Field Theory Fundamentals in 20 Minutes!

[@wayneyadams]

10:38 Partial derivatives seem intimidating at first, but here is a simple way to understand them. By the way, this is how I taught them to my students. You are standing at the base of a hill. The slope changes differently depending on the direction you walk. You want to walk up the hill and retrieve your drone which just crashed on the hill northeast of you. Let's say the hill slopes upward one foot for every five feet you walk toward the east. This is like the partial derivative, it gives you the slope in the easterly direction only, ignoring any slope to the north (or south). You begin to walk east until you are directly south of the drone, in other words, it is due north of you. Let's say you walked 20 feet to the east. How high are above your starting point? That's easy, it's simply the slope (partial derivative) multiplied by the distance you walked. Remember that the hill rises one foot for every 5 feet you walk. 1ft/5ft x 20ft = 4ft. You are now 4 feet above your starting point. Now you turn north. At this point the hill is much steeper, sloping upward one foot for every three feet you walk toward the north. Again, this slope is like the partial derivative, it gives you the slope in the northerly direction, ignoring any slope to the east or west. This time you walk 15 feet to reach the drone. 1ft/3ft x 15ft = 5ft. You are now 9 ft up the hill, 4ft from walking east, and another 5 from walking north. You could have walked north first then east in which case you would have to know the slopes at two points, the first to the north of your starting point then the slope to the east at the point where you turn east. Regardless of the route you take, using the slope in one direction at a time allows you to calculate the height of each leg of your walk which you then add together to get the total height. Just like this imaginary walk up a hill, partial derivatives allow you to calculate changes in steps by calculating how the change in one variable affects the change in your target variable. The first partial derivative on the right side tells you how the field changes with position, while ignoring the position (just like we ignored the slope northward while walking eastward). The other partial derivative tells you how the field changes in time while ignoring any changes from position. In this way the total change can be calculated. Wayne Y. Adams B.S. Chemistry M.S. Physics R&D Chemist (9yrs.) Physics Teacher (33 yrs.)

[@Naman...123]

Glad to see you Sir

[@a.thiago3842]

I'm very bad at math, i have high difficulties in learning physics, maybe due a lack of will at same time. And i understood very well.

[@joeybasile545]

Great explanation. Thanks.

[@wayneyadams]

@@a.thiago3842 Thanks, nothing makes a teacher happier than hearing that people have learned.

[@wayneyadams]

@@joeybasile545 Thank you.

[@kka107]

Yes, I’m very very interested in learning all of it. Your channel is unique in that you’re able to teach very difficult topics in just 20 minutes and not only do you do it by giving us the big picture, but also by getting into the math. You’re helping us learn things in minimum time and with minimum effort. Thank you for your contribution.

[@PhysicswithElliot]

Thank you so much Koorosh!

[@jacobvandijk6525]

I recognize your remark: "Just want to know all of it". Had that same feeling years ago. But the immense amount of math you need to really study Quantum Field Theory lowered my interest substantially. What you see here is just the very basics. Read about Renormalization.

[@kka107]

@@jacobvandijk6525 I believe you. I think I’ll be ok if he skips the lengthy derivations and mathematical complexities as long as he can still help us see the big picture through math.

[@jacobvandijk6525]

​@@kka107 I agree with you on that, Koorosh. The real mathematical details are only understood by experts, for instance at CERN. We, laymen, must be satisfied with the global contours of the field. May I ask from what country you are? Armenia? I'm from the Netherlands.

[@kka107]

@@jacobvandijk6525 Born in Iran, but have been living in the US for the past 28 years. I don’t have a physics degree. Still there’s a great deal of math in electrical engineering which I’m majored in. I always craved to learn modern physics but never had the time to do it the formal way, like by reading a textbook. Elliot’s short lessons are perfect for me. 🙂

[@jacobsilver2476]

You've just taught the Lagrangian in the most straight forward and intuitive way that I've ever come across, and did it as a sidenote to a main topic. Thank you for your brilliant teaching. Keep up the good work.

[@PhysicswithElliot]

Thanks Jacob!

