Special Theory of Relativity

Course guarantor:

David Břeň

Lecturer:

David Břeň

Tutor:

Supervisor:

Department of Physics

Synopsis:

Students extend their knowledge of classical, non-quantum mechanics of the special theory of relativity fundamentals.

Requirements:

Syllabus of lectures:

1. Introduction, history, experiments leading to special theory of relativity, Newtonian mechanics, the electromagnetic field theory, basic principles.

2. Galileo transformation, Lorentz transformation and its consequences. Relativity of simultaneity, time dilation, length contraction, velocity-addition formula, four-dimensional formalism, spacetime.

3. Transformation of variables and their properties, tensor, covariant and contravariant indices.

4. The event, space-time interval, proper time and their transformations, general Lorentz transformation, rapidity, Minkowski (metric) tensor.

5. Light cone, causality, relativistic paradoxes superluminal speeds problem.

6. Dynamic, four-speed, four-acceleration, mass, collisions, conservation laws, four-force, Newton's equations of motion in the Special Theory of Relativity.

7. Energy, momentum, the relationship between mass and energy.

8. Aberration of light, Doppler effect, wave four-vector and its Lorentz transformation.

9. Continuity equation, the four-current, Maxwell's equations, the four-potential.

10. Lorentz gauge condition, the electromagnetic tensor, Lorentz. transformation of four-potential.

11. Lagrange function, continuum, energy-momentum tensor.

12. Equivalence principle, locally inertial frame, a very brief introduction to OTR

13. Metrics of curved spacetime, the gravitational redshift, cosmological redshift.

Syllabus of tutorials:

Study Objective:

Acquired knowledge:

Students extend their knowledge of classical, non-quantum mechanics of the special theory of relativity fundamentals.

Acquired skills:

The emphasis is put on the applying of new abstract concepts on the description and solution of relativistic physical situations and phenomena

Study materials:

Key references

[1] Votruba V.: Základy speciální teorie relativity, Academia, Praha, 1977

[2] Kvasnica J.: Teorie elektromagnetického pole, Academia, Praha 1985

[3] Semerák O.: Speciální teorie relativity, skripta ke stejnojmenné přednášce MFF UK, Praha 2012, http://utf.mff.cuni.cz/~semerak/STR.pdf

Recommended references:

[4] Kulhánek P.: TF4 Obecná relativita, skripta ke stejnojmenné přednášce FEL ČVUT v Praze, Praha 2016, http://www.aldebaran.cz/studium/otr.pdf

[5] Misner C. W., Thorne K. S., Wheeler J. A.: Gravitation, W. H. Freeman, San Francisco 1973

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (elective course)
• Jaderná a částicová fyzika (elective course)
• Matematické inženýrství - Matematická fyzika (elective course)
• Kvantové technologie (elective course)
• Quantum Technologies (elective course)
• Nuclear and Particle Physics (elective course)
• Mathematical Engineering - Mathematical Physics (elective course)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (elective course)