After a brief review of gauge invariance, Professor Susskind describes the introductory paragraph of Einstein's 1905 paper "On the Electrodynamics of Moving Bodies," and derives the results of the paragraph in terms of the relativistic transformation of the electromagnetic field tensor. This paragraph asks the fundamental question "what is the difference between a charge moving in a magnetic field, and a fixed charge in a changing magnetic field." The answer to this fundamental question must be "nothing" if the principle of relativity is true. This conclusion is what led Einstein to develop the special theory of relativity.
Professor Susskind then moves on to present Maxwell's equations. He discusses the definition of charge and current density that appear in them, and then derives the relationship between these quantities. This relationship is the continuity equation for charge and current, and represents the principle of charge conservation.
The lecture concludes with the presentation the first two Maxwell equations in relativistic notation. This single equation is the Bianchi identity, and this identity makes it clear that magnetic charge sources (monopoles) and magnetic current do not exist.
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, we will take a close look at the special theory of relativity and also at classical field theory. Concepts addressed here will include four-dimensional space-time, electromagnetic fields, and Maxwell's equations.