Electromagnetism as a Gauge Theory

[@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

[@peacepoet1947]

What type of energy gives particles their endless spin.

[@pmadjidi]

Very well explained. I always wanted to have a better understanding of SU(1), and I had a vague idea about the complex phase spinning around, but I could never put the fragments together. Now, thanks to your explanation, I have a better understanding of what is going on. I find it very satisfying that one can derive the electromagnetic field right out of pure mathematical reasoning about the Lagrangian density of the Dirac field. That part was pure magic. Thank you once again.

[@santiagomartinez3417]

Hi Richard, this is all very interesting but highly theoretical. I was wondering if you can show theory vs experimental data in the most simple and boring of the chemical reactions, maybe one involving hydrogen. So is it possible to plug reactants into these theories and get the chemical products as an output? How is calculated all the process?

[@Lesser302]

33:01 only half hr in but I will be back, life calls ya know My dragon is yawning and turtle is moving her rocks about looking for food. She is making noises from her tank hence need to feed them. Love you work so far though. I’ll be back. Oh though I was Not watching just listening yet I was imagining my cube to follow along well not mine but the one I made. Amazingly enough it helped with the visualisation as you got to the flags I was already at the horizontal on a 3d plain I wondered as we all do How did I do that 😂 What cube I hear you all ask? Drill out the dots on a dice I made in from some hard wood a fallen piece from my possum tree 8cm x 8cm x 8cm Not all lines line up yet one can see how to join 3 vectors in unison with out a break or connection with in the massless of mass of the whole with in and with out of the holes to visualise all the Spin up or spin down and visualise your numbers of squiggles and invisible lines 😂 🙋🏻‍♂️👉🏼👁👁👈🏼 easy to see Oh place a marble in 1 and shine a light in the centre of 3 and 5 in the dark to make a projection of ? Well you see 😂 🙏🏼👍🏼

[@nguyensontung5923]

Sir I badly need your hydrogen 3 on fine structure. The way you relate mysterious concepts demistify them.

[@BleakStarshine]

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

[@RichBehiel]

😂

[@lad4694]

Duuuude, I just set my phone to charge and just made the "mistake" of opening KZbin 😂😂

[@nxtech201]

It’s true 1:19am here

[@uditamehta3927]

Liar u dont have a babe

[@ten5ionator]

Yay, got work in 4 hours 😂

[@eigenchris]

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

[@RichBehiel]

Hey Chris, thanks for stopping by! :) For those who don’t know, this is the legendary eigenchris, who made the Spinors for Beginners video series. Check out his channel!

[@faisalsheikh7846]

Yes sir

[@9WEAVER9]

​@@RichBehielThanks for the videos! You should consider making a video for the 4th Summer of Math Exposition, run by 3B1B, in 2025!

[@hayjaydee873]

Eigenchris, Rich Behiel. We just need 3B1B in the collab and we have the holy grail of physics Videos

[@SMujiH]

lol

[@TheoriesofEverything]

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

[@RichBehiel]

Thanks Curt, that means a lot coming from you! I’m glad you enjoyed the video :)

[@Zookeeper.]

What would really rattle your gauges is knowing how non-zero vacuum expectation value kind of negates the idea of a "big-bang".. Aka *_"How'd you like them Apples?"_* 🍏🍌😉

[@BAROMETERONE]

I was going to say. Richard's logical presentation was very easy to follow and I'd recommend it to anyone interested in understanding electromagnetism and gauge theory.

[@rudyj8948]

Love it when my fav physics KZbinrs support each other 🤩

[@timelsen2236]

I would like a definition of Gauge in Gauge field theories which is general. Field invariance, Local phase invariance, Electrostatic potential additive constants and Magnetic vector potential additive gradients without physical significance are good, but seem varied and suggest a general definition.

[@SafetySkull]

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.

[@Pinkfongfan24]

I’m so pumped. I ❤ these videos. Learning is the new black 😂

[@Velereonics]

have you seen down the rabbit holes 5 hour disambiguation of Eve Online

[@starrmont4981]

Such as?? Don't leave me hanging!

[@Lorendrawn]

@starrmont4981 mandalore gaming and patrician tv.

[@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

[@RichBehiel]

Our modern technology gives us great potential for teaching each other. Video is like a blackboard that can come to life, and the great part is, once the video is done and uploaded, it takes of a life of its own and can teach people even when I’m doing other things. I love it, and I hope my videos can be a positive example for others to follow. I can’t take credit for the methodology though, 3Blue1Brown is the OG! His videos are what inspired me.

[@Sol-En]

@@RichBehiel yea, I will follow you. You are doing really inspiring stuff

[@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!

