Single-Course English 5 ECTS

# Theory of Relativity

## Overall Course Objectives

To give the student a basic understanding of the special theory of relativity and its importance for modern physics. Examples of applications
of the theory are studied in the context of electromagnetism, atomic physics, high energy physics, and astrophysics.

Learning Objectives

• Account for the principle of special relativity, inertial systems, and the form invariance of the laws of physics.
• Account for the Lorentz contraction, time dilation, and the concept of simultaneity.
• Reproduce the Lorentz transformation and apply it on position, velocity, and acceleration of a particle.
• Account for relativistic invariant quantities, space-time diagrams, 4-vectors, and proper time.
• Account for relativistic energy-momentum 4-vector, conservation of energi-momentum, kinetic energy and reaction energy.
• Account for relativistic particle dynamics, the center-of-mass concept, and elastic scattering.
• Explain the relativistic Doppler effect and gravitational red shift.
• Account for the basic elements of relativistic electrodynamics.
• Derive the Dirac equation in the relativistic quantum theory of the electron

Course Content

The course treats the special theory of relativity. The starting point is electromagnetic phenomena, in particular the electromagnetic fields around a point charge as observed in different inertial systems. Then follows a discussion on the form-invariance of the laws of physics as well as the two postulates of Einstein, and the Lorentz transformation is derived and used to prove Lorentz contraction, time dilation, and the concept of relativistic simultaneity. Transformation of particle position, velocity, and acceleration is treated, and invariant quantities are sen to lead to space-time diagrams, 4-vectors, and proper time. 4-vectors are applied to particle dynamics, energy-momentum 4-vector, the center-of-mass concept, as well as relativistic energy (kinetic and reaction energy), and energy-momentum conservation is applied to elastic scattering (the Compton effect). Relativistic Doppler effect is treated, followed by a relativistic description of plane waves, the 4-vector phase, and the group and phase velocity. Finally, elements of relativistic electrodynamics and the Lorentz transformation of the electromagnetic fields are treated, and the Dirac equation in the relativistic quantum theory of the electron is derived. The general theory of relativity is introducered in a breif overview and its importance for the GPS technology is discussed. Throughout the course are given examples of applications of the theory within electromagnetism, atomic physics, high energy physics, and astro physics,

Recommended prerequisites

10033/10036, Mechanics and electromagnetism at bachelor level.

Teaching Method

Lectures and problem solving

Faculty

See course in the course database.

## Registration

Language English 13 weeks Physics DTU Lyngby Campus 10405 Candidate Week 35 Week 48 Mon 8-12
Price 7.500,00 DKK