I dont know what a tensor is, and at this point im too afraid to ask

Im a level -1 tensor boi. I accidentally found this channel and have no idea whats going on but i watch anyways.

Thank you so incredibly much. The fact that the Electromagnetic tensor is simply defined to be the partials of A and the origins of A was extremely confusing to try and self learn. I couldn't be more grateful for your service. I have been looking online for a while and was so confused but you cleared up everything. You're a legend. Thankyou!!! All your videos too not just this one. I always find myself landing on your videos and they make everything seem so clear and straightforward.

You are the only light that can guide me through the dark alley of tensors and four vectors, will never be able to thank you enough! :')

Thanks a lot brother. This was really really helpful. Again your tensor calc playlist is the best source for its introduction available as of now on youtube. Keep up the great job!

First time I've ever clicked on a video within 10 minutes of it's release

I was in a bit of a rut with my interest with Physics. Well, i've been binge watching your Tensor videos, so, THANK YOU SO MUCH. I needed a gateway back into enjoying this stuff, and you're the perfect level of difficulty/relevence for me. So, thanks :)

Just been revising electrodynamics for my third year exams (which are all online now) here in the UK and I just have to say that the expression for the Faraday tensor in terms of the 4-potential and 4-gradient is just one of my favourite equations I've come across so far in my physics career, it's just so satisfying!

A Hodge star video would be great, especially given this video was just made, it would make a nice compact summary of the different EM formulations i.e the dF = 0, d*F = J forms

Just went over this in final undergrad E&M semester...great timing!

KHaN acadeMy didnt prepare me for this!!!

When is the Dotson Product going to be a thing? Let's make it happen.

I feel so comfortable watching your videos - they are tough and ambitious but I really enjoy how you explain the things in your point of view. I am just an ongoing physics teacher in second semester, but I feel like I should actually do all that epic theoretical deep stuff that the "real" physics students also have to do. I just can't stop asking for deeper reasons of why things are the way they are 😄

Thank you, I finally have a basic understanding of the Faraday tensor that I can build on. You the man! 😊🙌🏽🎊

I’d love a video on how you felt about chemistry - what classes you took, what topics you liked and didn’t like. I am a chemistry major and intimidated by the higher level math of physics but got into physics concepts because it and chemistry go hand in hand in a lot ways! Physical chemistry is scaring me to death :-)

Excellent vids! Can't wait for dual tensor derivation!

This is a great video, it’s very useful for learning about the field strength tensor!

Good explanation.. thanks, Andrew! Just one suggestion: keep the use of spatial indices 1,2,3 versus x,y,z consistent.. for instance, in your final tensor, there's both B^3 and B^x entries. (Actually, this is a big problem in a lot of physics material.)

..brillant , as always..hell job ,doctor Dobson!!!

Thank you, Andrew! This video helped me to do well ( I hope 🤞 ) on my electrodynamics final exam!

sweeeeeet, I saw this in Griffiths and have been looking for a good walk through.

You should introduce differential forms at some point. Then the definition of the field strength tensor makes sense

Nice! We're doing this right now. Great timing

Wow, thanks for a great video! I've wanted to learn about this since I first heard about it!

You need an upvote even though I didn't understand a word you said. Also I miss the Physics Phlogs

I wish I took physics... I ended up taking chemistry and bio to fill my science requirements. Maybe i'll use some of your videos to teach myself.

Thank you explained tensors in a way that wasnt stupid like trying to use twnsors to define cube or problems that arent optimized to be solved with tensors like idk spitting aphere into a mercarder projections because honestly tensors are for turning well sefined easy to understand boundary conditions such as idk spacetime, heat flow, etc. Where there are clear dead stops and complete reflections and so many hardstops that are suited to be solved with continuous functions.

Wow, I watched the entire video -- he is a decent teacher. But mostly, very handsome.

12:52 well that popped out elegant af👌👌

Helped a lot. Is there goong to be a Video on the other field strenght Tensir too?

thanks for the video, very helpful 👍

Amazing video, as always. Please do make a video on the Hodge dual of the electromagnetic field tensor. Also, question: why do we introduce the vector potential? Does it have any uses other than defining this tensor? If not, wouldn't it be simpler just to define the field strength tensor component-wise?

I can't wait till i understand these equations...

I dont know if this is a better question for a mathematician, but so just finished reading Flatland and it got me thinking. Can you do a video on the 4th dimension and how it can be interpreted by us? I that there are some things which have a sort of 4th dimensional connection like using a triple integral to find mass and total electric charge. Are there any other examples or is the concept of a 4th dimensional totally out of our use?

THANKS YOU!! THAT WAS THAT I NEEDED ❤️

Lol I have my advanced classical physics exam on this topic in 3 weeks, literally covering all of this video, ty >3 btw consider using natural units, then c=1 ;)

Terrific video!

