#science #physics #ideas The Biggest Ideas in the Universe | 15. Gauge Theory

#science #physics #ideas The Biggest Ideas in the Universe | 15. Gauge Theory 137,605 viewsJun 30, 2020 Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #15, "Gauge Theory." Here is where the last couple of ideas come together, and we see how geometry and symmetry underlie the fundamental forces of nature as they are currently understood. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image: http://www.desktopwallpaperhd.net/blu... #science #physics #ideas #universe #learning #cosmology #philosophy #math #gaugetheory #symmetry 285 Comments rongmaw lin Add a comment... Shortcut Shortcut 1 year ago Sean, you have no idea how much i appreciate you doing this, and putting all this effort and work out. Thank you so much. 44 MakeMeToasty MakeMeToasty 1 year ago 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 YouTube. 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 131 Quaere Verum Quaere Verum 1 year ago 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. 57 Jonathan Saraco Jonathan Saraco 1 year ago (edited) 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? 8 Kobev3li Kobev3li 1 year ago 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. 20 Pavlos Papageorgiou Pavlos Papageorgiou 1 year ago 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? 6 Nathaniel Gregg Nathaniel Gregg 1 year ago (edited) 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? 2 Mikkel Højbak Mikkel Højbak 1 year ago 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 YouTube for a while. Thanks again. 👍 1 R C R C 1 year ago 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. 2 Paul C. Paul C. 1 year ago 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. 20 Denis Nichita Denis Nichita 1 year ago 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! 2 Church Of Thought Church Of Thought 10 months ago 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. 1 MrIvansilni MrIvansilni 1 year ago This has been my favorite episode where many previous ideas all came together. 2 Milos Marinkovic Milos Marinkovic 1 year ago 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. :) 3 MMBPNG MMBPNG 1 year ago 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 2 Stephen Pilling Stephen Pilling 1 year ago Thanks so much for these videos. There are many of us who really want to know about our reality and how it works. I find your videos by far the best. Although these recent ones have been quite hard and I will have to go through them several times. I am wishing I paid more attention now during my calculus classes at school. 1 reda abakhti reda abakhti 1 year ago 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 Too Crash Too Crash 1 year ago Thank you Sean, I experience a strange combination of seeing the explained, and getting lost in my fantasy. My maths desperately needs my attention :) 1 sachiraj mishra sachiraj mishra 1 year ago (edited) 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... 6 SkateKraft SkateKraft 1 year ago 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. Mirynna Fronea Mirynna Fronea 1 year ago Thank you so much for this lecture. It really helped me to understand better this topic! stat a87c stat a87c 1 year ago Yes! I love this series sean thanks for putting these out 2 Ciro Santilli 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、巴拿马文件 邓家贵 Ciro Santilli 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、巴拿马文件 邓家贵 1 year ago (edited) 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 :-) 1 Adam Kadmon Adam Kadmon 8 months ago I love your books Sean (multiverse one is my fave), and I'm digging the Lockdown locks too. michael blacktree michael blacktree 1 year ago Wow, I learned a lot from this video. Thank you so much! 👍 1 Bob Bobbity Bob Bobbity 1 year ago I must thank you again for such a wonderful series! 