[@RichBehiel]

Thanks for the kind comment, and I’m glad you enjoyed the video! :)

[@leif1075]

​@@RichBehielThanks for sharing. Do you have plenty of time to travel.and for vacation in your job? Thanks very much.

[@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 KZbin.

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :) Yeah, honestly this one took a lot of effort to make 😅 It turned out to be way more work than I was expecting (I thought this would just be like an hour). But that’s ok, it was a very satisfying project.

[@Flourish38]

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 💗

[@michaelmerkle297]

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.

[@RichBehiel]

Thanks, that’s exactly the kind of comment I was hoping for! :) And yeah, I feel your pain 😅 I hope this video makes the topic a bit more accessible.

[@ゾカリクゾ]

I kinda forgot many things about this topic/still a newb too... is gauge symmetry the same as U(1) symmetry?

[@michaelmerkle297]

​@@ゾカリクゾIn the case of E&M yes. There are other gauge theories whose symmetry is described by some other Lie group. For example, Yang Mills theories have SU(n) (special unitary group) symmetry.

[@ゾカリクゾ]

@@michaelmerkle297 oh, cool! thanks. i hope to be the one answering these questions one day

[@Naman...123]

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

[@ugurgazeloglu2070]

Weird how when I sleep, autoplay tries to make me smarter.

[@Aworldof1]

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!

[@RichBehiel]

Thanks, I’m glad you found the video helpful! :)

[@hodysensei3438]

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

[@RichBehiel]

Good morning! :)

[@MoreinDepth]

You make a student feel smart whilst they are learning, which is a truly uncommon and empowering feeling. With this topic you've changed my world view in 3 hours, I shall never be the same! Thank you!

[@RichBehiel]

Thanks for the kind comment, I’m very glad to hear that! :)

[@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.

[@RichBehiel]

Thanks for saying that! :) I’m glad there are people out there who appreciate the technical details. Even though it takes more work to learn the details, that’s where a lot of the beauty can be found.

[@johnsjarboe]

@@RichBehiel I just finished Sean Carroll's recent book on QFT that is also trying to fill a gap in this space as well. Keep it up, Richard.

[@obamahimself2885]

fell asleep with autoplay on. woke up with a nightmare about some major equation thing.

[@FartingCoffinYT]

Literally happened to me. Had the strangest dreams last night

[@coleashcraft6890]

I stumbled across your video on spinors a few months back, leading me to watch your full series on quantum physics. After doing some more research and developing a better intuition, I came back to your spinors video and suddenly everything just clicked. This has reinvigorated a curiosity for physics that I haven't felt in years! Thank you for creating that pedagogical masterpiece. Now I'll have to take notes on this one for the next couple days as well.

[@leofun01]

02:36:50 - it's beautiful. The longest lecture I've ever had, but interesting enough to keep me viewing to the end. I paused the video on each statement wich I have to checkout. And the part with derivatives is the easiest part. Man, this video is a lot of work.

[@nexaentertainment2764]

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

[@RichBehiel]

Thanks for the kind words, and I’m glad you enjoyed the video! :)

[@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

[@gianlaager1662]

This is the first time I've given someone a Super Thanks, but for this video, a like simply wasn't enough. Thank you for spending countless hours creating this. I'm only 19 and have wanted to explore quantum mechanics beyond Schrödinger for a while now. This was incredibly insightful and "easy" to follow. Thanks a lot!

[@RichBehiel]

Thanks for the Super Thanks! :) I’m glad you enjoyed the video and found it insightful.

[@joshuajacobs8061]

As someone who has a bachelor's in physics and math but didn't go further, this video is perfect for me. It makes a complex graduate topic that is tough to self study a lot more accessible. Thanks for the effort you make to create these videos. There is something truly beautiful about this topic.

[@RichBehiel]

I’m glad to hear that you enjoyed the video! Physics is beautiful :)

[@2imon203]

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

[@alexarnold8461]

Laying out exactly how you get the E and B fields from the potential/ E-M field tensor, whilst seemingly obvious just minutes after you laid it out, was really impressive - which i think is the sign of a great teacher. Also im annoyed at how i think i will forever remember the way of the 6. Very clear and elucidating all around. Great video so far, thanks for the awesome content.

[@markomihajlovic8943]

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

[@RichBehiel]

Thanks, I’m glad you appreciate the video! :) It was a lot of work, but it’s great to see that people are enjoying it and learning from it. All this positive feedback is very rewarding. And I do get a bit of revenue from ads and patron, not a huge amount but it’s a nice bonus.