Hey Andrew, could you do a video "deriving" the existence of the magnetic field from Coloumb's law and special relativity. I've done a simplified version of the derivation using the trick of a current flowing down a wire and then applying the Lorentz transformation to a moving charge and you can work out that the force is precisely qv(mu_0 I/2pi r), but I couldn't work it out more generally. Say you have an arbitrary E field, applying the Lorentz transformation in a moving reference frame, charged particles should be deflected in unexpected ways, essentially constituting a "derivation" of the Lorentz force law, F_B = qv x B, where B is some auxiliary field that would satisfy Maxwell's equations, and this would constitute a theoretical "discovery" of magnetism. Love this video btw!

Thank you so much ! This is just what i want !

Thank you for nice explanation.

Why do I watch these I don't understanding anything lol.

I think it's called scalar potential only because it is the gradient of a function of R^n->R therefore called a scalar field.

Hey Andrew! Big fan of your videos! Have you ever thought of making pdfs from these topics you talk about and leave a link for them in the description? I think that would be extremely helpful! Thanks

we wunt string theory !!! btw thanks for tensor videos although i think the best way to comprhend tensor is to start by geometric meaning of it ,vectors covervteor and how they transform under change of cooardinates, lowering and raising indesices ones thats done it will be lot easier to deal with any tensor thanks from algeria.

Do you have a good explanation why we wrote all of physical quantity (space component, 4-potential, 4-current, etc) with contravariant indices naturally?

amazing vid boii

Great vid lad

Thank you so much. 🖤

What about squaring it since the tensor squared is part of the maxwell and qed lagrangian

I had my radiation and relativity exam last week, man i should have found out about this vid earlier

Can you give an explanation for the covariant form of this tensor, I tried it actually but I got stuck, the Electric field components get their signs reversed (this part I figured out) but the magnetic field components have the same signs, that I can't figure out

Because of antisymmetry you only need to know either the lower or upper triangle in Fuv

how can I formulate poynting vector in terms of EM trensor?

So, Andrew can we expect in the next video on how to tensorically express Maxwell's equations in two equations, one of which is Stress tensor and one is taking dual of it? Because I couldn't well understood it in my EMT course work?(EMT:- Electromagnetic Theory class)

Hey Andrew. Miss your daily uploads. Anyway can you please recommend a book on statistical mechanics for undergraduate. Thank you.

Please make a video about Einstein notation for 4-vectors. I tried Griffiths EM book, but I find it very confusing, especially when multiple different indices are used. I just don't get anything of it...

thanks andrew

Tnx man,it helped me.

So I'm in honors high school physics right now. You know how it is. When we did the whole W=Fdcosx thing we were to assume a constant force. And we just finished up kinematics, where we were told to assume constant acceleration. And I know that could be useful but it rarely is, right? So, I'm really interested in more advanced physics, which is why I watch your channel which inspired me to take AP physics next year. Being in Honors Physics pains me, because I'm in AP Calc right now, so I know a lot of the math skills necessary to do more advanced physics where you do not have to assume forces and accelerations and stuff and other variables as constant. I also spend a lot of time researching, mainly through youtube videos like yours to understand more advanced physics, not just the really cool cosmic stuff like black holes and stuff. But also stuff that is really relevant to Earth and our everyday life/progression of the human species. Its just frustrating not being able to take an integral or a derivative, when I have the necessary skills. But, really cool physics you got on display on this video, I like how I can mostly understand whats happening as a high school junior. That speaks a lot about how well you know the subject and I really appreciate how you take the time to explain what you are doing to me. Thank you.

The Faraday tensor resembles the stiffness tensor of an elastic material in Mechanical Engineering

Very nice 👍

Hey Andrew, have you seen the Michio Kaku AMA on r/IAMA?

15:38 , Instead of X_(i) , it will be X^(i) . Btw amazing video

Do you need the (1/c)(E^i)? Should it not be be-E^i = (1/c)( d/dt(A^i) ) + ( d/dx(phi) ) ? Just quibbling.

Thank you so much for your videos! Some questions to this one: 1. If you say A^\mu = (..,...) you're actually saying that a component equals a vector. Is this just sloppy physicist style or is A^\mu really the name of the whole vector? 2. Why do you write the indices of the E up? 3. Taking down the indices of the partial derivatives (while regarding the sign), does it just "work" or is it mathematically correct? Because applying a dual object to a "normal" object isn't the same as applying a "normal" object to another "normal" object. ("normal" = not dual)

Sir how to obtain Maxwell s equation from Lagrangian..

Awesome video. But why can't the electric and magnetic fields be represented as four-vectors instead of a tensor?

I'm never going to unsub

Man this is damn good!!

I always made it difficult for the correctors by going for the -,+,+,+ convention instead and stating that at the start of the test/homework >,< It gave me less minus signs to work with.