1 Steve Hosier Steve Hosier 1 year ago (edited) Sean - thanks for doing these wonderful videos. I would like to question your comments (starting about :51) about how a charged particle (electron) can emit photons with no energy. Photons do have energy (E=hf) and momentum (p=hf/c). So emitting photons of any frequency would still violate energy and momentum conservation laws. This has bothered me since I first started looking closely at the Standard Model. The "virtual" photons that theory requires do not seem to be photons at all but something completely different. If they are completely different why are they considered photons? Elwood Downey Elwood Downey 1 year ago (edited) 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. Dale Housden Dale Housden 1 year ago My favourite episode yet, thanks Professor! 3 Erik Dahlgren Erik Dahlgren 1 year ago Sean is so good to tie all the things togheter, now we know why its important to know the stuff. 1 Lajos Baranyi Lajos Baranyi 1 year ago Thank you! The clarity of your explanations is just superhuman! roberto zompi roberto zompi 1 year ago Thank you Sean for your excellent lessons! Could you please tell us which blackboard app are you using (so effectively) ? Roberto Bartosz Piorunski Bartosz Piorunski 1 year ago This series is fantastic! Thank you Mr Sean Axis Axis 1 year ago Hi Sean, thanks a lot for these videos! It's fascinating to see how certain laws of physics and facts about the universe emerge from these symmetries, but my question is, is there a fundamental reason why these specific symmetries are used, as opposed to some other symmetries? Is it just an empirical observation, or is there a deeper mathematical reason why they have to be SU(3)xSU(2)xU(1)? Why not SU(5)xU(2)xSU(8)x(U9), etc? 1 Lio Mendonça Lio Mendonça 1 year ago 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 ^^. Cloud Room Beacon Place Cloud Room Beacon Place 1 year ago 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". Guglielmo Ferranti Guglielmo Ferranti 11 months ago This video strikes the PERFECT balance between fluency and accuracy. Amazing as an appetiser/reminder for preparing a quantum field theory exam. Haydar Masud Haydar Masud 1 year ago Thanks for the expository lectures, Dr. Carroll. Please make another video on renormalization. 1 Gilbert ENGLER Gilbert ENGLER 1 year ago Thank you very much! This is soo good explained sir Sean Carroll. Elli Heyes Elli Heyes 8 months ago This was super helpful, thanks very much Sean! Nathan Gonzalez Nathan Gonzalez 1 year ago 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! BallLightningbyVuyk BallLightningbyVuyk 1 year ago Sean Carroll, thank you for this. However, if you are so certain that Su(1,2 and 3) is the base for the universe, then you have the tools in your hand to know how it works. Is there no more? 2 Robert Zanatta Robert Zanatta 1 year ago You are an excellent communicator. Thank you for sharing your knowledge. baldrbraa baldrbraa 1 year ago That lecture felt like 5 minutes. Do I have another 5 minutes to watch it again? Yes I do. 2 theosib theosib 1 year ago I'd really like to know how it's determined that the graviton has a spin of 2. 23 Mike Ross Mike Ross 1 year ago Brilliant talks. They inspire me to follow up and read the books. 2 Jay Wheeler Jay Wheeler 11 months ago Hi Dr. Carroll, Love the show! I have a different set of equations that may help explain this. I would love to hear your opinion as to their feasibility. Kind Regards Sir! Magnetism Squared = Energy; Energy Squared = Mass; Mass Squared = Magnetism; of New Magnitude #EMBUnification Fractal Universe Baby E^2=M M^2=B B^2=E' David Hand David Hand 1 year ago 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? 3 Jack CF Jack CF 1 year ago I discovered these videos a couple of week ago and I'm now all caught up. What a trip. 1 Joel Curtis Joel Curtis 1 year ago 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. Igor Shvab Igor Shvab 1 year ago 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 1 ProfessorBeautiful ProfessorBeautiful 1 year ago This is the payoff for me. Beginning to get an inkling. Now, how does electroweak unification come about? How does that relate to symmetries? 2 Loz Shamler Loz Shamler 1 year ago Hi Prof Carroll, it's a toss up between you and Prof NdGT as to who's my favorite physicist ;-) Could you give us some real world examples where you used all this maths and physics to make, predict or otherwise do something, please. Great lectures btw (a bit of buttering up there!) Cheers. 