[@kathykrol5942]

Amazing!!!!!!!

[@radimnovotny6534]

For those people that are thinking about watching this video but dont wanna commit because its 3 hours long. It is super worth it. Really great video, it doesnt even feel like 3 hours dont worry :)

[@joelproko]

To be fair though, it's a bigger investment than just 3 hours. There's a lot of pausing, digesting and going back to check previous parts of the video or even previous videos involved in understanding it all. And I'm still not quite satisfied with my understanding, with no fault on the video.

[@LHSchramm]

THANK YOU! By far the best 3 learning hours I spent in a long while. As an electrical engineer I has always been curious about the deeper meaning of the quantum origins of electromagnetism. In the EM classes I had, the A vector was just a cryptic, obscure element no one could explain properly, but they always said it was very important and profound. From the mathematical perspecive, it made sense, but it seemed to me back then, it was just a variable trick. Your video is absolutely enligthening, clarifying the origin of A: it's the seed for EM itself.

[@ERICLRICH]

During my studies of Electrical Engineering, I was never under the impression that Maxwell's equations have such deeper meaning! Excellent video!!

[@efekaanaltas]

Probably the most anticipated/happiest youtube upload of my life, I have been researching all about EM as a gauge theory since the spinor video (I was even reading about it yesterday night!). Can't wait to watch this 3 times! Your content is invaluable, thank you so much

[@RichBehiel]

I’m glad to hear that! Thanks for the kind comment :)

[@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.

[@J3R3MI6]

That’s awesome! This AI revolution will make learning and understanding all of this much easier.

[@joshuariefman1984]

I am a second year engineering student who's looking to specialize in physics. Your videos on Schrodinger's equation ignited my interest in quantum physics, and since then I have been spending much of my free time trying to teach myself. Now, just as I've finished Griffith's Introduction to ED and have been searching for a good follow up to learn about gauge theories, you release this. Moments of serendipity like this never cease to amaze me.

[@RichBehiel]

That’s great! Perfect timing :)

[@danielgovender874]

Literally about to write an essay on how gauge fields describe interactions - ABSOLUTE LEGEND 💯

[@solophysicist]

This is BY FAR, the BEST introductory Quantum Field Theory lesson on the internet! Superb work, Sir. Awesome derivations and explanations for us amateur Physicists out here who obsess over finding all of the meaning behind the connection of deep mathematical concepts underlying our physical reality! I'm right here in the fight with you; Researching, wondering and searching for the reasons and answers behind this amazing physical reality and our consciousness that brings it all to life for each one of us to observe daily!

[@RichBehiel]

Thanks for the kind comment, that means a lot! I’m glad you enjoyed the video :)

[@justynpryce]

Imagine never hearing about electromagnetism and this is how you're introduced to it

[@tomgraupner171]

if there will ever be a poll for the best physics video here on the tube: IT'S THIS !!! Thank you so much for your hard work.

[@RichBehiel]

Thanks for the kind comment! :)

[@Ema-yh5br]

You made and uploaded a 3h video, which is basically a full lecture. Just that shows how amazing this channel is (also your videos are amazing lol)

[@tablettorrensabellan]

It's not a full lecture... It's half a course!!!!

[@J3R3MI6]

“An expansion pack you put on your worldview” I subbed right after you said that

[@scottbehiel5019]

Your videos continue to impress! Not being a math guy, this all goes way over my head. What I enjoy is reading the comments from others and am heartened to know there are so many curious and intelligent thinkers out there.

[@RichBehiel]

Thanks Dad, that means a lot! :) It’s amazing how positive the comments always are. People are excited to learn!

[@MrCharlyAndy]

Rich. Thank you for this! The tale of how electromagnetism emerges naturally from the local phase symmetry of Dirac’s equation has to strike awe in one’s sensibility. The magic can only be told using the language of mathematics. You have done a magnificent job.

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :) I agree, the beauty of the math is awe-inspiring.

[@nilessamaniego2783]

Coming here as a rising senior studying Electrical Engineering, I was not expecting to be out of my depth within the first 10 minutes 😂 Much love! I can’t wait to revisit this after reading up on that textbook you mentioned and watching your other videos!

[@thepewplace1370]

Lol, coming here as a 2nd year electrical apprentice who last touched physics in any rigorous way in AP physics like 15 years ago, but also having a huge ego, I didn't listen when he told me I'd be out of my depth in first 30 seconds. I've given it half an hour of what largely sounds like a foreign language before throwing in the towel, ordering that textbook, and consigning myself to relearning calculus, among many other things. Ouch.

