PH 3501, Relativity

This course is designed to help the student acquire an understanding of the formalism and concepts of relativity as well as its application to physical problems. Topics include the Lorentz transformation, 4-vectors and tensors, covariance of the equations of physics, transformation of electromagnetic fields, particle kinematics and dynamics. Recommended background: knowledge of mechanics and electrodynamics at the intermediate level. This course will be offered in 2006-07 and in alternating years thereafter.

The required textbook for our course is "Introducing Special Relativity", W.S.C. Williams, Taylor and Francis Inc., London (2002), ISBN 0-415-27762-0. The recommended text is "The Principle of Relativity", A. Einstein et al., Dover Publications (1952), ISBN 0-486-60081-5. The supplemental text is Chapter 15 of "Classical Mechanics", J.R. Taylor, University Science Books (2004). It is on reserve in both the Gordon Library and in the Physics Department Office.

We meet at 10:00 on MTRF in OH 223. As usual for a physics class, expect regular homework and two or three exams. Additionally, early in the course I’ll ask you to be “Prof for a day” and, later, to do an end-of-term assignment.

Course objectives

Final grade determination

"Prof for a day"
End-of-term assignment


Please read the grading guidelines below before writing up your final version of homework. Although the homework is nominally due at the beginning of class, if after class you want to show me your work and ask me a few questions, you may submit your homework as late as the afternoon of the day that it is due, as long as you have my permission. If you choose not to attend class, I expect to see your homework in my mailbox before 10:50 am. Some of the homework entails writing abstracts for the original relativity papers. Find hints in the template provided at myWPI.

Grading guidelines

I will use the following scheme for grading. You'll notice a big emphasis on effective communication, an aspect of your education that corporations examine during the hiring process.
Points For each problem (out of five possible points):
-1 to -5  Write-up hard to read or understand
No commentary
Missing or incorrect units on numerical answers
-1 No boxes around answers
  In general, for any given problem:
 5 =  Very good -- write-up clear and correct
 4 = Good -- write-up clear and mostly correct, or understandable and correct
 3 = Acceptable -- write-up understandable and mostly correct
  And for an entire assignment:
-5 Electronic submission
-1 No name
-1 Ragged edges
-1 No staple


The exams are closed book, closed notes, although you may bring a formula sheet, limited to one side of a Letter page, and a calculator. There is a 10% penalty on make-ups.


The participation grade depends on classroom and field-trip attendance, your willingness to ask and answer questions during class, your level of office visits, your enthusiasm for group activities, and how many errata you find in our textbook.

"Prof for a day"

I would like each of you to present one to three sections of the book to the class and provide lecture notes and homework solutions. We’ll do it early in the course with the easy material. This means that the first student will lecture on Friday, 12 January 2007. I expect we shall cover three to six sections a day.  Please write only on one side of a page for the lecture notes and homework solutions.  The homework solutions should be given to me separately from your homework. You could, for example, make a copy of the solutions to staple together with the rest of your submitted homework.

End-of-term assignment

The end-of-term assignment will be an extended abstract and presentation on the history of relativity or a special topic in relativity. For the project topics, you will submit to me at least two articles on a subject of relativity of interest to you. These will then be approved and returned to you. If two or more of you overlap, I will ask you to adjust your topic. The abstracts should be 300-600 words long, single-spaced, and fit on one page. Please use "Writing an Extended Abstract.doc." as a template. Your presentations should be three to four minutes long. The grade for the end-of-term assignment will be determined from your promptness and cooperation in finding a topic, the quality of your abstract, the timeliness of your talk, the clarity of and appropriate referencing in your slides or chalkboard notes, and your delivery of the material. The five items will be equally weighted. You will upload your slides to myWPI before class on Monday, February 26 (hard deadline).


