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Explore the fundamental principles of electrodynamics and Einstein's theory of relativity through this comprehensive 22-hour theoretical physics course. Begin with classical concepts of space and time from Aristotle through Galileo and Newton, then examine Euclidean and non-Euclidean geometries including Cartesian, spherical, and Lobachevskian systems. Master the wave equation and its symmetries, including Lorentz transformations, while studying sound propagation and the strong Huygens principle using Fourier transforms and Green's functions. Delve into Maxwell's formulation of electrodynamics and the discovery of electromagnetic waves, analyzing the contradictions between classical electrodynamics and Galilean relativity highlighted by the Michelson-Morley experiment. Investigate Einstein's revolutionary concept of simultaneity and the development of pseudo-Euclidean geometry by Einstein and Minkowski. Examine relativistic "paradoxes" including Lorentz contraction and the twin paradox, while studying the relativistic motion of charged particles and the speed-dependent nature of inertia. Understand the profound equivalence of mass and energy (E=mc²) and explore the electromagnetic field as a 4D differential two-form with its Lorentz transformations. Learn to work with tensors versus tensor densities, apply Stokes theorem, and formulate Maxwell equations in curvilinear coordinate systems. Conclude by examining the Lorentz force, remaining theoretical challenges in physics, and gain insights into particle-field interactions, local and global inertial frames, and gravitational theory.
