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

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.

#science #physics #ideas #universe #learning #cosmology #philosophy #math #gaugetheory #symmetry

[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).

[Mickolas]

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.

[HughesMath]

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

[matt]

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!!

[isaacanderson]

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

[simplelife]

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

[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.

[paulc]

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 !!

[TheMemesofDestruction]

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

[Clifton]

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.

[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?!

[airtonrampim]

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

[trevormugalu]

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

[Attlanttizz]

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

[scottdorfler]

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

[johndunn]

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

[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)

[sadsalidhalskdjhsald]

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

[kobevli]

Even the Q&A video on this topic is amazing

Thank you again Dr. Carroll