[@Litepaw]

Within the first 3 minutes you completely blew my mind about the concept of a "field". I've never really thought about it. I now understand space-time and gravity a bit better as well! Thank you!!

[@aieousavren]

Once again, Mr. Behiel, you've absolutely knocked it out of the park. I am consistently stunned and blown away by the sheer quality and care of your presentation. I say this as someone who has passionately studied physics on my own for all of my life: This video, and all of your other works, are utterly invaluable. I have been studying the topic of "the U(1) gauge theory of electromagnetism" for at least 4 years now, even to the point that I am currently diving deep into connections on principal bundles and covariant derivatives on vector bundles just so I can finally wrap my head around "just how all of this machinery really fits together", so it really says something that this video still actually taught me a lot. It's given me a lot to think about and ponder. I love the way you give intuition-focused breakdowns for the different "moving parts" in both the equations, and the physical situations. The animations are incredible too. The way you blend the rigorous, algebraic expressions, with reference back to the "what is really going on in the physical universe, what does this mean", is truly invaluable for really extracting insight from these often opaque, yet inherently beautiful processes. The way you illustrate the journey... the usual narrative from "demanding local phase invariance of the Dirac field", to "well, local phase transformations result in the addition of a spurious term to the Lagrangian", to "what if we added something that canceled that out?", and so on... this journey is one that has been presented many times before by great educators, but you show the path in its entirety, in a very lucid and well-composed way, and I am deeply grateful for that. More amazingly insightful to me, is how you showed the way that the four-potential is "brought to life" by, apparently, the fact that that antisymmetric quantity (the Faraday tensor) is apparently "immune to" or "untouched by" local phase transformations. And thus, these "wigglings" are allowed to "scrunch up freely". I don't believe I have ever actually thought about it that way before. It will be very interesting for me to investigate later how this figures into my understanding of F as the curvature 2-form of the connection 1-form A on the principal U(1) bundle. In short, this video is nothing short of a masterpiece. I wish I could go part-by-part and really get into just exactly what I love about it. For now, it will suffice to say that this video is an invaluable resource for people like me. Your lucid, detailed-yet very well-paced and friendly-leadings-through of these physical and mathematical notions, vividly exposing the beauty inherent in the "mathematical machinery" of physics, are truly a gift. Thank you for this kindness. Your work is helping people. I hope you have a wonderful night and/or day.

[@RichBehiel]

Wow, thanks for the amazing comment! :) I’m very glad to hear all that, and I really appreciate your kind words, that’s very encouraging. I’m glad you enjoyed the video, and I can tell that you’re someone who has studied this topic in depth, so that really means a lot.

[@aieousavren]

@@RichBehiel Absolutely! I've always been fascinated by electromagnetism as long as I can remember. I feel very lucky that I've been able to slowly work my way up to "the real stuff", above the mere classical "vector calculus" formulation. This is part of that! I am deeply grateful for the part you've played in my never-ending quest for deeper insight. ^^

[@hypnozpie4071]

the fact information like this is freely accessible gives me hope in humanity

[@funyunfinnyun]

Who else woke up to this in the middle of the night

[@schrod-f1s]

This is one of the best videos I've ever seen in my life. This video probably summarizes an entire course in relativistic quantum mechanics. It showcases such deep fundamental beauty and elegance in the logic and belief in the symmetries that blossom into concrete physics reality . It's just beautiful in every sense of the word

[@RichBehiel]

Thanks for the kind comment, and I’m glad you enjoyed the video! :)

[@schrod-f1s]

@@RichBehiel appreciate you man

[@kenkiarie]

Seated and ready! That you would educate us this deeply is amazing. Thank you.

[@RichBehiel]

Thanks for watching! :)

[@liledw13]

My word... As an amatuer AF math hobby enthusiast, this video was both thrilling to watch, and also made in such a way that my feeble brain was able to absorb it and gain great insights. Absolutely wonderful job good sir!

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :)

[@Grabahan]

Wow, this is amazing. I’m a pure math guy, and there’s a reason I skipped E&M but took classical, quantum, and statistical mechanics at university. This was an excellent derivation, thank you. The one thing I still have to wrap my head around is the fact that the “coupling” of fields seems to be asymmetrical when we minimize the action? I hope that this was a presentation choice for the video rather than a mathematical choice. Meaning if you look at the full QED Lagrangian without a priori knowing what psi is, but having the same initial condition, then one can first solve for psi as an electron and then solve for the photon field with psi fixed as was done in the video. Edit: I am definitely being dumb. I see the derivation is independent of psi and the dependence is the current J. It is hard to be locked in for 3 hours straight! Again, this was amazing. Thank you!