1 Rohan Jagdale Rohan Jagdale 8 months ago 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 !! Boris Petrov Boris Petrov 1 year ago (edited) Wow - for me one more attempt to understand gauge concept. A Q: Is it mot that EM and Weak are actually same/one "force"? Or I missed you saying that in this lecture... Or you are saving this for "Zucker kommt zu letzt". Many thanks for all your efforts !! PS1: Will you ever discuss Hopf fibration - what is it and why some claim that it is "all important"? PS2: Also -- Higgs field/mass is function of temperature - at high temperatures - no mass to any particles 1 Michal Plichta Michal Plichta 1 year ago I always want to know how proton and neutron looks together, I know it there is no shells around 3 quarks, but I wonder if since 'inside' of proton are 3 quarks on average, how we can distinglish proton from neutron (firm quarks perspective) or in heavy elements like Pb there are just quarks not protons and neutron... it is hard to me to ask question.... Imager Imager 1 year ago Best explanation of gauge ever! 4 Dr.Beanut Dr.Beanut 2 months ago I don't know what it is about you Sean, but gosh darn you incite so much excitement and joy in learning this stuff! imperatoreTomas imperatoreTomas 1 year ago Thank you for this. I really appreciate you making this video. Kevin McCarthy Kevin McCarthy 1 year ago (edited) 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. U A U A 1 year ago (edited) 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. Alex Tritt Alex Tritt 1 year ago 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? 1 Brandon Lewis Brandon Lewis 1 year ago (edited) Could you give us a concrete example how a gauge theory is used to answer problems in physics? If not the whole thing, show us how you "set up" the problem in terms of the gauge theory, and then perhaps comment on what mathematical techniques are used to then obtain the answer. Jeff Bass Jeff Bass 1 year ago My head hurts! It's safe to say I am very lost, but I'll attempt some questions. First, is it simply through trial and error that we know the electron field has U(1) symmetry (for example) or is there a more fundamental way to discover that this is the correct symmetry? Also, is it reasonable to think of the photon field as somehow emergent from the electron field, given that this symmetry exists? How does combining electromagnetism and the weak force fit into this symmetry picture? Expression of Freedom Expression of Freedom 1 year ago 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. Laurent Cohen Laurent Cohen 1 year ago Question: I understand that symmetries go a long way in specifying fields. What are the other independently required ingredients to reach a full specification ? Format (scalar, complex, tensor....)? Some constants of nature? What else? In other words, what are the minimal ingredients (in some current theory) for fully specifying what exists? Thank you very much for your teaching. Foo Bar Foo Bar 1 year ago (edited) In the end of the video it is noted that protons and neutrons are not a proton and neutron "separately" when put together, but rather a "six quark bound state." Does this somehow explain the fact that lone neutrons quickly decay outside a normal nucleus? (I'm not certain if I even want to think of what's going on inside a neutron star...) 1 Lucy Calder Lucy Calder 1 year ago the gauge in a rail track is the space between the rails, so it does matter a lot how big the gauge is! 1 Graham Lawton Graham Lawton 6 months ago 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)! 2 Jimmy PK Jimmy PK 9 months ago Perhaps the greatest explainer since Richard Feynman! Fer Shred Fer Shred 1 year ago I keep watching while understanding nothing. I lost track a few videos ago. This would be much easier to understand if most of quantum theory wasn't relying that much on "we don't know why but hey math predicts" Feeling Creative Feeling Creative 1 year ago 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. 