The Biggest Ideas in the Universe | 15. Gauge Theory 

*disclaimer* I am a night shift Clinical Laboratory Scientist after a long night shift. * I watch this series after a fighting the Covid all night in Arizona. I come home, have a couple shots of Titos, and watch Sean as I "try" to fall asleep. I'm such a nerd! My mind races as I lay here contemplating how our world works. What can I do to make it thru this weirdness? Alas, I am a mere mortal at best... I go to the Colorado River and watch the waves on the river, the birds going about their day, and the beauty of the landscape. That's what keeps me grounded it this crazy time. Thank you Sean for doing what you do. It's helping a lot of us.

I'm a 4th year physics PhD student and these videos are still interesting and illuminating. Thanks!

I really love how in depth you get, most science communicators stick to the fluffy, eye-grabbing, more theoretical kind of things without actually conveying much information about them or how we came to those discoveries. Not a science student but definitely an enthusiast, and I really appreciate these videos as well as the many lectures you’ve done that people post to RU-vid. I finally feel like I’ve broken through that surface level knowledge that people like to spout and have become at least a little bit knowledgeable about the subject I love the most. I dunno, I’m gushing, you’re cool, hope you read comments

This is the first and only clear explanation of what a gauge theory is, that I have come across. I'm so glad you uploaded this. It connects many of the dots for me.

Sean, you have no idea how much i appreciate you doing this, and putting all this effort and work out. Thank you so much.

This video strikes the PERFECT balance between fluency and accuracy. Amazing as an appetiser/reminder for preparing a quantum field theory exam.

This has been my favorite episode where many previous ideas all came together.

I'm an EE who designs antennas. I consider Maxwell's equations as the foundation of E&M but you are going much deeper. It is wonderful to now see the photon as being the connection field among rotations within different locations of the electron fields and how the laws themselves can be derived, they need not be postulated. Wonderful stuff, thank you so much for what you are doing for us.

I am late to this party……….. but wanted to learn about Gauge Symmetry/Theory as this was left unexplained in a more casual book I read which ended with superstring theory and GUT/M theories. So oddly, I started here and was more enlightened. But……after going back to video 1, watching them up to and including this one again (and Q&As), then doing a little more digging on spontaneous symmetry breaking and then rewatching this for a third time, I am there. Kudos Doc - you got me there and yes, it is very rewarding. I am not a physicist, but historically and engineer, so also have a certain amount of pride in finally getting it. Looking forward to the rest of the videos (not lectures)!

I don't know what it is about you Sean, but gosh darn you incite so much excitement and joy in learning this stuff!

Geometry, Topology, Symmetry, and Gauge Theory. What is amazing is that I am getting this thanks to Sean Carroll. Well done, Professor! I am just an "absolutely everybody".

Perhaps the greatest explainer since Richard Feynman!

Preemeninent physicist: "Here's 'space'. Ah, we're getting good at drawing 'space' now."

Sean is not just great but unbelievable too. The funny thing is I only know basic stuff but still listen to his talks again and again in the hope of understanding it.

I had to watch this a few times to fully appreciate how amazingly wonderful this video is. Thank you SO much for the lecture Dr. Carroll !!!! Cannot even begin to imagine how you'll top this in the next video.

this series is perfect for ppl who have a decent mathematical background (i'm a computer scientist by trade) and want more than just the usual wishy-washy pop science communication; its so refreshing to get given an idea of how certain things are mathematically justified and where theories have come from.

Tremendous payoff indeed! I love the way Sean Carroll has laid the groundwork for us to follow and receive a valid broad stroked familiarity with one of the most popular yet inaccessible (to the layperson) theories in the Standard Model, namely QCD.

I'm a semi-retired Canadian university psychology professor (45 years of teaching). I think I'm pretty good. I have a side passion for physics. I listen to Dr. Carroll's sessions and I realize......how much I have to learn about physics. It's a humbling experience.

Perfect timing dr Carroll - just doing the main part of my Solid state Physics PhD experiment (magnetism) and feeling frustrated by all the complexities and intricasies of the aparatus, human nature and Nature itself. However, seeing this s*it, you theoretical folks, have to deal with I'm feeling much better about myself, my life choices and the Universe as a whole. So, thank you, thank you very much indeed. :)

My conclusion is that Sean Carroll understands it.