[@Moleculize]

​@@PhysicswithElliotHello what math Should i specially need to learn to understand this video (especially the field theory part) I kinda know how to differentiate and integrate what else i need to learn? I will be happy if you can guide me

[@debrucey]

Jeez, was it really? I couldn’t understand it at all 😭

[@Byron_Vega]

The square is always so funny to me because the first time I saw it in a book I thought it was a symbol that couldn't load properly and I kept closing and opening the book until I decided to finally search for the "missing" symbol online and found out that there was never a problem. Please upload more, this was awesome!

[@schrodingerscat7218]

d Alembertian, second partial with time. Shorthand.

[@jpa_fasty3997]

This is about 2 lectures worth of work in the maths/physics degree I took. You presented it in 20 minutes, and I genuinely gained more from this than those lectures. Incredibly succinct and clear. Really good video.

[@ClemoVernandez]

You're very talented at presenting and teaching. I've never seen such highly quality, clear explanations for such advanced topics. The animations and drawings add an aesthetic touch which makes it even better. You deserve so much for this kind of dedication man. Keep it up!

[@PhysicswithElliot]

Appreciate it!

[@doit9854]

I second this.

[@speeshers]

This is, without exaggeration, one of the best videos I've ever seen. I'm a first year PhD student in physics, and this connected so many distant ideas and everything just clicked in place. Thank you so much!!!!! You method of explaining is extraordinary, and also really appreciate you going through some of the math and rigor, since a qualitative description can only go so far. :D

[@shubhsrivastava4417]

There are many science channels on KZbin which get into the detail of the topic but don't quantitatively explain the concepts. Since I like getting into the rigors of calculations, your channel helps me a lot in gaining interest in new topics. Thank you Elliot!

[@bartpastoor1028]

So exited you are started posting these videos on Field Theory now, together with the handouts. All of your videos and handouts, not shying away from math, are of an exceptionally clarity and even entertaining. They close the gap between (semi)popular video´s and semester long university courses you sometimes too can find on YT. But the latter, how good they may be, are very long and you easily lose the full picture of it. I studied Theoretical physics in the eighties and then drifted to ICT. Last couple of years taking it up again and am hoping to get some more insight into QFT, which we barely touched at the time. After some MIT Moocs, am now into the very good book of Robinson: Symmetry and the Standard Model. It goes slow, but then I have the time. Your videos so far and the ones hopefully to come, are of tremendous help in getting a fresh expose on the subject. Proud to be one of your patreons.

[@PhysicswithElliot]

Thank you so much Bart! I'm glad it's helping with your QFT studies. It's a tough subject!

[@pranaynayak]

I agree! the explainations are very clear and consice

[@owen7185]

I love how so many areas of physics and mathematics come out of something so elegant yet powerful

[@georgekomarov4140]

You're natural born teacher. I'm not unfamiliar with the topic (as far as a non-physicist can be), and still I feel I understand the topic more clear than ever before. Thank you.

[@douglasstrother6584]

You crammed a lot of Physics into 20 minutes, Elliot! Herbert Goldstein concludes his "Classical Mechanics" with Field Theory. Michael Faraday's concept of the electric and magnetic fields, and his collaboration with James Maxwell were the first steps in a modern unified field theory.

[@user_2793]

Mathematicians : Wait what

[@michaelb6349]

Same

[@GaryBernstein]

Please elaborate

[@michaelb6349]

@@GaryBernstein In mathematics a "field" is a structure that we study, so we would expect "field theory fundamentals" to be about things like this: en.wikipedia.org/wiki/Field_(mathematics)

[@pseudolullus]

​@@michaelb6349come on, do you also think the Lord of the Rings is about a genius in algebraic geometry? :p

[@namehkoudsie6075]

​@@michaelb6349 too bad we live in a physical world, not a mathematical one

[@fuencisclobuenasfuentes4523]

Superb work!!! As a physics student, I can say videos like these are extremely usefull for understanding the concept behind many tools we use. A lot of times this point of view of physical theories is lost in many textbooks in favour of mathematics and calculus (which is usefull too), so it’s extremely helpfull that people like you make this kind of videos. Pd: english is not my native language, so sorry for any mistake I might have made in the coment :)

[@PhysicswithElliot]

Thank you Fuencisclo!

[@SliversRebuilt]

This is everything I've ever wanted out of a physics education. Thank you so much, man. Plus this video reminded me to buy in on your patreon now that my financial aid refunds came through (I certainly feel comfortable calling it an educational expense lol) May many more follow in your footsteps. Think of the things we could achieve with the fruits such efforts bear across even one generation.

