*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 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 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 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.
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'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 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.
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".
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.
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.
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.
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?
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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. 👍
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
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...
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. :)
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!
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!
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.
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.
@39:00 : there is another reason why taking the square doesn't make sense namely the Lagrangian is real valued so it forces you to take the norm instead of the square.
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.
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
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?
4:20 the quarks come in 3 colors; 3 fields. And they have a Special Unitary Group Symmetry of (3), SU(3), as there are Symmetries for the rotations of the 3 Complex valued quark Fields. 6:39 “How do you rotate in Color-space at different points of physical space at the same time, when at every location in space there is a value of the field?” I’m finding I really don’t have a good grip on what unitary groups are, or what the color spaces of quarks are, or what the deep connection symmetry has to SU Groups, or what is meant by being able to locally rotate the color Fields and why we need to be able to describe it. 11:40 In order to compare differently rotated color Fields, you need to be able to do Parallel Transport, which means you need the instructions that tell you what it means to keep a vector pointing in the same direction, those instructions are called the Connection Field, also known as Gauge Fields. I don’t understand why you need to compare locally rotated Color Fields, physically speaking. Because I don’t know what Color Fields describe, so I don’t understand what the Connection Field describe (physically). Also what happens to the Flip symmetry, why is there only a repeated focus on rotational symmetry? Anyway it describes the Strong Force. And it’s a physical feature of the world so who cares if we call it a force or not. 32:30 if the Lagrangian = Kinetic - Potential, then roughly speaking the Kinetic energy depends on the time derivative, while the Potential depends on the value of the field 36:00 43:00 50:00 [] and Stong interactions 1:04:50 Weak interactions
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 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.
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.
@ 1:16:00 So np and pn are really hexaquarks and they're everywhere. This means (to me anyway) that it's not so weird that we are now seeing pentaquerks (news from this week).
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 !!
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?
No, since photon itself also carries linear momentum. Remember that momentum is a vector. So it's possible for the linear momentums of electron and positron to sum up to the momentum of the photon, while simultaneously conserving the energy of the photon in their mass and kinetic energy.
Can anyone help me...56:03 if a gluon can couple to 2 other gluons than how is energy conserved, when it can than produce infinite quarks and anti quarks?
As far as I understood it, gluons are "free" (as in beer) and therefore cost nothing to make so long as they remain close together. Only when one tries to pull the quarks apart, they become so energetic that they create other quarks, thus normally they stay confined. Energy is conserved because one has to apply energy to pull the quarks apart and this energy supplied creates the new quarks,
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.
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?
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 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.
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.
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!
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?
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.
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?
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 ...?
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?
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.?
I am not sure if this will answer your question or not. In the video he skirted around this issue a little probably not to confuse people. There is a U(1) force and a SU(2) force in the standard model. However, the U(1) force is not the electric force. Some linear combination of the standard model U(1) and SU(2) form what we think of as the electric force. This is due to how symmytry breaking occurs with the higgs. I think that is why they SU(2)xU(1) form a unified electro weak theory, as opposed to just saying they are two different forces.
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
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).
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.
Things are scalar, tensor etc because they transform as scalars or as tensors under some transformation. The things they transform under as scalars or as tensors are the symmetry transformations.
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
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.
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?
I was trying to follow the massless proton explanations. Why is potential of the photon field subject to U(1) invariance? Isn't that only required for the electron field?
*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 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.
My conclusion is that Sean Carroll understands it.
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'm a 4th year physics PhD student and these videos are still interesting and illuminating. Thanks!
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
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I don't know what it is about you Sean, but gosh darn you incite so much excitement and joy in learning this stuff!
This video strikes the PERFECT balance between fluency and accuracy. Amazing as an appetiser/reminder for preparing a quantum field theory exam.
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'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 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.
An extremely clear and insightful introduction to the laws of nature! Also very helpful to graduate students majored in physics like us.
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".
Thank you! The clarity of your explanations is just superhuman!
This has been my favorite episode where many previous ideas all came together.
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.
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
Sean is so good to tie all the things togheter, now we know why its important to know the stuff.
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.
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 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. 👍
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 :)
You are the best, Dr. Carroll.
My favourite episode yet, thanks Professor!
I'm at my third view of this video, as I am for most of this briliant series
Thanks for sharing
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...
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 !!
This is very well done 🎉
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. :)
Hilarious
This so good. Pure gold. Thank you.
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.
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!
49:36 what would it take to observe gravitons? Some kind of gravitational interference patterns? What size would this be? Something else?
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!
Yes!! I've been waiting for this one.
27:45: _Think about that, you totally understand that._
Oh man, if you knew...
You are an excellent communicator. Thank you for sharing your knowledge.
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.
Best explanation of gauge ever!
1:10:28 - I thought that the Higgs field was a scalar field with no direction, why is it shown as a vector field here?
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.
The best video on youtube, possibly the internet.
It would make me so so happy if there ever was released a lecture on gravity as a gauge theory :D
reeeeeally love this series
This was super helpful, thanks very much Sean!
