Special Relativity and Classical Field Theory

In 1905, while only twenty-six years old, Albert Einstein published "On the Electrodynamics of Moving Bodies" and effectively extended classical laws of relativity to all laws of physics, even electrodynamics. In this course, Professor Susskind takes a close look at the special theory of relativity and also at classical field theory. Concepts addressed here includes space-time and four-dimensional space-time, electromagnetic fields and their application to Maxwell's equations.

Lecture 1 introduces the idea of how time simultaneity changes across frames. It shows then quantitatively, how space and time coordinates relate to each other, leading to the derivation of Lorentz transformations. This also allows discussion of time and space dilations between frames. Lecture 2 introduces light cones and extends discussions on proper time - the invariant in space-time. The lecture then forwards to discuss 4-vectors and their notations to be utilized ahead. Lecture 3 derives energy and momentum conservation equations in the relativistic domains. Here the discussions include lagrangians as well. Lecture 4 introduces the concept of fields. By forming and solving lagrangians for the fields, its equations of motions are also derived through Euler-Lagrange equations. Einstein notations are further developed as well. Having derived the equation of motion through lagrangians individually for the particle and the field, this lecture incorporates them together and derives the equations. This discussion continues in lecture-5 and is developed further with moving particle cases. This lecture then moves ahead to discuss more notations developed by einstein to make equations concise. It includes covariant and contravariant notations. This lecture ends with a discussion of Klein-Gordan equations and their solutions. Lecture 6 introduces electromagnetic tensors. Through the lagrangian methodology, it derives the equation of motions for the electromagnetic field. Lecture 7 discusses the basic principles and mentions the new and important ones including locality and gauge invariance. The lecture discusses about gauge invariance and shows its adherence to the electromagnetic tensors equation. Lecture 8 moves ahead to discuss and derive (broadly) Maxwell's equations. It also includes a discussion on Lorentz transformations on tensors.  Lecture 9 introduces the relativistic formulae of Maxwell's equations. It progresses by using the equations and discussed properties to further scrutinize the electromagnetic field propagation. It then completes deriving and discussing Einstein's version of Maxwell's equations. Lecture 10 connects the classical field theory to relativity. It discusses the momentum and energy density concepts as well.

My sincere regards to Prof. Susskind and Stanford for making this lecture series publicly available.

Click here to read my notes.