[@PhysicswithElliot]

Many thanks!!

[@cezarionescu75]

This is quite impressive, even for someone who has studied the field its lovely to gain new insight on the subject matter.

[@afshinsadeghi8074]

Thrilled to see this on KZbin. I always was watching the pop science clips but my search was giving zero results on formulas explanations in the KZbin. The more I searched the less I found. And I am not so in favor of reading the boring textbooks. This is well delivered. Now I can self teach a bit real field math. Thank you.

[@Cowux]

Your explanation is so GREAT. If I had these videos in my PhD years, probably I would not give up my journey in theoretical physics........

[@finnfinn4736]

Why did you give up?

[@sauravkafle8156]

This channel is just pure gold. Although I am a high school student and did not understand most of it, I really enjoyed watching the full video. Big appreciation to you.. Wish you for amazing success..

[@PhysicswithElliot]

Thanks Saurav! Check out my "help room" playlist for more introductory videos while you're working your way up to the more advanced stuff!

[@sauravkafle8156]

@@PhysicswithElliot Sure, Elliot.

[@tomgraupner171]

Please, Elliot, I need "the rest" for the other spins as well. All insights in this topic is wonderful! Thank you so much for your efforts !!!

[@panoskotoulas759]

That's actually a GREAT explanation. I can't think of anything you left out. You provided all relevant information in an easy to digest way. It was both formalistic and intuitive at the same time. I have no words, probably the best physics explanation video I have ever seen.

[@stevewhitt9109]

After studying tensors, I am now understanding this video. You say things that relate different areas of science: like the math that is used in both QFT and cosmology. I can't really put it into words, but thanks. The math of Dirac fascinates me.

[@fugitive6549]

Wow, this is amazing. I always wanted to learn about the Field Equations and now I have the basic idea where it all come from. Please continue with this series. This definitely guaranteed a sub.

[@pipea1512]

Absolutely incredible. Didn't think it could be possible to explain this topic with such clarity and conciseness while maintaining engagement through the narration and great aesthetics. Thanks a lot

[@vsevolodnedora7779]

Outstanding. I've heard tons of lectures on physics and field theory (I am a physicist myself), but this is just perfect. If I ever end up teaching this subject I will come back to this. Thank you.

[@paoloazzini9003]

Really appreciated this video! This finally helps me to connect the dots of many concept i encountered during my physics degree, without having to take a full semester theoretical physics class. I'd really appreciate a video on spinors' lagrangian too.

[@maxamadamiin]

I love physics for the sake of it, even though it is not what went for college. For these twenty minutes really helped me excited about field theories. In the begginning, I was little hesitant to look unto QFT due to the weird notations, but now you gave me a push to dive into. I love your videos Ellisiot. Thank you alot.

[@Adeodatus100]

You make these topics much, much easier to understand than my undergraduate physics tutors did 40 years ago. I seem to go through your videos saying "Oh, _that's_ how that works!" about every 2 minutes!

[@bulldozer6710]

I WANNA LEARN MORE! This was done so elegantly and was so incredibly helpful. My professor explaining this was the first time I'd heard of Field Theory, this video cleared my many misconceptions up a ton. Thank you!

[@PhysicswithElliot]

Glad it was helpful!

[@AngadSingh-bv7vn]

Its incredible the quality of content you have created that doesn't leave any gaps in math or understanding. I'm beginning to look forward to every video you put out :) keep up the good work! Well maybe not a completely rigorous math lesson but definitely super motivating to check out your notes.

[@joaopedrogoncalves6505]

Please continue these videos! They have really helped me when studying Theoretical Physics at the University of Birmingham and I really would like to see a video about spin ½ and 1

[@PhysicswithElliot]

Thanks Joao! Glad it helped!

[@AndyGD137]

This content is amazing, I can´t thank you enough for all this hard work and yes, we want to learn more about everything ;)

[@PhysicswithElliot]

Thanks a lot Andy!

[@diraceq]

This was amazing and super informative. Everything made perfect sense to me as someone taking the second term of quantum mechanics. I would love more of this.

[@PhysicswithElliot]

Glad to hear it!

