None of this would have been possible without the Noether's theorem. It is really the foundation of entire mathematical physics. She deserves much more recognition.

omg a channel that actually is happy to do like mid-level-ish physics, rather than either total beginner stuff that assumes this is too scary or advanced cutting-edge research lectures that assume you already know this stuff by heart Really glad to see this!

I truly love this channel! Every physics channel on KZfaq is either extremely oversimplified analogies creating more questions than they answer, or actual PhD level lecture notes and there's rarely any channel which actually explores why the mathematics are they way they are! Thanks for the work :)

I'm doing my PhD in theoretical high-energy physics, and I have to say this is one of the best intuitive introductions to gauge theory I've ever seen. I've been binging your videos, keep it up!

Absolute gold , please do a video on the Higgs mechanism

I just spent 2 months to understand this subjects separately from different sources and end up in deep confusion now you saved my day thank you so much

I'm an Accelerator physicist and everything I've derived started from maxwell equations. I'm obsessed with going deeper to derive Maxwell equations themselves, this is exactly what i needed 💯

When I was studying electromagnetics in the third year of an engineering program, our professor mentioned gauge theory as an aside and I was very intrigued. This led me to a furious night of wikipedia binging, link chasing and textbook hoarding but I was still left hopelessly confused. I was disappointed that despite having studied so much mathematics I was still so far away from understanding these ideas. A semester later after being fed up with the lack of math and physics, I transferred over to the math department and graduated with a double major in math 😅 Now years after my undergrad I'm self-studying physics and am this close 👉👈 to finally understanding gauge theory. Your channel helps a bunch, I swear. It's a fascinating time to be alive, but my past self is super jealous of my present self for having this video! Thanks for all these wonderful videos 🙂

I just finished Noether's Theorem, ready for more symmetry! Bring on the Higgs!

This channel explains very complicated topics in a very simple way, but does not oversimplified it. Thanks for sharing your knowledge. Marvelous!!!

You bring so much insight and clarity to some of the most advanced concepts in physics to make it so accessible to us, engineers. Always looking forward to your videos.

@3:45 - Yes, please do a video on the Higgs mechanism and other aspects of the standard model. Maybe some videos on the different types of QFT’s that there are, things like QED, QCD and lattice QCD, the weak interaction theory, the electroweak theory etc. Also topics like the eight-fold way method, S matrices, the spin-statistics theorem, Feynman’s path integral and Feynman diagrams for different types of scattering interactions, scattering cross sections and decay-widths, abelian and non-abelian gauge theories, neutrino flavor oscillations and the ways neutrino masses are incorporated into the standard model, and other topics of the standard model of your choice that you think are interesting. Just some ideas if you feel so compelled please. Thanks 😁. Also, the videos you have done so far are great and I have learned much from them 👍👍. I am very appreciative as I know videos like these take a lot of careful thought and time, and are not easy to do. Keep up the good work!

Great content and superb explanation of the concepts pertaining to field theory. Coming from an Electrical Engineering background with basic foundation in undergrad Physics and Mathematics, I can confidently say this is the first time I come across a very high quality video that deals with particle Physics in a very elegant and logical manner. Thank you so much for working so hard on producing this video, cannot wait to start learning about String Theory from your channel (it would be a great tribute to the late Joseph Polchinski).

This video finally answers a question that’s been bothering me for a long time… why is charge conserved? To summarise, 1) Conserving charge means satisfying a charge continuity equation. 2) Lagrangian density of a field is rotationally symmetric in complex space as it is the product of a complex field and its conjugate, which depends only on the magnitude of the field and not its angle. 3) From Noether’s Theorem, if we choose a symmetry such that dL = 0 - such as the rotation symmetry in complex space - then we get a conserved quantity Q. This quantity is a bunch of derivatives in space and time now since the field is itself also a function of space and time. This is the continuity equation which conserves charge. I’m not clear on why taking the covariant derivative preserves symmetry - in changing the definition of the derivative, why should the system be symmetric in the same way as with normal derivatives? On another note, I would really look forward to more in-depth explanations on the last bit involving Maxwell’s Equations, and perhaps a video or problem sheet on how substituting plane waves into N gives rise to the number of particles minus the number of anti-particles.

Please keep this series going, I can't wait for more videos on this topic. Really well done.

I'm guessing getting used to the compactified notations just takes time and practice. _Lots_ of time and practice. Either they're not as complicated as I'm making them out to be, or even experts sometimes get lost in the abstraction. Anyway, whenever you ask if we want to see a video on another topic, the answer is always yes!