The syllabus is embodied by this calendar. "S" refers to sections of Williams' book, and "T" to sections of Taylor's book.
Week of Monday Tuesday Wednesday Thursday Friday
7 January 2007
What's due 
Today's material

HW1, your input
P and E
14 January  --
Relativistic kinematics I
ABS1, E=mc^2
Relativistic kinematics I
S.3.6, 3.9, 3.10

Relativistic kinematics I
HW2, Ch.2&3
21 January
ABS2, Lorentz contraction
SR Foundations

SR Foundations
HW3, Ch.3&4
Photon kinematics
28 January
t and l

, Ch.1-4

HW4, Ch.5&6
Scalar product
4 February
Light cone
ABS3, Einstein's kinematics
Relativistic forces
Bates Linear Accelerator Center
Project topics
Massless particles
HW5, Taylor Ch.15
11 February
EXAM2, Ch.5, S.6.1-6.4, T.15.4-15.11

Advising Day

No class

18 February
ABS4, Einstein's E&M
General relativity
HW6, Taylor Ch.15
General relativity

Project abstracts
General relativity
ABS5, g and hv
General relativity
25 February
Project uploads
Project presentations
Project presentations

EXAM3, T.15.12-15.18, GR

Schedule for "Prof for a day"

"Guest professor"
Homework solutions
Verlinden, Nicholas
2.5, 2.6
2.1, 2.2
Stevens, Keeley
2.7, 2.8
2.3, 2.4
Scheid, Eric
2.5, 2.6
Petrova, Olga
2.7, 2.8
Osborne, Kenneth
3.1, 3.2
Morin, Nathaniel
3.9, 3.10
3.3, 3.5
Foltz, Ryan
3.6, 3.7
Labounty, Meghan
3.12, 3.13
3.8, 3.9
Kraft, Daniel
3.10, 3.11
Kejriwal, Akhil
4.3, 4.4
3.12, 4.1
Harvey, Clifford
4.5, 4.6
4.2, 4.3
Gould, Elizabeth
4.7, 4.8, 4.9
5.1, 6.1
Gao, Jean
6.2, 6.3
DeGraf, Colin
6.5, 6.6
Bruner, Christopher
5.4, 5.5
6.11, 6.15
Artim, Gregory
5.6, 5.7
T.15.7, 15.13
Abebe, Eyuel
T.15.19, 15.28
Kavulich, Michael
5.9, 5.10
T.15.29, 15.33
Shizume, Tesia
T.15.37, 15.42

Communication and office hours

My office is OH 219. I am sometimes in my lab, OH 009, in the Physics Library, OH 118, or in the department office, OH 119. My mailbox is between the doors of OH 118 and 119. Email, web, office phone with voice mail (508) 831-5365; fax (508) 831-5886; my basic weekly schedule is posted at Please put "PH 3501" in the subject line of your emails for a faster response. Drop in for quick homework hints any time I am free; otherwise for longer discussions please come to an office hour or make an appointment. Generally good times are after class and after 2:00pm, although check my schedule for specifics. The web address for this page is My research is described at and at links therein.


If you need course adaptations or accommodations because of a disability or if you have medical information to share with me, please see me. Students with disabilities are encouraged to contact the Disability Services Office (DSO) as soon as possible to ensure that such accommodations are implemented in a timely fashion. The DSO is located in Daniels Hall, (508) 831-5235.

Academic dishonesty

Individual integrity is vital to the academic environment because education involves the search for and acquisition of knowledge and understanding, which are, in themselves, intangible. Evaluation of each student’s level of knowledge and understanding is a vital part of the teaching process, and requires tangible measures such as reports, examinations, and homework. Any act that interferes with the process of evaluation by misrepresentation of the relation between the work being evaluated (or the resulting evaluation) and the student’s actual state of knowledge is an act of academic dishonesty. The moral equivalent of academic dishonesty in larger society is treason.

You are encouraged to collaborate on the homework, although you must prepare the homework for submission yourself. You may not submit homework after the answers have been made public. You may bring to the classroom exams a formula sheet; it is limited to one side of a standard Letter-sized page. During an exam, you may have only the exam, your formula sheet, a calculator, and writing implements on your desk. You may not give or receive information during exams, except to ask the instructor to clarify a question.

Educational research has shown that:

  1. The most learning occurs in an environment characterized by high expectations and respect and care for individual students, and where the value of collaboration is stressed over competition.
  2. The most learning occurs in an active classroom environment where students take responsibility for learning rather than being passive receptors of the professor’s knowledge.
  3. Students can learn as effectively or more effectively from peers than from a professor.
  4. Facilitating development of students’ communication, teamwork, and interpersonal skills is as important as helping them learn physics.
  5. Professors and students are equals in the learning process. I have as much to learn about teaching and people as they have to learn about physics.
Adapted from Prof. Chrys Demetry, WPI Materials Science

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N.A. Burnham, January 2007