5 John P John P 1 year ago Since this theory seems to apply to gravity, is it the leading candidate to be the "theory of everything"? If not, what's the gap? Also, was it used to predict the Higgs boson? nosirrbro nosirrbro 1 year ago This certainly was a payoff episode, a whole lot from this series and elsewhere just clicked for me. Plus, you hear about gauge theory all the time, but its never explained for fear of being 'too complicated'. Well, this series just keeps getting better and better! Vincent Button Vincent Button 1 year ago So thrilled to find out why the strong nuclear force works. Now to find out about the weak nuclear force. Thank you! Jim Rishebarger Jim Rishebarger 1 year ago I can’t believe how lucky I am to be living at this time! Your teachings are exactly what I hoped that I would learn in retirement. These lessons are invaluable to me. Do you have a favorite charity to which we can donate to show our appreciation for all of the time and effort you have put in for us? It could be the Make Sean Smile fund. It would be the least that the tens of thousands of happy followers could do to show our appreciation. A1dancarter A1dancarter 1 year ago If gravity is a non abelian gauge theory then how does it fall in to the coulomb phase? Is that a low energy approximation? Is there any idea or theory that predicts which phase gravity falls under in the high energy regime? Thank you kindly. bruinflight bruinflight 1 year ago (edited) Preemeninent physicist: "Here's 'space'. Ah, we're getting good at drawing 'space' now." 45 Ga vin Ga vin 3 weeks ago Thx for the video! But I would like to know, why is the Lagrangian invariant under gauge transformations? In other words, why is leaving the Lagrangian unchanged a defining characteristic of local symmetries? Is it because all the observable quantities must be invariant? I am a G12 student and I am about to make a presentation on this topic to my class. Apologies if the question sounds stupid. Sarojini Chelliah Sarojini Chelliah 1 year ago 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. Jay Wheeler Jay Wheeler 11 months ago The Photon is only Massless when the EMB wave is in BE phase. In the EM or MB phase, it will have mass. This explains why high energy particles consume less volume. The magnetic shell collapses all or some of the contained E into M at high enough E. Or sumthin Herpe Derpe Herpe Derpe 8 months ago (edited) This is what youtube was made for. Giving guidance for how all the puzzle-pieces fit together, to be used to direct audodidactic studies. Dead Talk Live Dead Talk Live 1 year ago Nice video ♥! As a fellow YouTuber, I am always looking for new ideas! Nice Job! 1 Michael Osei Michael Osei 1 year ago Nice video but you made a mistake (3:13) The idea of quarks being composed of 3 colors wasn't proposed by Murray Gell-Mann but it was proposed by O.W. Greenberg. He proposed the idea of quarks coming in colors in order to help solve the dilemma that the quarks seem to violate the Exclusion principle, particles like delta and omega have identical quarks. wayne Last wayne Last 7 months ago 49:36 what would it take to observe gravitons? Some kind of gravitational interference patterns? What size would this be? Something else? John Baillot John Baillot 1 year ago 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. Nikaluss Nikaluss 1 year ago I’m totally with him on science issues. But I’ve seen, in other videos, Sean’s absolute intolerance to ideas like faith and religion. A belief in a creator has no place in this dude’s mind. I’m NOT very religious, some might call me agnostic. However the fact of the matter is I DONT KNOW, and neither does Sean. You’ll never catch me trying to say, with absolute resolve, that there either is or isn’t a god. One thing about the unknown is that there may be some science yet undiscovered in our universe, a science that has a place for god. If we as people continue down this path of hardline atheist or hardline theist with no overlap, we are going to take much longer than necessary to unlock the theory of everything. There’s something to the god idea, I can’t understand or explain it but there is something yet undiscovered regarding god which could lead us to unlocking the knowledge necessary to begin exploring other star systems within a human life span. Being as hardline atheistic as Sean removes potentially crucial information and discoveries from the table all together. krzysztof mekwinski krzysztof mekwinski 1 year ago Beautiful thing!! How those symetries explain all forces. However it is hard to understand sometime. I wanted to apply thing like tenperature to quantum mechanics. Does anyone understand how this worl and can share some link. Heat is kinetic energy of massive particles , so is kinetic energy of electron just producing more photons ? And also all particles are different and have different connection fields. So how heat is increasing kinetic energy of all fields. Sorry of this is not great question, but I would love to understand heat from molecular level to wave functions to particles to forces. Shikhar Amar Shikhar Amar 1 year ago Thank you Professor! 