Ahh I love tensor calculus 😁👍🏻👍🏻

Hey I was wondering abt what you mentioned in 2:49, you were talking about how the terms that make up a tensor equation must be tensors themselves. Is that the case in general? I might be misremembering or misinterpreting but I think this is not the case for the covariant derivative, were to variant terms come together to create a tensor. (Coordinate derivatives aren't tensors and chirstoffel isn't a tensor).

hey ! i’m a hs student who is planning on majoring and getting a phd in something with astrophysics but i can’t take a physics class right now because to say the least , the teacher quality at my school is subpar. i was wondering if you had any books that you’d recommended or any resources i could use to learn some before i get it thrown at me in college ?

Cool

In min 7 you said the curl of the electric field is zero if we have static electric field I think its also true if we have static magnetic field because a moving charge induces magnetic field but only change in magnetic field induces electric field Correct me if im wrong please!

I love it

@15:39, that should be del/delx^i instead of covariant...I think

But how would we know that we have to start from a anti symmetric sensor exactly like that?

A gift from my physics professor: A dipole moment is placed in a uniform electric field oriented along an unknown direction. The maximum torque applied to the dipole is equal to 0.1 N.m. When the dipole reaches equilibrium its potential energy is equal to -0.2 J. What was the initial angle between the direction of the dipole moment and the direction of the electric field? Probably a piece of cake for you but I cried. Have fun with it :)

cool af bro

Hello Andrew, is there a book on Set Theory that you can recommend me? Thanks :)

did you mean to write B^3 as B^z as the component F^12?

🔥👽Awesome. And i have more perspective: We often use 4x4 matrix transformations in 3d computer graphics. The magnetic B-field is located in the field tensor matrix locations mathematically referred to as "shear." 🤯 [CGI uses (x,y,z,w) points and the physics here uses (w, x, y, z) 4-tensor] The Electric Field wasn't "unified" with the "magnetic field", it was collapsed into the electric field as shearing. It shouldn't be called the "Electro-Magnetic Field"... it would be more accurately called the "Electro-Electroshear Field." A change in the electric field is a perpendicular electric shear, moving at the speed of light. The "magnetic field" doesn't exist and is explainable as the electric field masquerading under shear as the "magnetic field", it's the same field acting in different ways. I suggest that they thought it was two different fields because those modes of the electric field must be measured differently and so assumed they had their own distinct "field" or "dimension." A model that i like is that an electric charge is like the displacement of a boat on the field of water. We measure the displacement of boats differently than how we measure the wake of a moving boat. Magnetism is like the "wake" created when that displacement shears with itself (moves across the water). The wake is perpendicular to the direction of change. granted, the the magnetic wake happens across the field itself at each point when a charge is moved. The change of electric potential at each point (from the movement of a charge) shears with itself to create magnetism, so it's 5th+ dimensional. But the boat and wake analogy is an easy way to think of it. If you shear the electro-shear (aka a changing magnetics), you get back to the direct electrical forces. Exactly as expected. In a photon, when at the maximum electrical potential, it would also be at the maximum shear/magnetism. They cycle in unison. This groks with using special relativity to translate between the shear inertial frame and the electro-static inertial frame. there are many videos on TY on the use of special relativity to make magnetism into a relativistic effect of the electric field. Magnetism is electroshear. 💥

(+ - - -) I see you are a man of culture, Andrew.

I wonder if these videos are making him Ricci.

👍😊😊😊👏👏👏

Wait, how is a derivative of a tensor equal to a tensor, since A is a rank one tensor, to get another tensor you need to apply the covariant derivative (the big D). I think that you have been doing that all along (defining these 'partial' derivatives as gradients).

5:32 My professor gave the same reasoning, but this is simply wrong. That there *exists* a vector potential follows from the poincare lemma. You and it seems many physicists confuse the trivial implication that "B = rotA => divB = 0" with the poincare lemma "divB = 0 => there exists an A such that B = rotA"!

you are big smart

Much Physics, such wow, much Math

Do you have a twitter or something like that ?

But isn’t the metric tensor d(-1,1,1,1) instead of d(1,-1,-1,-1)?

haven't even seen it completely i just know it's gud. I literally never clicked so fast XD

I likes da video, but is very basic for me big brayn.

"Not too long video". "Just the definition." *Looks at the video length* Wha-- But not complaining though lol

Pretty sure you were thinking of Levi Ackerman when you corrected yourself when mentioning the Levi-Civita symbol at 19:41 haha

Electromagnetic field go together for physics, electrical and electronic engineers merely watch video as talking how to tensor calculation in electromagnetic field 😂☺️

nice audio

Good video, down with the mathematical snobs ;-) No need for mathematical precision here...it's physics!

As someone who just finished learning algebra 1, what the heck?!?!?!?!??!???