Electromagnetism as a Gauge Theory

"Why is electromagnetism a thing?" That's the question. In this video, we explore the answer given by gauge theory. In a nutshell, electromagnetism arises from local phase symmetry. But what does that mean, and how exactly does that work? That's what this video is all about! :)

Video notes PDF and python animation codes are on patreon:

*This video is quite long and technical.* Think of it as a video textbook, so you can skip around to different parts if you’d like. But I wanted to err on the side of rigor and thoroughness, to show comprehensively how local U(1) symmetry blossoms into electromagnetism. So the ideas are all there for you, but you don’t have to watch this in one sitting! 😅

This video frequently references "Introduction to Elementary Particles" by David Griffiths, which is one of the greatest textbooks of all time. Highly recommend checking it out or buying a copy.

Also, see "An introduction to spinors" by Andrew M. Steane, for an explanation of how the spinor flag diagram works:

See also the famous YouTube series "Spinors for Beginners" by eigenchris, for more information about spinors.

Shoutout to Curt Jaimungal for introducing me to the spinor flag diagram, and for the video editing advice! Check out his YouTube channel, Theories of Everything:

Chapters:

0:00 Intro - "Why is Electromagnetism a Thing?"
14:24 Dirac Zero-Momentum Eigenstates
39:10 Local Phase Symmetry
52:07 A Curious Lagrangian
1:11:43 Bringing A to Life, in Six Ways
1:27:40 The Homogeneous Maxwell's Equations
1:39:25 The Faraday Tensor
1:47:49 F_munuF^munu
1:53:05 The Lagrangian of Quantum Electrodynamics
1:58:14 Inhomogeneous Maxwell's Equations, Part 1
2:11:07 ... Part 2, Solving Euler-Lagrange
2:31:10 ... Part 3, Unpacking the Inhomogeneous Maxwell's Equation(s)
2:37:55 Local Charge Conservation
2:42:20 Deriving the Lorentz Force Law
3:01:25 Miscellaneous Stuff & Mysteries

#math #physics #quantum #relativity #electromagnetism

[RichBehiel]

Hey everyone, thanks for checking out the video! :)

Timestamps:

0:00 Intro - "Why is Electromagnetism a Thing?"
14:24 Dirac Zero-Momentum Eigenstates
39:10 Local Phase Symmetry
52:07 A Curious Lagrangian
1:11:43 Bringing A to Life, in Six Ways
1:27:40 The Homogeneous Maxwell's Equations
1:39:25 The Faraday Tensor
1:47:49 F_munuF^munu
1:53:05 The Lagrangian of Quantum Electrodynamics
1:58:14 Inhomogeneous Maxwell's Equations, Part 1
2:11:07 ... Part 2, Solving Euler-Lagrange
2:31:10 ... Part 3, Unpacking the Inhomogeneous Maxwell's Equation(s)
2:37:55 Local Charge Conservation
2:42:20 Deriving the Lorentz Force Law
3:01:25 Miscellaneous Stuff & Mysteries

[BleakStarshine]

"Sorry babe, I cant go to sleep right now Richard Behiel just uploaded a 3 hour video on electromagnetism"

[eigenchris]

Came for the physics. Stayed for the "pew pew pew" noises.

[TheoriesofEverything]

Best 3h spent this year. Thanks for the shout-out, Richard. The most digestible introduction to Abelian gauge theory I've seen.

[JakeFace]

Usuallyy when I'm this excited for a 3 hour youtube video it's an unhinged video essay about a game I've never played.

[Sol-En]

Do you know what you're doing? You are taking education to a whole new level, you are making a breakthrough in the methodology of education

[arossconpollo]

I feel like this video is a triumph for humanity. You’re making this topic accessible for way more people than could previously grasp it. And it’s so beautiful!

[michaelmerkle]

When I was newer to gauge theory and first heard that "U(1) symmetry gives rise to E&M", it took me many painful hours to get to the bottom of it. This video does an amazing job organizing the story, and the visuals give me something to grab a hold of.

[TheLethalDomain]

Having made a 2 hour video on theoretical physics with stock video/photos I paid for and text that Powerpoint animated as I recorded live in a sitting, I know for certain that what you achieved here is far beyond anything my patience is ready to produce. This is just absolutely fantastic.

If anyone wants clarity on sections I covered regarding electromagnetism, this is the video I will send them to from now on. There's no question about it. This is the best current summary I know of on Youtube.

[Naman...]

Legend is back with straight 3 hours quality essay .... GREAT MATE

[Flourish]

The “words of encouragement” section at 13:49 actually made me cry. I didn’t realize how much I needed to hear that. Thank you 💗

[imon]

why do you drop this the same day i finish my electrodynamics course😭😭😭😭

[hodysensei]

The only time i can be awakend from my eternal slumber is whenever this guy uploads.

[leonardoreiter]

Idk why but 1:07 the fact that the blue particles are positive and the red ones negative makes me uncomfortable

[Aworldof]

This answered a LOT of questions for me even though I don't have the mathematical background to follow 90% of it. It really just helps put things in order while contemplating the nature of reality. Thank you sir!

[Gladicuss]

What this guy is basically saying ' for the laymen ' is that 1x1=2. =D Kidding aside, I grew up in a low income home. I wasn't able to go to college. Being 48, that doesn't mean I cant [try] to understand this. It is beautiful. 99% of what was said was over my head. But I'm a history nut, and love Newton, Durack, Feynman, Krauss, there are just to many to list. I love the way you explain things....which makes it sounds like I understood what you said in this video lol, but it's very unique to come across someone that teaches the way you do. I person can go to school and get a major, that DOES not mean they are good at explaining or teach said topic. I'm a guitar teacher and guitarist of over 34 years. So sir, I didn't understand pretty much any of this. BUT I want to learn. And you have a great way of talking / teaching. I know this video took you a long time to put together. Your right, we live in a time where a person like me can learn this stuff because of the resources we are able to obtain that you couldn't get back in the 90's unless you went to a university. Thank you.

[nexaentertainment]

This channel is easily one of the best educational channels I've seen. The quality is off the charts, seriously. There are channels with 100x as many subs that put out worse content.
Thank you for this feast <3 and your continued content.

[johnsjarboe]

I think I make this comment on just about every one of your videos, but I want to continue to express my thanks that someone is making videos that lean into the technical/math aspects of these topics.

[markomihajlovic]

I am honestly out of words, the amount of effort that was obviously put into the production, length of video and putting it out on the internet for free, just out of words

[quarterbells]

All I did over 4th of July weekend was sit inside by myself and try to unpack these equations. Best summer holiday. Thank you RB