I love the *Windows 98 background* so much I cannot even express! 😳🤩

Thanks for this video - this is the only video of Guage theories that I did not quickly get risky lost in unnecessary detail and give up.

Sean is so good to tie all the things togheter, now we know why its important to know the stuff.

Thank you sean caroll for all these things. i am a physics student from India completed my masters this year.i am enjoying your videos and also share your videos among my colleagues. I have one request for you sean Carroll. If you can upload some lecture videos at the basic level of physics I mean starting from highschool to undergraduation level physics,it would be of Great help.it will help a wide range of students.in our locality the biggest problem is undergraduation education. you are great person in physics and surely a lot of college students Will be motivated by your lectures...

Thank you! The clarity of your explanations is just superhuman!

27:45: _Think about that, you totally understand that._ Oh man, if you knew...

that's a wonderful way of introducing vector bundles and parallel transport to the laymen I really benefited from your series thanks a lot dr caroll keep up the great work

Thank you Sean, you are an excellent professor. It's impressive how well you are able to understand what we might miss, so you provide multiple analogous explanations. Thank you so much for reaching out and teaching so accessibly to us mortals.

It would make me so so happy if there ever was released a lecture on gravity as a gauge theory :D

Have been on a long quest to better understand quantum mechanics and never found a clear explanation of how the four fundamental forces arise. This really helped to connect the dots. Can’t wait to understand how gravity relates to a gauge symmetry in Hilbert space. Not a symmetry in space but of space? It’s mind bending... More please!

Thanks for doing this and especially for these last few videos, Sean. Gauge theory is really hard to get into as an outsider, since every time you ask a question you seem to get an answer that gives you three new ones to ask. This has been a blessing, and something that has been missing on RU-vid for a while. Thanks again. 👍

Finally, I see the photon!

My favourite episode yet, thanks Professor!

16:53 "Photon field is a connection field" I wish they told me about that in high school... :-/ My jaw is on the floor, Professor Carroll.

The underlying simple and beautiful ideas were understood, Sean! Thank you! Please, keep them coming! Also some beloved references of yours about these ideas would be helpful!

I'm at my third view of this video, as I am for most of this briliant series

It is delightfull that there are a hundred thousand people who have watched a video about Gauge Theory.

32 mins in.. should go to bed as I have work tomorrow. I really have to commend Sean Carroll here for breaking down this subject in the simplest most terms without losing any of the knowledge or high level math.

Yes!! I've been waiting for this one.

Best explanation of gauge ever!

You are an excellent communicator. Thank you for sharing your knowledge.

At 27.45 Dr. Carroll says "You understand that sentence perfectly well . . . . . . . Progress is being made." Yes indeed. And I watch every episode twice (at least). But my brain still feels like it has been roasted, toasted, grilled and parallel transported in the neuron field. But seriously, these are really great lectures and I have learnt a lot. I am just worried that there's going to be an EXAM at the end. Is there going to be an exam Prof. Carroll ? Or just a quick test perhaps ? Please give us plenty of warning. Thanks again.

I discovered these videos a couple of week ago and I'm now all caught up. What a trip.

This so good. Pure gold. Thank you.

Yes! I love this series sean thanks for putting these out

That lecture felt like 5 minutes. Do I have another 5 minutes to watch it again? Yes I do.

I've promised to myself to go bed early but i can t stop to watch

Thank you very much! This is soo good explained sir Sean Carroll.

This was super helpful, thanks very much Sean!

I am 64 and during the closer of everything I was spending more time on cosmology and I came across a video on the formation of the elements. One thing led to another and next thing I know I am studying the standard model and particle physics. I find it is much more fun to study now that I am retired. Kevin from sunny Mexico.

Thank you so much for this lecture. It really helped me to understand better this topic!

50:00 Could you elaborate a bit more what a static electric or magnetic field looks like in terms of photons? Is there an infinite number filling space? Are they moving? If an electron passes by and is deflected does it interact with a stream of photons? How is the momentum carried?

Thanks for the expository lectures, Dr. Carroll. Please make another video on renormalization.

Thank you for this. I really appreciate you making this video.

This is what youtube was made for. Giving guidance for how all the puzzle-pieces fit together, to be used to direct audodidactic studies.

Thank you Sean, I experience a strange combination of seeing the explained, and getting lost in my fantasy. My maths desperately needs my attention :)

I am a pharmacy student . But still I want to learn about physics and specially QFT ., thanks to Prof. Sean carroll. I am watching your videos from India . Thanks for giving us lectures totally free !!