Perhaps the greatest explainer since Richard Feynman!
Actually better than feynman in my view
@39:00 : there is another reason why taking the square doesn't make sense namely the Lagrangian is real valued so it forces you to take the norm instead of the square.
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...
Thanks for the expository lectures, Dr. Carroll. Please make another video on renormalization.
I discovered these videos a couple of week ago and I'm now all caught up.
What a trip.
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?
4:20 the quarks come in 3 colors; 3 fields. And they have a Special Unitary Group Symmetry of (3), SU(3), as there are Symmetries for the rotations of the 3 Complex valued quark Fields.
6:39 “How do you rotate in Color-space at different points of physical space at the same time, when at every location in space there is a value of the field?” I’m finding I really don’t have a good grip on what unitary groups are, or what the color spaces of quarks are, or what the deep connection symmetry has to SU Groups, or what is meant by being able to locally rotate the color Fields and why we need to be able to describe it.
11:40 In order to compare differently rotated color Fields, you need to be able to do Parallel Transport, which means you need the instructions that tell you what it means to keep a vector pointing in the same direction, those instructions are called the Connection Field, also known as Gauge Fields. I don’t understand why you need to compare locally rotated Color Fields, physically speaking. Because I don’t know what Color Fields describe, so I don’t understand what the Connection Field describe (physically). Also what happens to the Flip symmetry, why is there only a repeated focus on rotational symmetry?
Anyway it describes the Strong Force. And it’s a physical feature of the world so who cares if we call it a force or not.
32:30 if the Lagrangian = Kinetic - Potential, then roughly speaking the Kinetic energy depends on the time derivative, while the Potential depends on the value of the field
36:00
43:00
50:00 [] and Stong interactions
1:04:50 Weak interactions
Yes! I love this series sean thanks for putting these out
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!
@14:27 How do we know exactly that Maxwell knew about Gauge Transformations? Thank you for the informative and wonderful film.
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.
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.
@ 1:16:00 So np and pn are really hexaquarks and they're everywhere. This means (to me anyway) that it's not so weird that we are now seeing pentaquerks (news from this week).
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 !!
This is what youtube was made for. Giving guidance for how all the puzzle-pieces fit together, to be used to direct audodidactic studies.
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?
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?
No, since photon itself also carries linear momentum. Remember that momentum is a vector. So it's possible for the linear momentums of electron and positron to sum up to the momentum of the photon, while simultaneously conserving the energy of the photon in their mass and kinetic energy.
Can anyone help me...56:03 if a gluon can couple to 2 other gluons than how is energy conserved, when it can than produce infinite quarks and anti quarks?
As far as I understood it, gluons are "free" (as in beer) and therefore cost nothing to make so long as they remain close together. Only when one tries to pull the quarks apart, they become so energetic that they create other quarks, thus normally they stay confined. Energy is conserved because one has to apply energy to pull the quarks apart and this energy supplied creates the new quarks,
@@elizondorj humm..that make sense! Thanks for the reply, will also try to do some reading on this, thanks once again!👍
Thank you Sean, I experience a strange combination of seeing the explained, and getting lost in my fantasy. My maths desperately needs my attention :)
Finally, I see the photon!
I love the *Windows 98 background* so much I cannot even express! 😳🤩
thanks for elucidating a pretty vague topic
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.
It is delightfull that there are a hundred thousand people who have watched a video about Gauge Theory.
Thank you very much!
This is soo good explained sir Sean Carroll.
Worth the price of admission. Thanks.
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?
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...)
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
السلام عليكم ....hello
شكرا على مجهوداتك.....thank you for your efforts ..... محاضرة ممتعة....شكرا.
شرح جميل ،منظم ومبسط .
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.
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.
That is awesome ! But I need to watch again !
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 .
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?
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.
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?
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 ...?
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?
I've promised to myself to go bed early but i can t stop to watch
Incredible. Bravo. Thank you.
for gravity, are there multiple symmetries for the spacial and time dimensions? maybe abilian for time and non abilian ones for spacial dimensions?
That lecture felt like 5 minutes. Do I have another 5 minutes to watch it again? Yes I do.
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.?
The GUT is done mathematically, we just havent confirmed with experiments yet, because required energy is too high for now.
I am not sure if this will answer your question or not. In the video he skirted around this issue a little probably not to confuse people. There is a U(1) force and a SU(2) force in the standard model. However, the U(1) force is not the electric force. Some linear combination of the standard model U(1) and SU(2) form what we think of as the electric force. This is due to how symmytry breaking occurs with the higgs. I think that is why they SU(2)xU(1) form a unified electro weak theory, as opposed to just saying they are two different forces.
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
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).
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.
Things are scalar, tensor etc because they transform as scalars or as tensors under some transformation. The things they transform under as scalars or as tensors are the symmetry transformations.
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
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.
Thank you for this. I really appreciate you making this video.
Thank you Prof. Carroll
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?
I was trying to follow the massless proton explanations. Why is potential of the photon field subject to U(1) invariance? Isn't that only required for the electron field?