Course syllabus for Special relativity

Linear algebra, real analysis, mechanics and electromagnetic field theory.

The course aims to give a wide understanding of the theory of special relativity as one of the pillars of modern physics. Starting from Einstein's relativity postulate the Lorentz transformation is derived and studied. This is thereafter applied on a range of classical models that are then modified, when so needed, to become relativistic. The student will revisit models treated in earlier courses but which are now treated from a more rigourous and axiomatic perspective. Furthermore a number of new concepts such as metric, space-time and tensors are introduced. These serve a purpose both in the course and as a basis for further studies within theoretical physics. The treatment of problem-solving in the course can be said to be two headed. One part of it aims to develop the ability to solve problems in relativistic physics whereas the other aims to develop the ability for relativistic problem-solving (the use of reference frames being a central component). Altogether the course gives an exciting glimpse of modern physics along with a firm basis for further studies of theoretical physics.

The ability to reason "relativistically" is central to the course. The focus, through out the course, is on developing, widening and deepening this ability. Furthermore there is a heavy emphasis on problem-solving and especially "relativistic problem-solving". Upon completion of the course the student will have developed a subject-specific competence and understanding sufficient for being able to

• explain in detail:
  
  - the role and function of special relativity
  - inertial frames, their existence, definition and use
  - the Lorentz transformation, it's derivation, properties, representation and immediate consequences
  - space-time and related concepts
  - relativistic mechanics, its axiomatic foundations and central applications
  - general tensors and vectors, the definition and special cases of special importance
  - Maxwell's equations in tensor form
• construct thought experiments and with the use of these, explain and analyse:
  
  - kinematic effects
  - relativistic collision problems
  - alternative theories (e.g. ether models)
• solve problems, relativistically, that concern:
  
  - kinematics
  - optics
  - particle physics and collisions
  - electromagnetic fields

The student can at the end of the course show deep understanding through:
- explain kinematic conclusions by use of dynamic models
- do short derivations alternative to the ones presented during lectures
- find or construct apparent paradoxes and dissolve them

• Inertial frames and the Lorentz transformation The definition of inertial frames. Einstein's relativity postulate and the derivation of the Lorentz transformation. The properties and graphic representation of the Lorentz transformation.
• Relativistic kinematics Length contraction and time dilation. Relativistic addition of velocities and the Lorentz transformation of velocity and acceleration.
• Relativistic Optics Relativistic corrections to optical phenomenon (e.g. the Doppler effect and aberration).
• Space-time and 4-vectors The metric and metric space. Euclidian spaces and the Minkowski space. From vectors in Euclidian spaces to 4-vectors in space-time. The light-cone, structure of space-time and geometry of 4-vectors.
• Relativistic mechanics The axiomatic framework of relativistic mechanics. Equivalence between mass and energy. 4-momentum and 4-force. Collision problems with massive and massless particles.
• Tensors From vectors to tensors. General tensors and 4-tensors.
• Manifest relativistic electromagnetism Maxwell's equations in the tensor formalism.

Teaching is done solely through lectures.

Written exam and hand-in problems.