Special relativity

Duration

15h Th

Number of credits

Lecturer

Jean-René Cudell

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course of special relativity starts with a discussion of the invariance properties of Newtonian mechanics and Maxwell equations. The resolution, changing the laws of mechanics is then discussed in some detail, and standard consequences are derived. Minkowski spacetime is introduce, as well as dynamics. Tensors are introduced, and the Maxwell equations are rewritten in their modern form. Finally, the metric of accelerated frames, and the energy-momentum tensor are derived.
Contents
1. Introduction: Electromagnetism and Lorentz transformations Lorentz transformation vs Newtonian machanics
2. Kinematics Simulaneity, Lorentz transformations in mechanics Graphic representation of the standard Lorentz transformation
3. Kinematics 2 Length contraction, time dilation, paradoxes Transformation of velocity and acceleration Spacetime and 4-vectors: 4-velocity and 4-acceleration
4. R1
5. Dynamics The equivalence of mass and energy Particles and Waves Four-force and three-force
6. Electromagnetism 1 Four-Tensors Tensor algebra and differentiation The metric tensor Maxwell's Theory in Tensor Form
7. R2
8. Electromagnetism 2 The 4-potential Transformation of E and B The electromagnetic energy tensor
9. Road to General relativity The mechanical energy tensor Accelerated frames and the Rindler coordinates
10. R3

Learning outcomes of the learning unit

At the end of the course, students will be able: 1) to understand the local symmetry of spacetime; 2) to solve XXth-century mechanics problems; 3) to understand the constraints on any fudamental theory.

Prerequisite knowledge and skills

Newtonian mechanics and electromagnetism.

Planned learning activities and teaching methods

This course is based on lectures,  and to discussion sessions where problems (see the course webpages for the list) are discussed, as shown in the table of contents. The problems will be solved by the students, under the guidance of the instructor. Preparing them is strongly advised.

Mode of delivery (face-to-face ; distance-learning)

The references for each lecture, notes and the list of problems are available on the course web pages.

Recommended or required readings

Rindler's scholarpedia articles:
http://www.scholarpedia.org/article/Special_relativity
 

Assessment methods and criteria

Written exam, followed by a discussion. The first question is on the theory, and the list of possible questions is available on the course web pages (it is subject to change during the year). The second question (given after the theory question is returned) is an open-book exercise. The written part lasts 2 hours.

Work placement(s)

None.

Organizational remarks

The course will be organised in 10 one-and-a-half-hour lectures/discussion sessions (see contents).

Contacts

Jean-René Cudell
Institute of physics 19A Allée du 6 août Bldg B5a (4th floor, room 4/44) University of Liège Tel.: 04/3663654
E-mail: jr.cudell@ulg.ac.be
Web pages: http://www.theo.phys.ulg.ac.be

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