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Special Relativity

Module PH2137

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2137 is a semester module in English language at Master’s level which is offered in winter semester.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 40 h 5 CP

Responsible coordinator of the module PH2137 is Antonio Vairo.

Content, Learning Outcome and Preconditions


The lecture course will provide a basic introduction to special relativity. The course will include

  • Space and spacetime
    • Euclidean space and Euclidean metric
    • Rotations in Euclidean space, the groups O(n) and SO(n)
    • The group SO(1,n)
    • Galilean transformations, inertial frames and the principle of relativity
    • Lorentz transformations
    • Minkowski spacetime and Minkowski metric
  • Foundation of special relativity
    • Galilean transformations and electromagnetism
    • The Michelson-Morley experiment
    • Einstein&39;s postulates
    • Relativity of simultaneity
    • Time dilatation and proper time
    • Length contraction and proper length
    • Application: relativistic wave equation
    • Velocity composition in 1+1 dimensions
  • Causality and relativity
    • Spacelike, timelike and lightlike intervals
    • Light cone, past and future of an event
    • (t,x) diagrams and Lorentz transformations
    • Example: motion of a relativistic train in a tunnel
    • Worldline
  • Vectors and tensors
    • Spacetime vectors and their properties
    • Timelike, spacelike and lightlike vectors
    • Velocity in spacetime
    • Momentum in spacetime, rest energy and dispersion relation
    • Velocity composition in 1+2 dimensions
    • Covariant and contravariant vectors
    • Example: gradient, d&39;Alembertian
    • Tensors: definitions and operations
    • Reducible tensors
    • Acceleration in spacetime
    • Example: world line of a free particle
    • Example: world line of an uniformly accelerated particle
  • Mechanics in spacetime
    • Energy and momentum in spacetime
    • Energy and momentum conservation in spacetime
    • Example: 2 → 1 scattering
    • Example: Compton scattering
    • Example: pair creation and annihilation
    • Particle collisions in accelerators
    • Nuclear fission and fusion
  • Electromagnetism and relativity
    • The electromagnetic current
    • The vector potential and the Maxwell tensor
    • Transformations of electric and magnetic fields
    • Electromagnetic waves and relativistic Doppler effect
    • Causality and the wave equation: retarded and advanced Green&39;s functions
    • The electromagnetic stress tensor
    • The Lorentz force
    • Example: motion of a charged particle in spacetime
  • Outlook: the OPERA experiment 2011

Learning Outcome

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Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Special Relativity Vairo, A. singular or moved dates

Learning and Teaching Methods

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Web page at



  • A. Einstein, Relativity: The Special and General Theory , Henry Holt and Company 1920


  • M. Fayngold Special Relativity and How it Works, Wyley-VCH 2008
  • P.M. Schwarz and J.H. Schwarz, Special Relativity , Cambridge University Press 2004
  • E.F. Taylor and J.A. Wheeler, Spacetime Physics: Introduction to Special Relativity, Palgrave Macmillan 1992
  • An extended list of relativity books can be found at

Lecture notes:

  • N. Woodhouse, Special Relativity and Electromagnetism, Oxford University 2006

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

The exam may be repeated at the end of the semester.

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