Wow, I learned a lot from this video. Thank you so much! 👍

Incredible. Bravo. Thank you.

Outstanding material!!!

Hey Sean, awesome video as always! I have a question that hopefully you can cover in the Q&A segment. You said something along the lines of "unless nature forbids it, it will happen" to talk about particles having mass. That unless there is a symmetry that takes away that mass (ie. there being no operation that gives you a mass term in the Lagrangian that satisfies the symmetry) then the particle will have mass. So my question is about neutrinos. It's an open problem as to why the neutrinos have mass, as they do not in the conventional Standard Model formalism. So, what is the symmetry that we give the neutrino field that takes away its mass that it doesn't actually have in the real world? Or is a symmetry spontaneously broken and that's why we think neutrinos have mass?

That is awesome ! But I need to watch again !

Worth the price of admission. Thanks.

What a good video. Congrats

So thrilled to find out why the strong nuclear force works. Now to find out about the weak nuclear force. Thank you!

reeeeeally love this series

Great talk, thank You!!

Saw David Gross say same thing in the video I was watching before this on the Yang-Mills theory millennium prize problem, no energy gap with QED photons "which is to say" in Sean Carroll speak that energy of photons can be as low as you want in QED. Great stuff, this is MUCH more interesting than the Yang-Mills millennium prize problem ... Hmm, what would life be like if I was half as smart as this guy ...?

Thank you Professor!

السلام عليكم ....hello شكرا على مجهوداتك.....thank you for your efforts ..... محاضرة ممتعة....شكرا.

Awesome video!

This is the one I had been waiting for. Some high level brushes were filled, but there's just too much missing in between them for my level of curiosity. Wonder if I'll ever have the patience to fill them. Just better QED would already be amazing to start with since it's the only useful one :-)

Thank you Sean for your excellent lessons! Could you please tell us which blackboard app are you using (so effectively) ? Roberto

thanks for elucidating a pretty vague topic

My god, such a different way to look on nature. So few physicists are actually getting to understand field theory let alone gauge symmetries. This way of looking shatters all naturally ingrained preconceptions of hard balls flying in static space

I think "gauge" of the railroads refers to the separation of the two tracks -- the rails -- not to distance, say, between two stations, or etc. Gauge, in that sense, is and was important because certain railroads had different rail-car and engine (locomotive) standards from other railroads, with DIFFERENT widths between the left- and right-side wheels. So, only cars and engines of the same gauge as the tracks could run on a particular railroad system (else, the steel rails could not support the wheels). A similar concept can be seen in automobiles, where I think this distance is called "the 'wheel-base' ", and, as it happens, cars or trucks with a pretty wide wheel-base are quite stable and hard to tip over on sharp turns, whereas vehicles of narrower gauge -- narrower wheel-base, I mean! -- could flip more easily. Cars don't need rails, though, thankfully. We're free to go even "Off-road". All best, and thanks for your teaching.

That quark soup tasted a bit strange. Had to lie down, but luckily didn't throw up.

I never understood this but I try again , to get my head round it

Cool. Lots of info. Thx

I meant to add, "Gauge" is important in MODEL railroading too ("Model trains"). Perhaps everybody knows about the different standards of gauge, there: there is "HO" (small), and others, like the Lionel Trains standard, where these gauges refer to the distance between rails, and hence also to the sizes and weights of the model train cars and the layouts of track that hobbyists build. It's been a long time since I looked at this, though, but the size differences are very marked between the different gauge standards.

Very good explanation

wow, this is amazing. Since Weinstein, I could never really understand gauge theory because the explanations were so abstract. I still don't quite understand it but the explanation is clearer ^^.

"The hope is... that the underlying details remain clear" : hope realised!

Thanks for making these, Mr Carroll. I've been wanting a deeper dive on these concepts for a long time. This video, I'm going to have to take a few passes at. I think what I'm lacking is exactly what you mean when you say that the connection field determines how the (non-spatial) axes of a field transform between points. I think I need to see an example walked through. Is it like the metric tensor in GR? Where each spatial axis sort of has a continuous transform, resulting in curvature? Are, e.g. the RGB axes curved continuously as you translate through space and time? Are these connection fields also oscillators, i.e. each point x in field F has dF/dt = Ad2F/dx2 - BdE/dF? Or simply, is each point's value of F pulled on by the neighboring points and its own energy curve? When you say fields are coupled, do those fields pull on each other the same way? When you say the positron field is psi_e*, does that imply that positrons are just phase-inverted waves in the electron field? How does that square with this "four component" electron I've heard about? If they are in the same component of the same field, how does the photon field know what charge they are?