[@BeAndNBovee]

I wish I'd had you as a math professor when I attended college: your explanations are super-clean and high quality. I would greatly appreciate if you'd "go down the rabbit holes" of the notations describing particle spins and their semantics.

[@mhinz80]

I am honestly impressed with anyone who understood even a little bit of what this guy was talking about.

[@pacotaco1246]

You forgot your base e's at 16:30 This video is smooth, and the videos make reviewing graduate physics more fun!

[@Slu54]

This has been a great video, it is the clearest explanation I've ever heard actually. Please do continue on field quantization and also the fields of other spins.

[@hrperformance]

I have a very good lecturer that taught this material to us (in my opinion) very well. But it was very easy to get lost in the detail and forget the big picture. This video sums up all the key points of about 6 hours worth of lectures unbelievably well. Having watched this video after struggling to grapple with my uni's material, I feel soooo much more confident. Thank you so much for this video AND the notes. You are awesome Elliot!

[@Celastrous]

Amazing video! Keep up this level of content. It is advanced yet easy to follow

[@PhysicswithElliot]

Thanks Sean!

[@I-M-2.]

Elliott, you are the best! This is the best and most coherent intro I heard of field theories. Your content is gold. Please do one on the Dirac field. Thank you so much!

[@PhysicswithElliot]

Thanks Gilad!

[@Pro-ish]

you are not worry about presenting the technical mathematical equations that underlay the theories of physics, this is fantastic !

[@PhysicswithElliot]

Happy it helped!

[@TakesTwoToTango]

"You'll learn about the Maxwell Equations in university, but probabely in a notation that makes them look much uglier". That one hit home. Nice! :D

[@aaravkansal4087]

Thanks KZbin algorithm for showing this channel to me

[@saqlainkhantrex4273]

Finally, someone came up with an actual physics video with math. Thank you!!

[@LoomMexatron]

Impressive work as always! Your ability to explain even one of the most complicated things such as field theory is genuinely fascinating!

[@DigiBentoBox]

A bit jealous of everyone here with the advanced knowledge and math skills to be able to understand and get the most out of the video. I can’t wait to be there one day. In the meantime, this video has given me a very valuable target which to for and guide my studies in the hopes of one day intuitively understanding these topics and the field theories that underlie Physics at large.

[@sifeyanis591]

I'm very grateful that I've met Elliott he's much better than my college professors

[@PhysicswithElliot]

Glad you liked it Sife!

[@Lavabug]

Incredible stuff, I wish I had this resource during undergrad. It would've saved me countless hours trying to understand Landau's field theory book. I think I learned most of this from Dirac's GR book but it was almost as impenetrable.

[@mjackstewart]

Dude, I’ve been poking around in physics for over a year. This is the FIRST video I’ve seen that integrates all the concepts I’ve learned individually! And notice I used the word “integrate.’ GET IT? Leave? Now? That’s fair …

[@stefanogallina3643]

Just discovered your channel and already binge watching all your videos. Keep up the amazing work!

[@PhysicswithElliot]

Welcome Stefano!

[@joshuanicholson23]

Amazing, as a senior physics student this is very accessible coming from undergraduate courses.

[@MrOvipare]

I started reading a QFT book some time ago and while I was able to progress in the frist chapters, it got so dense that I couldn't really see the big picture. Your videos help a lot! Looking forward to see more details on spin 1/2 and 1 field theories :D

[@jennj8149]

You’re my new favorite youtube channel! You’re also very great at explaining this in simple terms! Keep making good content man! 👍🏼

[@PhysicswithElliot]

Thanks Jenn!

[@Draginx]

I've just started studying quantum field theory and finished my courses on general relativity and have been extremely curious about what is to learn and confused about how my professor teaches. I love this video. Please make more like these describing different spin particles, quantum fields and especially spin 2 fields. It's all so interesting. You explain extremely well and have amazing editing. You've earned a sub from me. Thank you.

[@FermionPhysics]

If you’re interested in spin 1/2 field I’ve made a video on it on my channel if it helps

[@zacwarnest-knowles9139]

Videos like this are what’s made me want to become a theoretical physicist. Incredible content.

[@michaelpotter3418]

Thank you! It’s hard to find such a superb tour of this subject that includes the basic mathematical concepts. Lots of your audience have studied introductory quantum physics, but never got to see the next level.

