1. Special Relativity#

Principles. (1) invariant nature of physical laws, (2) \(c\) as the maximum speed of propagation of information in space. Every inertial observer measures the same speed of light.

Lorentz’s transformation as a special coordinate transformations for space-time description as seen by two inertial observers in relative motion with uniform velocity. Physical laws governing a physical process have the same expressions if seen by two inertial observers. In a homogeneous time-space the expression of equations of physics doesn’t depend on translation of origin of time-space coordinates; in a isotropic space the expression of equations of physics doesn’t depend on rotations space rotation; as two inertial observers may write the same expressions of the physical equations using their own coordinates, the expression of equations of physics doesn’t depend on Lorentz’s transformations.

  • standard configuration: derivation of Lorentz’s transformations from principles and symmetry considerations

  • composition of transformations and general Lorentz’s transformation

Some consequences and examples:

  • Finite speed of propagation and loss of simultaneity.

  • Speed of light and causality. Causality follows from the principle that \(c\) is the maximum speed of information: all the observers perceive causes before consequences.

  • Length contraction and time dilation

Mechanics. Point kinematics: 4-velocity and 4-acceleration; dynamics of free particle: 4-momentum, energy-momentum relation, rest energy; dynamics of particles in external force filed: which field? For particles in EM field, Lorentz’s force; Lagrangian approach

Electromagnetism. Special relativity and equations of electromagnetism. From classical electromagnetism to electromagnetism in special relativity theory; EM potentials, gauge condition, 4-current and EM field tensor; EM field equations; motion of a point charge in an EM field; energy balance equations. Relativity of electromagnetism: low-speed relativity for classical electromagnetism. Lagrangian approach for the equations of motion of charges in an EM field, and for the EM field equations.