I think it's important to note that I'm not necessarily picking up everything of the main message, but all your side notes are definitely causing a bout of curiosity. What you aren't talking about makes me want to do more research.

Of all the videos in this series this is the hardest one for me to get. not like I totally get everything in all the others, bit this one makes my brain hurt the most trying to understand.... I'll keep watching it again and again until I can make better sense of it.

I have been imagining photons as being let off of an electron whenever something the electron can interact with gets near. I went with that because it blends together most of the popsci interpretations of physics that I’ve seen. When you described photons as lines of force coming off of an electron, how literal were you being? Are there always photon streams, but we only see individual photons when we look?

Thank you!

I love your books Sean (multiverse one is my fave), and I'm digging the Lockdown locks too.

A truly splendid series of lectures for the mathematically challenged. At a purely philosophical level, I have three questions: 1. We read that all spacial dimensions, plus the time dimension, i.e., spacetime began at the instant of the Big Bang. Whereas one could possibly comprehend space expanding as the energy within it expanded, there is a paradox with time. If there is no time, nothing can happen, so the Big Bang could not have occurred. In other words, for the Big Bang to have occurred, there must have been "pre-time". 2. The laws of Thermodynamics, especially the Conservation of Energy, were broken at the Big Bang unless one assumes a parallel universe comprising the "anti" of everything that we know in this one. Alas, as I understand it, anti-particles do not have the stability of the ones that we know and love. 3. On the question of entanglement, experiments based on Bell's Theorem have apparently disproved the EPR notion of hidden variables. Actually, hidden variables are not necessary. Each particle, the field concentrated at a particular point in spacetime, has an in-built set of properties presumably described by its wavefunction or set of wavefunctions, inclusive of momentum, mass, spin, etc., dependent on what is applicable. If two particles are created such that they are entangled, then the laws of exclusion and conservation apply. So if a photon or an electron flies off into the big unknown and its entangled partner is instantiated, the opposite of that instantiation is what has already been predetermined for the errant and adventurous particle. We know that the wavefunction of an entangled particle collapses if observed because observation involves probing by either a weak or a strong influencing method. If strong, the wavefunction(s) are reset. If weak, seemingly the part of the wavefunction survives, as recent experiments have shown. Anyway, the point is that we don't have to assume a "universal" wavefunction for entangled particles that extends within and without the observable universe. If we do, then we have to accept that a universal wavefunction was created at the instant of the Big Bang, and if we understood it, we could predict the evolution of the universe and its ultimate demise. Does this seem reasonable? A bit on the iffy side, surely. Full marks for your lectures, Sean, they have been a revelation.

Hi Sean, very interesting talk - and channel overall! As a lay person with a great interest in these topics (but maths-illiterate unfortunately), you have helped me immensely in grasping the fundamentals behind these very complex concepts. Slightly unrelated however, but may I ask what software you are using as your whiteboard and broadcasting solution on these talks? Kind Regards

I'd really like to know how it's determined that the graviton has a spin of 2.

Very nice! Thank you alot :)

I just knew that there was a big payoff coming in this one. I had to watch it several times myself. Thank you for explaining all these wonderful concepts so that we can get a glimpse of what’s going on. Thank you. I love and appreciate what you are doing.

Poincaré: exact accent and good pronunciation, très bien! ⭐️ Just as you correctly spelled and pronounced De Broglie (yes it is [debroy], even in French it’s counterintuitive).

Pretty rad to see Yang-Billz in this vid

So, just for some clarification, where exactly do the W, Z and Higgs bosons come from in terms of directions of the full Higgs field?

Me: It's 1am, a few more lines of code and then bed Sean Carroll:

Gauge theory is the "biggest head-melter in physics", for me at least.

For anyone looking for a deeper dive pitched at the same level, Jakob Schwichtenberg has a great book all about gauge symmetry called 'Physics from Finance'. It's available as an ebook as well. It's built around a 'currency exchange rate' metaphor, which I actually don't fiind especially illuminating, but nevertheless it really helps get your head around this stuff.