[@samsyet-0074]

I would definitely want more of these videos, your videos are super nice for me! As a High school student with interests in maths and physics, its hard to manage doing college level books and preparing for entrance exams, but your videos really help me freshen up with something exciting. So its a no brainer for me to say yes to more of these

[@PhysicswithElliot]

So glad they've been getting you excited about physics!

[@aleksandr_berdnikov]

I'd love to see your explanation of how one can visualize QFT. Usually, for QM the algebraic perspective (vectors-operators-eigenthings-commutators) and the geometric one (functions-bundles-connections-PDE's) are both talked about a lot, so that it coalesces into a construct that is convenient to handle from any side. But for QFT I found the introduction to be (most of the time) quite "procedural" (again, operators-commutators or Feynmann integrals) and not providing the glue of "visual manifestations" of the concepts to tie them in my head into a coherent picture and tie it back to QM...

[@brendanfan3245]

your deep understanding of the physics principle is fantastic.

[@joquino73]

Excellent video I will used in my classes. Excellent job.

[@PhysicswithElliot]

Thanks Jose!

[@lardmaster4349]

Excellent, excellent explanations for what even universities struggle to teach in an intuitive, easy-to-grasp manner. Great job with the concrete examples, the explanation of physical meaning and intuition behind the maths, the overall structure of the lesson, the motivation behind the concepts and maths, the animations to illustrate the point, the reminders of what we’re measuring - I cannot express just how excellent this is as a science communication and educational video!

[@PhysicswithElliot]

Much appreciated!

[@TheCrunchyGum]

Very nice video. I'm takin qft next fall and this was a good intro. The derivation with the differential of curly L broke the pace a bit since it wasn't immediately obvious what steps you were taking between subsequent results, but everything flowed smoothly otherwise. I hope you continue to make videos on the topics mentioned at the end. The videos make field theory seem very accessible with basic undergraduate knowledge.

[@sambhavgupta4653]

You are the best explainer in Physics. Please continue making these videos! Thanks

[@zeratulg]

Perfect !! If it is possible to conduct two dedicated series, one for special relativity and another for general while diving into details , that would be great !!!! Thanks for these videos in all cases :)

[@_Noopy_]

Finally a physics channel that doesn't dumb down things/rigour...... Please make more, encore! I'll pay for your full course on QFD.

[@vtrandal]

Thank you! I became Patron today. Your teaching is absolutely refreshing.

[@PhysicswithElliot]

Thank you so much Vincent!

[@Danial.Ghamari]

Your video was absolutely incredible. Thank you so much. And yes, I am tremendously intrigued by the other things you mentioned at the end and will deeply appreciate it if you make videos on them as well.

[@feynstein1004]

Wow this was really well done. Although I found it to be a bit too advanced at times. Will have to give it a few rewatches 😁

[@frequency8612]

I really wanted to thank you because you pass by the mathematical developments in a logic way that really help to understand

[@MikeOxmol_]

Elliot, I love you videos so much that if you released a series of 20 lectures on any given topic I would watch them in one sitting. Absolutely brilliant stuff. On a side note, what's the tablet/software you use to write the formulas in you videos (at least the previous ones)? The letters always seem so nice and even, lines are always straight etc.

[@PhysicswithElliot]

Thank you! I made those with the app Procreate!

[@NovaWarrior77]

This man has so much strength.

[@bingusiswatching6335]

Absolutely amazing. I love how much you get into the nitty gritty of the mathematics. And your videos explain it so well, especially combined with the visuals. Great job man

[@PhysicswithElliot]

Thanks Bingus!

[@paulschmidt4095]

Thıs video is just awesome. Contrary to other pop sci videos that just tell stories and doesn’t explain anything this video helps people conceptualize both the mathematics and the logic behind this theory. Whoever makes these videos is pretty good at their job

[@kka107]

I would love to learn more about the details of spin-1/2 (Dirac) and spin-1 (Maxwell) fields. I also love to see how the 4 del-based Maxwell equations can be re-formulated in such an elegant way. I thought Maxwell made it elegant enough. Apparently not. I love your approach to teaching physics. And I love that you spend a great deal of time on classical formulation rather than jumping to quantization. This way I can get the big picture and compartmentalize the key ideas in my brain before I get into the implications after quantization which are much harder to grasp or visualize. I am an engineer but have learned a great deal of physics on KZbin from people like you. Your channel is unique because you’re not afraid get into the math. Thank you.

