The Biggest Ideas in the Universe | 15. Gauge Theory
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- เผยแพร่เมื่อ 29 มิ.ย. 2020
- 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.
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#science #physics #ideas #universe #learning #cosmology #philosophy #math #gaugetheory #symmetry - วิทยาศาสตร์และเทคโนโลยี
*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!
Sean, you have no idea how much i appreciate you doing this, and putting all this effort and work out. Thank you so much.
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 TH-cam. 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
@pyropulse smartass
@pyropulse PBS Space Time has some episodes that get into things a bit, but not at this level. They are a good gateway for a mere enthusiast like me, and now this is perfect - it has been missing for a while.
Thanks Sean! 👍
The only thing I've seen online that's anything like this is Leonard Susskind's "continuing studies" lectures on Stanford's youtube channel. They're a gem, but for an amateur, this series has worked better for me, and also has the advantage of being made directly for youtube.
pyropulse . That’s literally what he just said you douche
pyropulse I was referencing headlines you see that make claims like “parallel universe confirmed” or “time travel possible within the next 20 years” when the actual study will barely mention these things as potential conclusions to be drawn but acknowledging that much more is to be learned before you can prove those claims to be true. Like any time a scientist is setting up to detect neutrinos every media outlet wants to talk about abstract theoretical implications of what is possible in quantum mechanics.
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.
agree 100%, i like the historic reason why its called gauge too
I have tried many versions of the gauge theory but never really understood it, finally Sean tells me 'don't worry,no one understands it'.
They aren't dots, they are "particles".
«Connect the dots», I see what you did there
88i8888⁸8kiií8iiiiiiiiii
This has been my favorite episode where many previous ideas all came together.
This video strikes the PERFECT balance between fluency and accuracy. Amazing as an appetiser/reminder for preparing a quantum field theory exam.
Preemeninent physicist: "Here's 'space'. Ah, we're getting good at drawing 'space' now."
Exactly - Who knew that Space had 3 sharp corners and 1 rounded corner !!
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".
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.
took me a few years but i can understand these lectures now which for me was a huge accomplishment
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.
Perhaps the greatest explainer since Richard Feynman!
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.
My conclusion is that Sean Carroll understands it.
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.
Dr10Jeeps Don't feel bad prof. I'm a nuclear engineer with a graduate degree in EE. I have studied partial differential equations and complex math, and I too am humbled and realize how much I have to learn about physics just like you. This material is certainly not intuitively obvious.
@@Cooldrums777 i was a nuke in the navy and thought when i was 19 that i understood this stuff, 23 years later, i am finally, kind of, understanding this lecture series
this is the beauty of these videos :)
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 TH-cam for a while. Thanks again. 👍
Thank you! The clarity of your explanations is just superhuman!
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. :)
Finally, I see the photon!
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.
27:45: _Think about that, you totally understand that._
Oh man, if you knew...
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.
Yes!! I've been waiting for this one.
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...
My favourite episode yet, thanks Professor!
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!
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
I love the *Windows 98 background* so much I cannot even express! 😳🤩
You are an excellent communicator. Thank you for sharing your knowledge.
I discovered these videos a couple of week ago and I'm now all caught up.
What a trip.
It would make me so so happy if there ever was released a lecture on gravity as a gauge theory :D
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
Thanks for the expository lectures, Dr. Carroll. Please make another video on renormalization.
It is delightfull that there are a hundred thousand people who have watched a video about Gauge Theory.
This was super helpful, thanks very much Sean!
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.
Haha high school? I went through four years physics undergrad and never learned that
Best explanation of gauge ever!
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.
This so good. Pure gold. Thank you.
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!
Thank you very much!
This is soo good explained sir Sean Carroll.
Thank you so much for this lecture. It really helped me to understand better this topic!
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'm at my third view of this video, as I am for most of this briliant series
Thanks for sharing
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.
Paul C. This lecture series would definitely require two midterms and a comprehensive final exam !!!!
If you're ok with two watches you're great! In my first watch I'm feeling totally stupid, after the second I've got the general concept, and in the 3rd-5th I start feeling I'm getting the picture
@@thoel1 i'm on 4 or 5...
Never heard of gauge theory explained in the way you talked about it a few days ago in line with this video.
I always thought it was invariant in the sense that the gauge was able to be defined and scaled from any origin and the transform applied would be universal from that origin.
Wow, I learned a lot from this video. Thank you so much! 👍
That is awesome ! But I need to watch again !
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.
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.
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?
Awesome video!
Worth the price of admission. Thanks.
