The Biggest Ideas in the Universe | Q&A 15 - Gauge Theory

[@seancarroll]

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).

[@etzie1728]

You get that on the big jobs. You're only human 👍

[@Mickolas21928]

I'm going to rewatch all of these videos again until they sink in. As an amateur, thank you for making these.

[@qclod]

You're a true role model. Thank you for this series, Dr. Carroll. I hope you know how heavily your work is appreciated.

[@HughesMath1]

As I listen, I am so grateful for your conversational way of explaining. So amazed at the variety of idioms, colloquialisms, and manner. Thanks

[@simplelife1021]

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

[@matt5347]

I am a PhD student in high energy physics. I find these videos incredibly useful! I'm confident in the mathematics such as group theory, calculus etc, but my way of understanding the theory has been 'chugging away, solving the equation'. These videos are really helpful for understanding the overall concepts, motivations for certain things etc. Thanks Sean!!

[@isaacanderson8231]

Hey Sean , been enjoying this series planning on buying some of your books.

[@discreet_boson]

I love it when Sean uploads

[@markdeslauriers6549]

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.

[@TheMemesofDestruction]

1:00:42 - The effects of gravity on Earth wouldn’t be enough to skew observations to this extent would they?

[@hgfuhgvg]

I see Sean Carroll video.. I like.

[@EzraAChen]

Most wonderful teacher

[@kobev3li385]

Even the Q&A video on this topic is amazing !!!!!!! Thank you again Dr. Carroll

[@Cygnus__X1]

This video is absolutely amazing

[@MrFedX]

Mindblowing and really, really fascinating video!

[@sadsalidhalskdjhsald]

Anyone else use these videos almost as ASMR to help them sleep? Sean has such a soothing voice.

[@johndunn5272]

I'm starting to see that the enormous efforts described in physics by what Sean Carroll has presented has been an attempt to build a TV set where the picture shown is of the best description of reality. So quantum mechanics is the tool heavily relied on to build this TV set

[@mr51406]

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! 🌟

[@AdamGenesisArt]

SU(5)....thank you Sean!

[@paulc96]

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.

[@felipereyes8922]

They are labels. If you had a column of three numbers, you could label each one with a number from 1 to 3. A subscript i represents all of the components of the column, because we make it represent any of the three possible values. If you don't have a column, but instead have 9 numbers arranged in a square, then ots useful to label each with its row and column. This way, you now need 2 indices to account for all components, therefore two subscripts. The riemann tensor is a group of 256 numbers, each one labeled with 4 subscripts that can take 4 different values (4×4×4×4=256). Those labels are the four greek letters that you are asking about. They carry additional meaning whether they are subscripts or superscripts (not exponents), and since this array of numbers has certain useful properties, we call it a tensor

[@paulc96]

@@felipereyes8922 Thank you very much Felipe. That really is a big help. I think I finally get it. Thanks again & best regards.

[@paulc96]

@@GammaPunk Thank you Blazeorangedeer, that is a big help. I only just read your reply today (Fri 10th), so apologies for delay in responding. I do appreciate you taking the time to provide such a full explanation - so thanks again.

[@apaeterable]

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.

[@chhatvotthoeun1062]

*Sean Carroll* អរគុណច្រើនបងប្រុស🇰🇭❤️❤️🇰🇭😍😍បងប្អូនយើងកុំភ្លេចជួយគ្នាទៅវិញទៅមកណា🇰🇭❤️🇰🇭😍😍

[@stridedeck]

Now it makes sense! Maxwell's and QFT!

[@ToriKo_]

2:30 mass of a field? man I’m having an extremely hard time keeping up anything now 19:00 Spontaneous Symmetry Breaking. Why is it spontaneous? Well because the theory has the complete perfect symmetry but the state it is in (like the vacuum state) does not 46:50 Electrons and the Higgs Boson 53:35 So the Higgs give mass to the : 1:01:40 String Theory and E8 1:15:15 Symmetries cause you to have a Connection Field? That’s sloppy language. 1:19:00 Reiman Curvature Tensor (invariant) vs Connection Field (more dependent on coordinate choice, & in 1 direction)

[@cutebabyseal621]

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."

[@airtonrampim806]

27:00 Actually, the value of the potential at the brim is -μ⁴/(16λ). The potential is zero at phi1 = phi2 = 0.

[@paulc96]

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 !!

[@simonsherwood3918]

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)

[@SkiPraetor]

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?!

[@preethamkumar4492]

53:20

[@Clifton100]

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.

[@chiphill4856]

Petra Kann Not to be too stodgy, but it depends on who you talk to about the fundamental nature of mathematics. Max Tegmark comes to mind, others as well.

[@I2yantheGreat]

Good title and really cool blackboard app. I wonder what it's called

[@gilbertanderson3456]

Sean explains his setup at 44:47 of the Q & A video for B.I.i.t.U.#3. He uses notability on his iPad, feeds it to his laptop where a video capture program gets input from the iPad, a video camera and a professional level microphone.

[@sirilandgren]

Don't your *dare* tell me how much detail I want or need! 😤😘

[@dingoo1971]

do you really think, data driven modeling equals existence or is it just a way of talking? thank you very much for the great content

[@anirudhadhote]

❤ Very good 👍🏼

[@larryboulware6483]

Even better the third time around

[@Lulu-kt6gr]

Sean Carroll: can we jump to a parallel universe? A parallel version of ourself if we’d made a different decision??

[@davidseed2939]

RAILWAY gauge is the width if the track. Not as you said

[@rhondagoodloe3275]

Great! Thanks!

[@trevormugalu3797]

Too bad the standard model isn't among the biggest ideas in the universe!

[@Petrov3434]

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.

[@doncavanagh7243]

Jeez after 5 mins I’m losing the will to go on

[@Attlanttizz]

I'm not worthy. I'm also not smart enough to follow. I'll have to restart the series I think.

[@discreet_boson]

Yaaaaaaay

[@tonydarcy1606]

I always thought Mexican hats had a wide brim. Silly me !

[@marklarocca131]

P

[@scottdorfler2551]

Has anyone ever told you your voice sounds a little like Alan Alda? You're way less whiney though. 🤣🤣🤣

[@edpiv2233]

Wth. Four thumbs down? Obviously Biden voters.

[@chiphill4856]

EdP IV Politics? Really? Not here.