This video is just what I needed! I'll have to rewatch it, and watch the follow ups, but this was a great teaser. Thank you

Thank you so much for what you're doing! I'm taking QFT right now and have forgotten some of this from previous grad classes and have struggled all semester (especially given the notation)

I love what you are doing. Please do a video on Higgs mechanism.

I love your steps to build all the concepts and how you present all great ideas in physics. Genius Eliot .

This was great! I have a background in math and physics and I felt that the derivations here were pleasantly explained. Thanks for making videos like this! So many videos on the subject skip the details but I love them and you do a great job explaining them.

BSChE here, about ready to retire in about a year and go back to my alma mater to get a BS-Physics. I have been watching a lot of videos (incl. MIT OpenCourseWare) and reading various books (Linus Pauling 1935, Griffiths ED and QM, and my old Halliday/Resnick beginners book). I have to say this was way over my head but... one of these days I am going to understand all of this... I hope! Thank you Elliot! Great videos.

I like the way you explain the equations ie how you get to them as so many texts skip/ assume one knows, leaving gaps in understanding.

QFT has been very challenging for me this semester. These videos really REALLY helped fit things together. Thank you so much Elliot.

Very beautiful explanation . As a fan of physics I appriciate your free help ( uploading videos that are explained with simplicity ) Thank you

Thanks a lot for these videos. It helps a lot. Videos on advanced topics is kind of unique. We all love you Elliot

This video is incredible. Your explanations are fantastic. I still don't *get* every part, but you've given me a great foundation to work from. Thank you!

It is ironic that this channel appeared in my life along with Bogolyubov's book "Introduction to Quantum Field Theory". Thank you for your work, you help to better understand the material!

When i studied CFT i didn't understand intuitively! A brilliant explanation!! Please make a video on SSB and higgs mechanism.

Thanx Elliot for this lucid explanation and the step by step mathematical derivation, really nice.

Amazing work, explaining this so well. Thank you.

This makes me wonder why the hell I paid tens of thousands of dollars for a physics degree when I could have just waited 15 years for a video with a better explanation

This is just amazing, keep it up!!

Awesome videos! Keep up the good work!

Your channel is great, Elliot. Congratulations 👏👏

Very information rich but still very approachable. Well done. Thanks.

One of must top 5 channels on youtube

Very interesting, informative and worthwhile video.

This was fantastic! A fabulous new perspective for me enjoying physics 15 years on from uni

Great work! Thank you very much. Would love a video about Higgs

You sir, are an amazing teacher.

Well done and an excellent introduction to this topic.

First time I watch your channel and, all i have to say is that you got a new sub haha looking forward for the next videos!

Congrats on the sponsorship!!!

This is so great! Keep going!

This channel is awesome! I have an advanced degree in particle physics and your videos have been really helpful to me and I can personally recommend your channel to my students as well. Keep up the good work!!! ❤️

Love it ! I would love more videos !

I am happy that there are more and more teachers like Elliot who can teach us high level Physics so that not only genius people but also ordinary people like me can understand it 😊

Outstanding Job.

Expressing the equations with differential forms is useful For example, Fuv is generated from Au by the exterior derivative.

Omg it starts to click, the dots start to connect :) It's all just old good electromagnetism, plus relativity, plus calculus, and the formulas indeed become so beautiful, and "simple" in some sense :) And we can get to standard model by just extending this a bit?! Awesome! :) It's so fascinating how it all comes from electricity. Even relativity kind of comes from the same thing: the electromagnetic waves, the light 💡!

Thanks for a quick but nice review...

Another video on the Higgs field ? ABSOLUTELY !!

Excellent video

I love this channel. Just amazing...

This is magisterial...

Would love to see a video on symmetry breaking and the higgs field

Thank you for this

Very clean, yet dense presentation! And this was just classical stuff - no second quantization yet :)

Thank you!

I knew Jay-Z would be relevant again someday

"Conservation" must be referenced to a volume defined by the light speed applicable to the locus field, whether a force field or the universal background or vacuum, within a time constant interval of equilibration. "Conservation" intrinsically is not absolute or instantaneous but is relative to an interval of measure.

Definitely interested in the higgs mechanism as well!

Thanks, Eliot.

Wonderfully explained. What software tools do you use to make these videos? Keep up the good work :)

Brilliant lesson! If I have had this 35 years ago I would not have quit my quantum field class.

👍 Higgs field video would be fantastic

Very very informative video Please take over the higgs field

Hi. Awesome videos truly. Can you please make videos on continuum mechanics? Many people with engineering background will definitely appreciate... Thank you so much!!