Outstanding material!!!
Incredible. Bravo. Thank you.
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?
reeeeeally love this series
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 :-)
thanks for elucidating a pretty vague topic
Great talk, thank You!!
Thank you Professor!
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.
I never understood this but I try again , to get my head round it
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.
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 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 !!
So thrilled to find out why the strong nuclear force works. Now to find out about the weak nuclear force. Thank you!
Me: It's 1am, a few more lines of code and then bed
Sean Carroll:
pyropulse I can get behind this comment.
@pyropulse Hi pyropulse - I like your comments / replies. No coke for me though, but I just have to smoke a big spliff before I watch these vids !!
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
What a good video. Congrats
Very good explanation
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.
Thank you Sean for your excellent lessons! Could you please tell us which blackboard app are you using (so effectively) ?
Roberto
Gauge theory is the "biggest head-melter in physics", for me at least.
Well ... high dosed acid ketamin trips give you an better understanding .
Cool. Lots of info. Thx
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 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.
I love your books Sean (multiverse one is my fave), and I'm digging the Lockdown locks too.
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 ^^.
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.
That quark soup tasted a bit strange. Had to lie down, but luckily didn't throw up.
"The hope is... that the underlying details remain clear" : hope realised!
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.
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?
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 ...?
السلام عليكم ....hello
شكرا على مجهوداتك.....thank you for your efforts ..... محاضرة ممتعة....شكرا.
شرح جميل ،منظم ومبسط .
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
Marcus M. Browning it's notability
Thank you!
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).
Very nice! Thank you alot :)
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...)
I'd really like to know how it's determined that the graviton has a spin of 2.
Hi! The graviton is an excitation in the gravitational field. That excitation is described by a two component tensor usually denoted h that is some perturbation of the spacetime metric g. The spin of a field is it's transformation property under a rotation. Since h is a two component tensor it transforms as h' = R * R * h, where R is a rotation matrix and there is two R's since you need one for every index of h. For rotations the angle of rotation add up for multiplied rotations, which means that you just need to rotate an angle 180 deg to get back your original h since for R*R the angle will be 360 deg. That you just have to rotate 360/2 deg to get back is the defining property of h being a spin 2 field. In general for spin x you need to rotate 360/x to get back to the original configuration. Hope it helps, otherwise there is a lot of information on wikipedia!
@@oliverthim7650 what is a graviphoton then?
Short answer is that the gravitational field is the metric, which is a rank 2 tensor. In quantum field theory, rank 2 tensor fields are spin 2 fields
@@oliverthim7650 if you were to add santa clause and random letters into your explanation it wouldnt change .
Explanations like these feel me make closer to actually understanding things rather than thinking I understand.
Even if I can locally rotate the colors, the physics should be intact. So it makes me think that the connections rotates to compensate. Say I have two red quarks. Like charges (likely) repel. Now if I rotate the second one to green then red-green interaction would be repelling (because unlike repel). Seems like this would not keep physics intact as it expect it to agree whether it repels or attracts. What I think actually happens is that the connection maps my red quark to correspond to green in the destination space. Red-red repels and green-green repels and physics is intact. But in the same go that I rotate my quark color the connection needs to change from red-red map to red-green map. If this is the case that relative color is inescapeable it feels in conflict that I can "separately" rotate colors.
Sombrero doesn't fully sink in but I think I got the breaking part through it. In the triangle example imagine that I color one of the vertexes red say C. Now rotations are no longer symmetries and many of the flips are ruined. Only flip via C and doing nothing remain. So even if I only know that one of the points will get colored I will know that only one flip will remain a symmetry even if I don't know which of A,B,C will get colored or which flip it is. If I like I can rotate the colored one to be C. The sombrero spinninng does the same thing but I can't keep track of that.
I got tripped up by sometimes there being one field with multiple details and sometimes multiple fields with few details. 1 three colors quark field or 3 one color quark fields? Two higgs fiels or one with 2 complex dimensions? Or is the only true unified object the lagrangian "the true field" and the others are just details of it? Is the connection for color independent from connection for the weak force? Or do they come from a common shared connection? Is that connection the spatial spacetime metric?
I got also more suspicoius on whether I know what charge and mass mean. It seems like charge is related to a phase of some complex amounts but if there is supposed to be a synonymity there it escapes me how it works. Is anti-phase anti-charge?
It feels like this needs multiple watches but it seems clear enough that one might actually bother to watch it again. I noticed that a lot of work done by just not having a "oh that is complex and scary" for the term non-abelian.