[@PhysicswithElliot]

I really appreciate it Koorosh! Glad it was helpful!

[@fazilnajeeb]

hEY Elliot, first of all, i wanna thank u for making this video. This video was sort of a semester worth of content so beautifully presented. Keep up the quality. Also it would be kind of u to make more of this field theory videos. It surely be very helpful. I know its a tremendous work, but this is my request.

[@PhysicswithElliot]

Glad it helped Fazil!

[@mikstern5471]

Thanks for the fantastic videos. I would love to learn more about field theory and in particular about Dirac’s equation.

[@jonathanalexandremorazalme7495]

I'm taking a one-semester introductory QFT course and your video just appeared in the recommended videos. I found it amazing! I've already subscribed to the channel to wait for the sequence!

[@arasgoshayeshi9156]

The fact that i can even understand these stuff as a person who has just started physics shows your talent😂

[@martineli15]

I love when the math is presented because that's the true lenguage of this topics. Very cool!

[@sbrunetton]

it's a king of magic !!! Thanks for these beautiful explanations !!!

[@joelcurtis562]

Amazing pedagogy here. Yes please, more field theory videos!

[@alkiviadiskaminaris1594]

This channel is exceptional.

[@gabrielmotterjonk559]

This is the best presentation i've seen so far of Field Theory. Wish i had it earlier on my studies of the subject. I will certainly recommend this video in my department.

[@trtess]

Yes, more field theories. All of the field theories.

[@christopherkulink3091]

Wow, I love it, I think you just filled a couple holes I had in my understanding, and answered some questions I’d actually been wondering about for the last month or so. All in all this was not only great in that regard, but I think covered the math pretty well and in such a way that I’m going to have to reference and rewatch this video several times as I keep absorbing everything here. Great work!

[@PhysicswithElliot]

Glad it helped Christopher!

[@noahwilliams9231]

This video might be the best on KZbin

[@namehkoudsie6075]

This is amazing mate, one of the best and simplest ways to introduce such a complex topic. Cheers!

[@jaimeduncan6167]

It’s the cleanest explanation I have ever seen.

[@SquashyPan]

This video is gold and a deeper dive in QFT in a similar fashon would be even more gold

[@alifeleparanj3688]

I'll definitely be a patron to find more videos on field theory. Your channel is awesome

[@sungbeom8796]

I'm graduate student and really enjoying your series nowadays :) If I would go back to the past, I'd say myself watch yours.

[@danielxf1353]

Amazing video, love the way you present the math!

[@saudyassin5352]

Thank you so much for digging deep into the mathematics and showing all the intricate details. I am very excited for the course that you will be me making about classical field theory and Lagrangian mechanics. This course would be of great benefit to me since i am self studying physics during weekends when i don't have school work. High school physics does not bring me closer to understanding the fundamentals of this universe.

[@PhysicswithElliot]

Thanks Saud! I'm very happy they've been helping!

[@marcaurel1830]

I'll take a course in classical field theory next semester and quantum field theory eventually so I'm definitely interested :). Great video btw

[@PhysicswithElliot]

Thanks Marc!

[@tornadospin9]

I am currently learning physics from an algebraic standpoint and have taking Calculus BC. I do not know the nature of partial differentials or physics with calculus applied to it so I do not follow along. However, this looks like amazing channel to follow for once I do learn these topics. You bridge the gap between Newtonian to Lagrangian and introduce field theory. I look forward to returning then

[@PhysicswithElliot]

Try out my help room videos, which are more introductory! They still use calc, but if you're taking a calculus course you'll hopefully be able to follow

[@namitshah9535]

This channel is good I understood this easily. You just have to know basics physics and calculus and you can understand the math.

[@danjunker3920]

Excellent whirl wind tour. It helps me understand the big picture behind the stuff I’ve studied.

[@samanthabuck3978]

Would love to see a follow up video outlining QFT. Very concisely explained; well done!

[@DmitryAblov]

Just say 'Thank you' - says nothing. It's really amazing, interesting, well prepared and illustrated, and clear for understanding!

[@mihagolod2393]

Incredible that we have access to content such as this video. Thank you very much!