Awesome video

Beautiful!

Very good 👍

At 21:43, I think the correct equation should be: dL = (EoM * epsilon) + d(Q * epsilon)/dt As always, the video was great at intuitively explaining such complex equation to us mortals. It will be helpful if you can create series of short focussed videos instead of 1 big video. Also, I think derivation of continuity equation through variation of phase angle was bit rushed which is odd when compared to your older videos where you show all calculation step diligently.

Conservation of Spatial Curvature: Both Matter and Energy described as "Quanta" of Spatial Curvature. (A string is revealed to be a twisted cord when viewed up close.) Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree. String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring? What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine. Quantum Entangled Twisted Tubules: “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr (lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958) The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics? When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry. Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change. ===================== Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons? Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase. Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length ) The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge. Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137. 1= Hypertubule diameter at 4D interface 137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted. The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.) How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter? Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles? I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles. .------------------

You put a full Stanford course in a video

Hi Elliot, since you are so good, could create a complete course of physics, I am hungry I can choke on a morsel. I need full course access. if you know the link where I can follow up on theoretical physics completely! Ur videos are awesome!

Hence quantum field theory EXPLAINS the existence of electric charges. I classical physics electric charges and associated forces are postulated ad-hoc. In contrast, the general statement that particles are described by complex local fields + adding the requirement of invariance under arbitrary local gauge (phase) translation, together mandate the existence of electric charges and the specific associated forces. For me that's a major explanatory contribution of quantum mechanics. Somehow I have never seen it stated as such in physics text books.

MORE PLEASE

Great. (Small error at 24:42 were some partial derivatives should be wrt. x instead. of t.)

Mad props to Jay-Z for being such a pivotal figure in electromagnetism

To understand difficult material requires the type of effort prescribed by a science friend of mine from long ago: To read, reread and re-reread. I suppose on KZfaq this would translate to listen, re-listen and listen yet again.

What tells you that imposing U(1) symmetry is the correct way to couple the EM field with electrons? What motivates the imposition of this symmetry? Was it just a guess whose results turned out to be correct? I never understood the motivation behind U(1).

This is a great refresher! What software do you use to make these?

Bruh this was literally on my midterm 2 days ago I wish I watched this lmao

Awesome. Can you make a video on Yang-Mills theory?

Symmetry groups are the universe. The universe, in my view, a mathematical truth/structure. It (reality) is what happens when you have these mathematical objects called quantum fields defined on a manifold (spacetime) in some type of initial ordered/low entropy state. In theory all possible self consistent mathematical structures exist, so a structure with interacting quantum fields defined on a manifold with more than 3 spatial dimensions can’t exist as any interactions in 4 or more spatial dimensions lead to non-renormalizability, meaning the math becomes nonsensical and inconsistent so it can’t occur. But one in 2 spatial dimensions probably could, in 3 or less spatial dimensions qft’s can be interacting and renormalizable (meaning they are predictive).

This video's are great. However I think they would greatly improve if they had a better timing. Like for example at 15:20 (among other moments in the video) you are saying some really important stuff but passing through it very fast. 3b1b used to suffer from this in the past. I understand that this would make the video longer, but perhaps it can be splitted in two better paced videos. At least that's my two cents from a person who wants to understand better all this amazing material you are throwing into the world. Keep the amazing work! I live this channel!

At 32:46 you define the gauge covariant derivative as /partial_mu \phi + iqA phi. When doing research elsewhere, it is defined with a negative sign in front of the second term instead. Is this because you are absorbing a sign into q?

I have two requests :-) Please make a video on 1) spontaneous symmetry breaking, and 2) the Higgs mechanism. Ideally they would not be too hand-wavy, and include some mathematically accurate-ish toy examples :-)

Mr. Elliot, if i may make a request, could you please make a video on the indexes (variant/covariant). The only class I took in undergrad that used those were back in 2020, so i didn't learn them as well as i should

I am interested in learning more about field quantization

I now see how intimately vector calculus ties in with QM, for example divergence theorem.

Emmy Noether changed physics

Which book you follow for field theory of particle physics and symmetry transformation

Are these topics covered in your course(s) Elliot?

Higgs video for sure!

Got a question: in 34:00 after introducing the covariant derivative. Why did you say that that phi has now an electric charge?

Great 💕

Awesome

For Noethers Theorem, I am working on the PVED Parity Voilation Energy Difference. How would you find the change in the Lagraian when the object (say a molecule is mirrored) So you have a molecule then you have a mirror image of a molecule, what is that equation?