Video lectures


Postulates of special relativity; maximal speed of signal propagation; relativity of time; definition of an event; simultaneity is frame-dependent; interval; differential interval; invariance of the interval; interval as a pseudo-Euclidean distance; time-like and space-like intervals; proper time and time dilation; future/past and causality.

Lorentz transformation

Transformation of coordinates and time in classical physics; transformation that leaves the interval invariant; hyperbolic rotation; connection between the "hyperbolic angle" and the velocity; final form of the Lorentz boost; inverse transformation; matrix form of the transformation; length contraction; time dilation; velocity addition.

Minkowski diagram

Setup of the diagram; lines of constant interval; axes of the K' reference frame; representation of an object (such as a ruler); length of a moving ruler; time dilation; frame-dependence of simultaneity; hyperbolic Pythagoras's theorem; time-like and space-like intervals.

Twin paradox

Proper time; Alice travels and leaves Bob behind; calculation from Alice's point of view; Alice's journey in the Minkowski diagram; Alice switches the reference frames; the missing time; resolution of the paradox.

4-vectors and covariance

What is a vector? From the group of rotations to the Lorentz group; coordinates of an event as a 4-vector (contravariant and covariant); Lorentz transformations in matrix form; definition of a 4-vector; Lorentz scalars; more notation: time and space-like parts and the metric tensor; determinant of a Lorentz transformation matrix; four connected components of the Lorentz group; the concept of covariance; 4-gradient; 4-velocity; 4-acceleration.

Relativistic mechanics

Action for a free particle; Lagrangian; canonical momentum and Euler-Lagrange equation; energy; rest energy; relation between energy and momentum; motivation for a covariant derivation; covariant variation of the action for a free particle; dependence of action on the end point; 4-momentum vector; threshold for a proton-antiproton pair production.

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