Physics for Everyone, Lecture 4. The Beating Heart of Modern Physics: The Dog Who Didn't Bark in the Night.

This lecture, recorded before lecture 5, which was released a month ago, actually more naturally follows it, which is why releasing it after lecture 5, while unintended, actually makes sense. In the last lecture I described the most important unification in all of physics, the unification of electricity and magnetism, a unification into electromagnetism by James Clerk Maxwell in the 19th century.

Because of its elegance, and its overpowering utility, the theory of electromagnetism has provided the prototype for all modern physical theories that have followed it. As I show in this lecture, the form of electromagnetism is governed by a new mathematical symmetry in nature, called gauge symmetry. It turns out the existence of this symmetry is profoundly important, and it not only governs the exact form of the theory, it turns out to govern the form of all the known forces of nature.

Before we get to gauge symmetry, I want to explore more generally what is meant by symmetry in physics, and then I want to redo elementary physics by thinking about symmetry. In my mind, the fact that basic physics is introduced without reference to the symmetries of nature is perhaps the greatest failing in the teaching of modern physics. Concepts like energy and momentum have relevance because of fundamental symmetries of space and time. The facts that energy is ‘conserved’, and momentum is ‘conserved’ in systems, which rigorously fix determine the form of Newton’s laws of motion, are often introduced as if they are dictates on high, like the ten commandments. However, once one understands that these arise from symmetries of nature, the fact that these quantities exist and are conserved, becomes immediate, as the remarkable mathematician Emmy Noether showed at the beginning of the 20th century.

Finally, as important as mathematical symmetries are in governing physical laws, it is equally striking that even if these fundamental symmetries exist in nature, they may not be manifest in particular situations. For example, gravity and electromagnetism don’t distinguish between left and right, but if I look around my room, the left side of my room looks very different than the right side. This is an example of what is called ‘broken symmetry’, one of the most subtle and impactful notions at the basis of what is now called The Standard Model of Particle Physics.

In this lecture I review all of these ideas, which are essential if we are to go beyond the physics of the 19th century to understand the physics of the 20th and 21st centuries.

Enjoy.

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