[@jdbrinton]

If there's such a thing a heaven, you're the first one getting into it. Thank you for you invaluable contribution to humanity! Your video shows there is no upper bound on the quality of educational content.

[@RBRB-hb4mu]

Great video. Dark background is a huge plus makes it easier to learn

[@cartihammond8741]

Easily the best youtube video I have ever seen! Thank you for this video. It was exactly what I was looking for. While I have seen nearly everything in various courses in University, that's the problem. No one ever showed how it all connects together. U(1) symmetry leading to EM sounds very complex, but you managed to show in an extraordinarily structured way how at heart it is (conceptually) very simple. Looking forward to future videos!

[@physics_enthusiast_Soorya]

Omgg let's goo! I'm soo exited to watch this video with my mom (she was also a science student and has done electrical engineering) right after my exams finishes! I know this will be a really great video! This man is literally the best person in the world❤️✨️✨️ Love your channel Sir 🤍

[@RichBehiel]

Thanks for the very kind comment! I hope you and your mom enjoy the video :)

[@chalkchalkson5639]

When I took a QFT class we derived F in class and then got deriving the maxwell equations as homework. It felt really weird. At this point in a physics degree euler lagrange and index raising are second nature. So you do the symbolic manipulation dance you're so used to, not really thinking about anything and pop! there is your entire theory of classical electromagnetism. It's like magic! There are 2 distinct other moments I remember as feeling the same: 1 - When you first do rot rot B and see a wave pop out 2 - Taking dirac or klein-gordon in rindler or schwarzschild metric, expanding to get the form of a schrödinger equation and finding + m*g*h + O(1/c2) at the end of the potential. Btw this video was amazing! I didn't expect to stay for the full 3h, but you've really managed to make this fun even for people who are reliving rather than experiencing the intense joy of seeing all of this play out. My only comment would be that it'd be nice if you wrote out the metric tensor and sums explicitly. I think a lot of "magic" regarding the co and contravariant things has happened here that make being very comfortable with SR a requirement here where more explicit notation would probably make things easier for people who only have some familiarity rather than full immersion in SR. Also, writing out the gs explicitly makes it much easier to see how gravity will end up effecting things. The sum symbol has less of a pedagogical justification and is just something I've seen many people get confused by where a simple symbol would clear things up.

[@leonardoreiter2299]

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

[@Naturally_CDG]

I have been looking for this video for a very long time… I didn’t know it existed, but the content you were covering here and how you’re explaining it is unlocking a lot of doors in my mind on these topics

[@henryrovnyak8743]

This is an awesome video! If you're interested, you should experiment with using OKLCH instead of HSL when representing phase using hue. You might notice that on a computer screen, pure blue appears darker to the eye than pure green. This is because the "perceived lightness" of a color varies by hue in HSL. This is what makes spinors look as if they're flashing. In OKLCH, the "lightness" parameter corresponds to perceived lightness, so panning through hue in OKLCH will fix the flashing. The tradeoff is that colors will appear somewhat washed out because using exclusively pure colors doesn't work for perceptual uniformity.

[@davidkohn753]

Halfway through this video and I have to stop it because my mind is blown. Omg. This is crazy. Reminds me of a really good prof who explained an entire confusing course to me in 2 hours and suddenly it all made sense. You have a gift for making complex things understandable. Please keep making videos! (I would love to see you cover the component concepts in more detail too as I bet it would greatly add to my intuitive understanding.) Can't thank you enough...for explaining the entire universe to me.

[@sfitzsi]

Love the relatable “you can do it” style of presentation and the amazing graphics. Doing the algebra in public is rare for KZbin but combining it with the geometry from the graphics is just what students need to connect the dots and develop intuition. While you’re driving the station wagon through the Grand Canyon of U(1) gauge invariance, it might be nice to take a side jaunt into Diracs magnetic monopole solution, with Wilson Loops and homotopy classes. Another fun side jaunt might be an intro to the path integral formulation of QM ala Feynman’s QED the A Strange Theory of Light and matter. As with most summer vacations it’s hard to say if the station wagon will be roadworthy next year. Anyways, thanks for your content. 😊

[@RichBehiel]

Thanks for the kind comment :) I’d like to do a video on Dirac’s magnetic monopoles one of these days, as well as the other things you mentioned. There are so many fascinating ideas in physics.

[@aryanmp9066]

How is it possible to explain such complex content so understandably?? I’m an undergraduate student and you’re making me understand graduate level physics. This is bananas.