2 pimnelson pimnelson 10 months ago (edited) I am still new to the idea of particles carrying forces. Particles are wavelike, but also point like/discrete, so how can a force, something in my mind continuous be mediated by something discrete? DaveDashFTW DaveDashFTW 1 year ago Is this breaking of symmetry what caused the big bang? A large potential that spontaneously breaks symmetry, which then has massive energy states - pushing everything apart (the opposite of constraint), before settling down at the bottom of the potential well and constraints start to happen? Expression of Freedom Expression of Freedom 1 year ago I'm certainly going to need to watch more from both you and Eric weinstein. Pardon my easy distractions. Also your a phenomenal teacher. Fuck if I know how you make me absorb any of this. Professr Frank Professr Frank 1 year ago 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). 1 Gilbert H Gilbert H 2 months ago Is there anything that stops gravity pre-Big Bang from being O(4) or SO(4) with 4 dimensions each of spacetime, where the Big Bang is the symmetry breaking event that split spacetime into 3 space and 1 time dimensions? ShamanicKnight ShamanicKnight 1 year ago Interesting article in this week's New Scientist: What does gravity weigh? The surprise answer that reshapes reality Claudia de Rham Rust in Peace Rust in Peace 1 year ago Are there hints that a ToE would be required to have a Gauge nature to it? 1 RD2564 RD2564 5 months ago (edited) 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 ...? Brian Cannard Brian Cannard 1 year ago 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. 3 pizzacrusher pizzacrusher 1 year ago 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. bmwm3cs bmwm3cs 10 months ago What are the physical excitations of the SO(3,1) gauge field? America Lost America Lost 1 year ago I love math too... And in some alternate reality I am also able to do it as well : ) Valdagast Valdagast 1 year ago I think the real consideration is maximization of the number of Nobel Prizes, rather than the gray hairs of the grad students. But there's a correlation between the two. 1 dawangai dawangai 1 year ago Gauge theory is the "biggest head-melter in physics", for me at least. 2 Theodor Samoladas Theodor Samoladas 1 year ago So, is it correct to say that forces exist due to the curvature of the fields? John Długosz John Długosz 1 year ago Why does the mass of the W affect the range of the force in the manner you describe, when virtual particles are not bound by the normal mass relationships? It does not have to come up with the energy to manifest a (normal) particle. Cortez Cabret Cortez Cabret 11 months ago Incredible. Bravo. Thank you. Brandon Lewis Brandon Lewis 1 year ago (edited) Where do particles "live" in gauge theory? You've stated that they're "excitations" of some underlying field. How is that represented mathematically? I feel like I'm missing something. It feels like in moving to gauge theory, both particles and space disappear from the math. Where did they go? Craig Simpson Craig Simpson 1 year ago "The hope is... that the underlying details remain clear" : hope realised! 2 Michael Fox Michael Fox 1 year ago At 42:00 and 54:42, a photon is shown turning into an electron and an anti-electron. Isn't this forbidden by conservation of linear momentum? NoWhereMan NoWhereMan 1 year ago (edited) Dr. Carroll how exactly do we know SU3 symmetry explains the strong force? What kind of experimental evidence is there as 'proof'? Hartmut Pfarr Hartmut Pfarr 1 year ago Great talk, thank You!! wayne Last wayne Last 7 months ago How can you say gravitons must exist according to the gauge theory when you have not started by describing gravity as a quantum field? J.F. G.H. J.F. G.H. 1 year ago Sean, when you say that the W,Z