
- Notes from Oslo.
- Notes from DESY.

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

- The wikipedia page on covariant formulation of electromagnetism.
- The wikipedia page on the Faraday tensor.
- The wikipedia page on the electromagnetic field transformations.
- The page on electromagnetism in special relativity, in lecture notes from Duke Univ.

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

- Twin paradox: wikipedia page on twin paradox, youtube video 01, youtube video 02.
- Time dilation: wikipedia page on time dilation, animation of mirror experiment (light clock),
- Length contraction: wikipedia page on ladder `paradox', video on `pole-and-barn' paradox,

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 practice and for learning the material more
thoroughly.

Solutions to previous exams + Sample Exams

Below are solutions to some past exams.

(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.