[@Crape711]

This is probably the best breakdown of this topic I've seen. I'd love to see you cover SU2 Electroweak theory someday, and how the weak force manifests from it. I always find things like neutrino scattering through the weak force a bit confusing, as well as what weak isospin and hypercharge actually DO

[@fffffplayer1]

I've been looking forward to this. Will save it for later, but this series has been very helpful in the technical side of my journey to understand QM/QFT.

[@mollago]

What does it mean if I fell asleep to Rhett and Link best moments for 1 hour, and woke up at 2:59:12 of this video

[@TheNikatlas]

Awesome work! 🎉 Thank you 🙏 New people to the topic will never realise how hard it was to understand these concepts in the past.

[@ゾカリクゾ]

"every pseudovector is secretly a plane" geometric algebra foreshadowing!!!

[@IdanShem]

I'm absolutely in love with this video Literally one of the only youtube videos I actually keep coming back to

[@RichBehiel]

Thanks, I’m glad you love the video! :)

[@NathanaelNewton]

I was at a dinner party yesterday for Canadian Thanksgiving and I was telling them about how if I leave my KZbin on autoplay for more than an hour invariably I will find myself back at the video about electromagnetism as gauge theory..... And here we are again 😂

[@RichBehiel]

Welcome back! 😂

[@JimmyMatis-h9y]

same here but it always lands on the "Fall of Civilizations" channel 🫤 it's a good channel and all but wth?

[@nice3294]

I love this channel, it's both incredibly insightful and amazingly playful in the explanation of very profound physics and math. Like the whole bit about the **Six Ways** and "2B or not 2B" had me grinning from both the humor and the excellent presentation of these ideas.

[@lolalucxyz]

> Over three hours EM vid comes out right as I develop a bunch of questions about it. Hold my algebra, I'm going in.

[@djdrocco]

Just before I woke up near the end of this video, I was having a frustrating dream about being "taught" advanced theoretical physics by a fast-talking professor who was oblivious to how lost the class was. I was the only one even bothering to TRY taking notes, but I just couldn't write fast enough. I kept trying to ask questions despite knowing that the answer wouldn't actually make me feel less clueless. But he wouldn't stop speed-lecturing, except for once or twice, when I could finally get a question in. But each time, he barely acknowledged me, and just kept going without answering! The one thing I understood was his in-depth explanation of scalars... except I already knew all of that! And even more maddening was that it was in response to another student's expression of confusion! He didn't even have to ask a question! Gonna go back and actually watch this for real. Maybe I'll have a shot at comprehension without the handicap of being unconscious. EDIT: Nope.

[@css2165]

this kind of stuff should be put in universities

[@jh_esports]

This channel is absolutely invaluable. The content quality and the way it is presented is unique, I’ve never seen anything like it. Even the videos I watched for academic reasons (hydrogen atom series) didn’t feel like study videos. If felt like watching a super entertaining documentary that, unlike all others, didn’t skip the math. Tons of love from a German physics student, please keep these coming❤

[@flynn0e987]

Can’t wait for the quantum chromodynamics video😈

[@lad4694]

It's so weird how as I'm now getting interested with gauge theory, you upload this banger

[@kingeternal_ap]

Math: the art of cancelling terms

[@constellationshots3893]

Even though I’ve just started my upper div courses, I understood a good chunk of this and I love it. This math is a thing of beauty.

[@goki6548]

Oh wow! 3 hour video! You should join SoME! You'll obliterate the competition edit: AND IT IS FOR GRAD STUDENTS??!! HURRAAAYY

[@RichBehiel]

SoME sounds like fun, I was thinking about joining it last year but never got around to it. Maybe I’ll join the next one! :)

[@roodog1]

2:08:00 I took a class on general relativity as a junior in undergrad, and we had a final project that we could choose. I choose to derive the action integral for space time. The process of building the lagrangian density and then doing WAY too many integration by parts to move the variation term around has brought back many memories, and actually makes this derivation pretty mellow to follow. I imagine it’s the same process for any complicated Lagrangian. It’s so cool when something I learn in school shows up in a random KZbin video a year later.

[@quintafo5119]

woke up to this like "where tf am I"

[@RichBehiel]

Concise summary of the human experience! :)

[@nolanpolansky]

same thing I just woke up just now. I hope you know I work at a gas station overnight. How did I end up here? I’m not this smart.

[@JimmyMatis-h9y]

you soon will be! 🙂

[@MirzaBicer]

Damn, and I thought that the ~1 hour spin video was long. You're making extremely hard concepts intuitive and understandable, and I firmly believe that this is the best resource on the internet for both graduate and undergraduate physicists to fit what they've learned into intuition. I hope these videos keep coming, honestly your channel has become one of the biggest sources of my physics learning for me. I'll go become a "patron" now, and I suggest anyone who benefits from these videos to do the same, because the audience for a 200-minute Gauge QFT video is pretty limited for Richard to self-finance from, I suppose.