force is ~exp(-r/\lambda), that is imprecise. If you assume the force is Yukawa-like, the potential is V=g²e^{-r/\lambda}/r, so F=-\partial_r V= g²e^{-r/\lambda}/r\lambda+g²e^{-r/\lambda}/r^2=g²e^{-r/\lambda}[(r/\lambda)+1]/r^2, so Yukawa-like forces are really not exponential, but exponential times a Newtonian-like contribution plus a 1/r force term. ironic legacy ironic legacy 1 year ago Why is it useful to have a transformation that’s arbitrary? Since I have no idea how it affects other things, it seems like it was something that was added and then a way to fix it using connection fields was put in. Is this what happened and the fact that the connection fields corresponded to “force” particle fields gave it some significance? Chirality452 Chirality452 1 year ago If SU(2) x U(1) is a unified electro-weak theory, then why isn't SU(3) x SU(2) x U(1) a grand unified theory of color-EM-Weak forces? Or, what do we need to go to SU(5), SO(10), etc.? 2 Vlad Petric Vlad Petric 1 month ago Is string theory essentially hypothesizing symmetries that aren't really there? pimnelson pimnelson 10 months ago It is delightfull that there are a hundred thousand people who have watched a video about Gauge Theory. chris homer chris homer 1 year ago I never understood this but I try again , to get my head round it 4 Jeff Bass Jeff Bass 1 year ago Yes!! I've been waiting for this one. 6 stridedeck stridedeck 1 year ago Are not the three phases (Coulomb, confined, and Higgs) from the same cause, but at different scale? Also, the photon does not exist, but is the pathway. Is it possible that the reason the strong force is strong, as two opposing directions are almost touching and trying to separate these two opposing directions takes a huge amount of energy? Is it possible that with high energy is when the two opposing directions are farther apart and thus has a weak coupling? 1 Moreno Sanguanini Moreno Sanguanini 1 year ago Q QCD describes a loop of destruction and construction in interaction with Gluons. Is QCD fully understood and are models to look at? Joe Deglman Joe Deglman 1 year ago (edited) The dipole moments of neutrons and protons debunk quarks. You lost me at 8 dimensions, complete sci-fi. Pvte Pyle Pvte Pyle 1 year ago Very nice! Thank you alot :) James Stewart James Stewart 1 year ago (edited) So QCD masses (lagrangian) are normalized? Forgive me if my physchem fondness for complex vector matrices have led me astray + QCD symmetry not conserved in weak interaction? #science #physics #ideas The Biggest Ideas in the Universe | Q&A 15 - Gauge Theory 46,097 viewsJul 5, 2020 809 DISLIKE SHARE DOWNLOAD CLIP SAVE Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #15, "Gauge Theory." We dig a bit more deeply into how spontaneous symmetry breaking and the Higgs mechanism work in the Standard Model, especially to give masses to various particles. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image: http://www.desktopwallpaperhd.net/blu... #science #physics #ideas #universe #learning #cosmology #philosophy #math #gaugetheory #symmetry 56 Comments rongmaw lin Add a comment... Sean Carroll Pinned by Sean Carroll Sean Carroll 1 year ago Arrgh, another mistake, this time trying to correct a previous mistake! Around the 44 minute mark I say that the force from a Yukawa potential is e^(-mr)/r because it's the derivative of the potential. That's obviously wrong, since the derivative of an exponential is still an exponential. The correct statement is that the Yukawa potential is itself e^(-mr)/r. You can get that from the equation of motion in spherical coordinates (look up "spherical Laplacian" for details). 21 qclod qclod 1 year ago You're a true role model. Thank you for this series, Dr. Carroll. I hope you know how heavily your work is appreciated. 15 Mickolas21928 Mickolas21928 1 year ago I'm going to rewatch all of these videos again until they sink in. As an amateur, thank you for making these. 11 Isaac Anderson Isaac Anderson 1 year ago Hey Sean , been enjoying this series planning on buying some of your books. 