Syllabus
* Introduction, starting principles
Special theory of relativity in physical picture of the world. A way to special theory of relativity from Newtonian mechanics via the theory of electromagnetic field. Basic experiments. 1st Newton law, principle of special relativity, principle of constant velocity of light.
* Immediate implications of the starting principles, Lorentz transformation
Synchronisation of clocks, relativity of simultaneity, length contraction and time dilation. (Special) Lorentz transformation; transformation of velocity. "Paradoxes" in special relativity. (In detail: clock paradox.) Lorentz transformation and four-dimensional, space-time view.
* Minkowski spacetime
Space-time, events and their coordinates, space-time interval and proper time. Light cone, types of world-lines and hypersurfaces. Real four-dimensional formalism: inertial frames, Minkowski tensor (metric tensor), vectors and co-vectors (contravariant and covariant indices), rising and lowering of indices. Lorentz transformation; invariance of interval and general properties of Lorentz transformations, inverse transformation. Transformation properties of quantities, tensors; tensorial formulation of physical laws.
* Relativistic mechanics
Four-velocity. Relativistic collisions, dependence of mass on relative speed, rest mass. Four-momentum. Equation of motion and four-force, comparison with Newton's equation of motion. Einstein's mass-energy relation, relation between energy and momentum. The question of (non)constancy of rest mass. The question of superluminal speeds and causality principle, hyperbolic motion.
* Relativistic electrodynamics (in vacuum)
Four-dimensional form of electrodynamics: four-current, four-potential, tensor of EM field, Maxwell equations; equation of continuity, Lorenz condition, wave equation; connection between tensorial character of equations and invariance of charge; relativity of electric and magnetic fields, EM-field invariants. Lorentz four-force. Plane harmonic EM wave, wave four-vector.
* Appearance of objects in special relativity
Basic aspects of appearance of an object - direction, colour and shape - and their dependence on relative velocity between the object and observer: aberration, Doppler effect and deformation. Composition of signal velocity with the relative velocity between the source and observer, the role of Lorentzian contraction and dilation. Comparison with classical results.
* Variational principles in special relativity
Lagrange function and action, Hamilton variational principle. Particle mechanics: Lagrange equations of the 2nd kind, finding the Lagrange function from d'Alembert and Hamilton principles, illustration on charged particle in EM field. Variational derivation of Maxwell equations.
Annotation
Experimental basis and starting principles of the special theory of relativity, their immediate implications and Lorentz transformation. Minkowski spacetime, tensorial form of physical laws. Relativistic mechanics. Relativistic electrodynamics in vacuum. Appearance of objects in special relativity. Variational principles.
For the 2nd year of physics studies (F).