[@RichBehiel]

Thanks, that means a lot! :) I’m glad you’re enjoying the videos.

[@ENDESGA]

At this rate your next video will be 9 hours long lmao

[@RichBehiel]

Let’s hope not! 😂

[@ENDESGA]

@@RichBehiel I sent that before I watched it, and now that I finished it I gotta let ypu know how good it is. Learned so much, holy shit, thanks for making it!

[@MarshalDonn]

A comprehensive and technical explanation of (relativity through) EMF Gauge Theory. We have our finger right on the button. Thank you Richard.

[@Giacomo-xt1xr]

This is simply awesome. Finally, after years of looking for a complete dissertation, there it is! Love this

[@rr51019]

This is an incredibly good video. I watched it start to finish. Sticking to plain vector calculus/Einstein summation notation made it so much more approachable, and I feel primed to jump into a textbook on the topic and not get so lost in notation. Thanks for this. 🙇

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :) I agree, the vector calculus perspective is more approachable. There are some slightly more elegant ways of formulating these concepts with fiber bundles and differential geometry, but it requires more esoteric math.

[@dancingmathusalem5451]

I am about to get a Master's degree and am applying for a PhD in physics. I have studied QFT for a few years now. While none of the information here was new, of course, the explanation is tiptop. It seems like the perfect thing for someone getting a bachelor who is thinking of getting into QFT for their masters, a perfect balance of handwaving and rigorousness. 10/10 no comments

[@denkosekkaoce]

Just watched it once, loved every minute of being reminded of grad school. Going to watch it again to take it all in better :D Really really amazing presentation of such beautiful concepts and mechanisms.

[@rb8049]

Wow! A video tuned just right to my level. Really appreciate videos at this level. Most are too simple and just words or for advanced grad students in quantum general relativistic theory

[@drhxa]

Thank you Richard. Great contribution! Also, love seeing your excitement for the math and the connections to our physical world

[@matusmoro955]

I've only just finished my undergraduate degree, so my experience with field theories and relativistic QM is absolutely minimal. Still I decided to watch the video and I must say my mind was completely blown by Bringing A to Life in Six Ways. Seeing the EM field come to life purely due to mathematics and the original assumption is crazy. I also found the derivation of Gauss's law for magnetism quite funny, because in my introductory course this equation was considered a postulate of sorts by recognizing that there are no monopoles (or something of that sort) and knowing that a divergence-less field can be written as the rotation of a vector potential A. Now I know where that actually comes from. Amazing video.

[@tsunningwah3471]

❤❤❤❤❤❤❤❤❤❤❤

[@Colecraft13]

been preparing for this video by watching and re-watching all of your other quantum physics videos!

[@SpartacusBurch]

FINALLY. I've always wanted a in depth explanation on this after so many years. It seemed like no one would ever give an example that would flesh out such a profound discover this is. As a chemistry undergrad it seems that nearly the entire field is ultimately dictated by electric charge, and I wanted to know on a deeper level where that came from. I am so glad you acknowledge that accepting something like space/time/matter is far different from accepting electromagnetism, I have always thought the exact same thing. Its almost felt like something "on top" of spacetime, and it needed more justification. Also, it's never touched on how this is so fundamentally different from many other applications of math within physics. Here the physical reality almost seems as just a manifestation of pure math. Incredible video!

[@laurenfowler2314]

You are my favorite youtuber. Even though ive only finished my first year of college ever and theres a lot of academic jargon i dont understand, i still find physics and your videos incredibly fascinating!! Thank you for being inspirational

[@RichBehiel]

Thanks for the kind comment! :) I’m glad you’re enjoying the videos.

[@Deralikeable]

This came on while I slept and I dreamed it was someone explaining time travel.

[@ArthurOgawa-q9z]

Having learned EM from Feynman's lectures on physics, I have been over this ground from early days, but you have added a level of detail that is both new to me and very satisfying as well. It was also delightful to see professor Dirac on video, whom I had the good fortune to meet in life. The impression I get from your presentation is that "requiring" local gauge symmetry directly(!) gives rise to how (Dirac) charged particles interact. By the way, I have always been inordinately fond of the Dirac delta function, and I notice that you repeatedly took advantage of the Kronecker delta function (without explicitly mentioning it). Very elegant how it crops up, nicht wahr? ~~~~Arthur Ogawa

[@michaelmitchell2213]

I'm rewatching your entire catalogue so I can fully contextualise this video. I'm a PhD student in physics. I can feel a level of intuition building with QM fundamentals because of your videos that I've only ever felt with classical and statistical physics until now. I'm HYPED!!!