8 apaeterable apaeterable 1 year ago Thanks for doing these videos! I really like that they're aimed far enough over my head that I have to stretch and strain somewhat to get it, but not so far above that I can't get there. Seeing the Lagrangian again I was wondering: What was the reason that all the energy (density) contributions are subtracted from the kinetic energy? If it has been answered before (and I suspect it might have been), maybe some of my fellow viewers remember where? Anyway, thanks again, looking forward to the next videos already. 3 Color My Math Color My Math 1 year ago (edited) As I listen, I am so grateful for your conversational way of explaining. So amazed at the variety of idioms, colloquialisms, and manner. Thanks CuteBabySeal CuteBabySeal 2 days ago I am rewatching these as I prep to embark on a deeper study of physics in my free time. Thanks again Sean for putting these out there. I love the level at which these videos are aimed. If someone who hasn't done any physics before was going to ask me where to start, I'd say "First watch Feynman's lectures. Then watch Sean Carroll's Biggest Ideas videos. Then grab some books." Mark Deslauriers Mark Deslauriers 1 year ago Dr. Carroll. I wanted to thank you for these. I was a chemistry major in college but always had a high interest in physics, and now, many years later, I find physics to be an amateur passion of mine. I love latching on to a topic and then searching arvix for all of the papers that I can find. Between the math, chemistry and physics that I've learned I can follow along with most of them pretty well, but I always find myself glossing over the bits where they describe symmetry and topology as I really never learned the details of those. I have a loose idea of how they contribute to the SM but not the details of how it works. You've just changed that for me. I now have a much clearer picture of how all of this comes together so that is a breakthrough for me that I wanted to thank you for. What's more, I now have a whole bunch of concepts that I can now selectively research more deeply, and as I live in central Vermont and winter is coming I want to thank you for that in particular. I know how I'll be spending a bunch of stormy evenings and weekends that are surely coming my way. simplelife1021 simplelife1021 1 year ago Leonard Susskind has a very accessible book on relativistic classical field theory. No spinors or su(2) doublets but it does go into the gauge invariance of the electromagnetic Lagrangian 2 Paul C. Paul C. 1 year ago (edited) Thanks again Prof. Carroll. It's late pm on Sunday here (Wales), so I will watch half now and the rest in the morning. It's just much too math heavy for me, all in one go, esp late at night !! Kobev3li Kobev3li 1 year ago Even the Q&A video on this topic is amazing !!!!!!! Thank you again Dr. Carroll Professr Frank Professr Frank 1 year ago (edited) Suggestion for a Mindscape interview about superstring theory: Dr Ed. Copeland from Nottingham University, who has talked about in on the 60 Symbols channel. 54:32, 56:11: The street corner we’ve been spending time on looks a lot like Times Square. Where α1 is 42nd Street, α2 is Broadway and α3 is 7th Avenue. A high energy convergence! 😎 I never understood derivatives well (that’s why I went into geography), but “infinitely” more now. Thank you for being there, Dr Sean! 🌟 Jai Bellare Jai Bellare 1 year ago I love it when Sean uploads 5 Rust in Peace Rust in Peace 1 year ago Can you tell us your thoughts on the non Background Independence of M Theory, and if you think it looks like we will ever get a Background Independent version? 3 Airton Rampim Airton Rampim 1 year ago 27:00 Actually, the value of the potential at the brim is -μ⁴/(16λ). The potential is zero at phi1 = phi2 = 0. MrFedX MrFedX 5 months ago Mindblowing and really, really fascinating video! C R C R 1 year ago This video is absolutely amazing 2 Coochicoo Coochicoo 1 year ago Anyone else use these videos almost as ASMR to help them sleep? Sean has such a soothing voice. 