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# TR

**Course:** Theory of Relativity

**Department/Abbreviation:** KEF/TR

**Year:** 2021

**Guarantee:** 'Mgr. Lukáš Richterek, Ph.D.'

**Annotation:** The aim of the course is to show the role of special relativity in the physical picture of the world.

**Course review:**

- Introduction, space and time in non-relativistic physics, ether and basic experiments for its determination, Michelson-Morley experiment, Einstein postulates, Lorentz transformation and its consequences (length contraction, time dilatation, relativity of time and space, transformation of velocity)
- Minkowski spacetime, event, space-time interval and true time, light cone, world line, causal structure of the spacetime, four-dimensional formalism and four-vectors, tensors in Minkowski spacetime and important operations with them, Minkowski diagram, covariance principle
- Equations of relativistic dynamics of a particle, four-force and four-momentum, equivalence of mass and energy, basic equations of dynamics of a particle system, collisions and scattering of particles, stability of particles, bonding energy, annihilation of electron-pozitron pair, Compton scattering, tensor of angular momentum
- Speeds over speed of light and causality principle, paradoxes, appearance of moving objects, speeds under and over speed of light, paradox consequences of speeds over speed of light and tachyons, twin (time) paradox and other paradoxes, paradox of rotating disk and non-Euclidian geometry, relativistic aberration, relativistic Doppler effect, experimental verification of theory of relativity
- Four-current and four-potential, Lorentz calibration condition, wave equations for field potentials, tensors of electromagnetic field and Maxwell equations, their transformations and field invariants, Lorentz four-force and its density, plane harmonic electromagnetic wave, wave four-vector, tensor of energy and momentum of electromagnetic field, laws of conservation
- Poincaré groups and their subsets, Lorentz group mad restricted Lorentz group, infinitesimal Lorentz transformation, Lorentz transformation with arbitrary direction of velocity, boost, superposition of Lorentz transformations in perpendicular directions, Thomas precession, variation principles in relativistic mechanics