[@RichBehiel]

That’s great, I’m glad to hear that! :)

[@Raspberry_aim]

Richard this is unbelievable as always - I can't imagine the time commitment it must take for you to produce something of this quality, not to mention your explanations are always excellent which makes the topics easier to understand. Thank you so much for making this video, along with all the others you have made!!! 3 HOURS!!!

[@erikstephens6370]

10:50-11:25, Omg, I know this is unrelated to the video topic, but you have no idea how long I've been looking for this simple explanation of second-order quantization. Pretty much everywhere else defines this as making psi an operator, but they never explain why. It always felt so arbitrary, but with the field itself being fuzzy, I can see why one might make it an operator (like we do for momentum and energy in the first quantization). (I wonder what the states are.., superpositions of possible states, each having a certain psi value, making psi fuzzy. Kind of like how the wave function for a single particle cannot be completely certain, if the particle is entangled with another, even if the entire state of the system could be determined.) Thank you for this. I've been looking for something like this for waaay too long.

[@person1082]

love the humor thrown into this video, from the six ways, to whether we can "mentally do this quantum physics," the "giving up" to remove the quitters, and the B+B law thank you for making it. It was really interesting for me to watch all the way through. The only part that has confused me a lot is how to justify that the dirac lagrangian should look like that at 55:08 (I'm aware that the dirac lagrangian and equation do imply each other but it still seems a mystery as it why it would have that form and not a form similar to the relativistic lagrangian)

[@EMPP81]

With life pounding and pounding at the moment, I'm glad I can watch this video for the second time during Christmas. It's a masterpiece of no comparison, that gives me so much Joy such that I can postpone driving my car into a brick wall at 200km/h. Maybe I will just finish my physics phd instead. The beauty of it is worth living to see as much progress in the field that you can possibly absorb.

[@RichBehiel]

Wow, that’s quite a comment! I’m glad you found so much joy in this video. Please don’t drive your car into a brick wall. I know life can be hard. The progress in physics is exciting. It can also be helpful to look forward to upcoming space missions, as an incentive to stick around and see what the future brings. I’ve used that trick before. We’re living in exciting times. I definitely resonate with you though. Just a few days ago, I got dumped by my girlfriend of three years. We had been living together for a year. I was convinced she was the one, and was saving up for a beautiful ring. But she recently moved 2-3 hours away to start her PhD, and we started to drift apart, with the distance. So we figured I should move in with her, keep our relationship going, and so I found a way to shift to more of a remote role at work, packed up my apartment, and was all set for the move. She was on board with all this, also excited to pick up where we left off. But, she had a last-minute change of heart. I don’t entirely fault her for that. Our lives just sort of diverged, I guess. But it’s weird now to be living in our old apartment, alongside the old things of hers that she didn’t take with her, realizing I’m in that category too. You know, when moving, you have to decide what to take with you, and what you no longer need. It’s not great to be in the category of no longer needed. I didn’t see that coming! To make matters worse, I already sold my bookshelf, as I was preparing to move. So now I’ve got books all over the floor. An unintended metaphor, I guess. The one silver lining is that when you’re at your lowest, it becomes most clear what you have to do. And no, it’s not driving into a brick wall, though I fully understand the temptation. In my case, I have to pick the books up off the floor and put their equations in the computer and share them with the people of the internet. In your case, it sounds like you have to finish your physics PhD. If you’re watching physics videos during Christmas, then I do believe you have the spirit and character required to complete that PhD! And the world will be better off having you in it, with your advanced knowledge of physics. We need more people like you.

[@EMPP81]

@RichBehiel Wow, that's very tough as well. We might be able to figure out the fundamental equitations of physics, the equations of love are a completely different cookie to crack. But don't worry, I'm not really going to drive into a brick wall. It was more an expression of how hard live can be, but if you don't experience the super hard part, you cant enjoy life's best. Thanks for your kind reply. Live is suffering, but we are in it for the great and beautiful moments. The piece of art you put here on youtube is one of them. Thank you for that. Despite everything, a merry Christmas and all the best for the new year.

[@cotwodogger5812]

Incredible!!! Best 1.5 hours I ever spent!!! Watched at 2x but the lessons were very clear. Thank You, Thank You, Thank You. Amazing that E&M comes out of the Dirac.

[@RichBehiel]

That’s great, I’m very glad to hear that you enjoyed the video. Thanks for watching! :)