4 Simon Sherwood Simon Sherwood 1 year ago (edited) QUESTION in case Sean Carroll is still reading. Sean, you say that U1 symmetry and the phase invariance of the wave function are different. I can see that. Quantum fields are very different beasts from wave functions. You go on to say in the Q&A that the U1 symmetry of quantum fields and the phase invariance of wave functions are different concepts. However you then say that there IS a link through the Dirac equation. If so, that is very helpful intuitively because it ties the phase invariance of fermion wave functions to the phase invariance of the Dirac Lagrangian. If nature requires this to be local, then that makes sense of the boson vector field's U1 gauge invariance. Is this right? And if it is, is there anywhere I can see how the math link through the Dirac equation works? I cannot find anything on the web. You mention the math is tricky but even so, it would be nice to see it. Thanks - Simon (PS I LOVE your stuff) Desi Desi 1 year ago Sean Carroll: can we jump to a parallel universe? A parallel version of ourself if we’d made a different decision?? The Memes of Destruction The Memes of Destruction 8 months ago 1:00:42 — The effects of gravity on Earth wouldn’t be enough to skew observations to this extent would they? Trevor Mugalu Trevor Mugalu 1 year ago Too bad the standard model isn't among the biggest ideas in the universe! 1 stridedeck stridedeck 1 year ago Now it makes sense! Maxwell's and QFT! 1 Henry J. Henry J. 1 year ago Yeah, well, you know, that’s just, like, your opinion, man. Seriously, these "Biggest Ideas" videos are really great. Thanks for doing them. 1 Rhonda Goodloe Rhonda Goodloe 1 year ago Great! Thanks! I2yantheGreat I2yantheGreat 1 year ago Good title and really cool blackboard app. I wonder what it's called Adam Genesis Adam Genesis 1 year ago SU(5)....thank you Sean! 3 Praetor2000 Praetor2000 1 year ago Unfortunately, the only LaGrange I know is a ZZ Top song and derivatives are what got AIG and Bear Stearns in trouble. Who the hell is Hilbert? Who can I blame for all the Greek letters? There's real numbers and...unreal numbers? They're all complex if you ask me. What's with everything getting squared all the time? I think my brain just spontaneously broke. Finally, how much Khan Academy do I need before this begins to make sense?! 1 Boris Petrov Boris Petrov 1 year ago (edited) Yellow and green colors look similar on my screen.... PS: Anyone has a recommendation on a good video that graphically explains each Maxwell explanation? Many thanks in advance. hgfuhgvg hgfuhgvg 1 year ago I see Sean Carroll video.. I like. 2 Paul C. Paul C. 1 year ago Dear Prof. Carroll & any maths-competent viewers, Sorry to sound a bit dim, or maybe I missed an important point earlier, but I have a question please, about the Riemann (Curvature) Tensor. Could someone please explain what the indices / exponents “lambda”, “meu” & “neu” actually mean or represent in the Riemann Tensor. I believe they are all a number from 1 through to n, but where do they come from / how are they arrived at ? How do they take on any particular value from 1 through n ? Do they represent the fields through which vectors are parallel transported ? I would be really grateful if someone could explain this, for the benefit of one of your more “mathematically challenged” viewers. With more words & less maths if possible. Thanks. Tony D'Arcy Tony D'Arcy 1 year ago I always thought Mexican hats had a wide brim. Silly me ! David Seed David Seed 1 year ago RAILWAY gauge is the width if the track. Not as you said Siri Landgren Siri Landgren 1 year ago Don't your dare tell me how much detail I want or need! 😤😘 1 Clifton100 x Clifton100 x 1 year ago Why am I watching this from start to finish? I"m not in school anymore. I could watch anything else. Math is not especially interesting, and I'm not particularly good at it. I'm a lunatic. 11 chhat votthoeun10 chhat votthoeun10 1 year ago Sean Carroll អរគុណច្រើនបងប្រុស🇰🇭❤️❤️🇰🇭😍😍បងប្អូនយើងកុំភ្លេចជួយគ្នាទៅវិញទៅមកណា🇰🇭❤️🇰🇭😍😍 1 Don Cavanagh Don Cavanagh 1 year ago Jeez after 5 mins I’m losing the will to go on 1 ILEGAL EAGLE IGLESIS ILEGAL EAGLE IGLESIS 1 year ago И еще э оно 2 засветили Scott Dorfler Scott Dorfler 1 year ago Has anyone ever told you your voice sounds a little like Alan Alda? You're way less whiney though. 🤣🤣🤣 1 Preetham Kumar Preetham Kumar 7 months ago 53:20 Attlanttizz Attlanttizz 1 year ago (edited) I'm not worthy. I'm also not smart enough to follow. I'll have to restart the series I think. 2 Jai Bellare Jai Bellare 1 year ago Yaaaaaaay 1 Mark Larocca Mark Larocca 1 year ago P EdP IV EdP IV 1 year ago Wth. Four thumbs down? Obviously Biden voters. Ron Ray Ron Ray 1 year ago