Visualization of tensors - part 2B
HTML-код
- Опубликовано: 18 дек 2024
- Part 2 is devoted to the electromagnetic tensor and deals mostly with this example. You can safely skip to part 3 for a more general tensor discussion.
Part 2B continues explaining how a sphere with arrows visualizes the electromagnetic tensor. This time we move to a 4-dimensional space, and show how now it can represent both the electric and the magnetic field. We show how different coordinate systems can cause it to change from electric to magnetic and vice versa.
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
Next up: a new sorting video. I plan also more parts in this series. Part 3 will continue with a more thorough mathematical definition of a tensor, and additional examples from physics.
I cannot wait for your part 3: it is really innovative in how it intuitively visualizes tensors and I am really curious to see how you visualize and motivate covariant transformations, also with Lorentz coordinate transformations. I never found anything so clear and intuitive before. (I do not understand how physics and geometry book define themselves as such when they do not have any single illustration or picture: is it for printing costs? I might be called naive but for me a picture is way clearer than 20 pages of formulas with Einstein convention that make understanding extremely difficult. Of course you need formulas and theorems to deepen comprehension, but a sane intuition albeit initial is essential.)
I'm waiting for part 3
Take your time, i'm sure it will be worth it. Thanks for your videos :D
Love the explenation, thank you!
plz do be faster..
Perfect, can't wait to the next episode!
I have actually been keeping an eye out for this upload. This series does a better job explaining tensors in a physical context than anything I have seen before!
Absolutely brilliant explanation, hands down the best video on tensors 👍
I am a physics major and was having a hard time visualising tensors. This series has been incredibly helpful. A video on tensor calculus would be super awesome. Thank you for making these videos!
I can't wait for the next episode! Best wishes & many thanks in making these!
Absolutely out of this world!
Thank you for the huge effort.
您的视频给了我们相当的震撼！希望您把这个伟大的系列视频继续做下去，尤其是协变变换和洛伦兹变换。
What this visualization can say is that electric and magnetic force are the same force but using two perpendicular coordinates.
It also reminds me what I was told about complex numbers. A polynomial can have more solutions if you extend in another axis.
9:44 For a second I've thought if you spin it just right you can give a partially exponentially infinite power or it will start moving downwards in time. While it's obviously impossible, I wonder what's the implication of this observation.
In the Euclidean picture, it would seem the particle could go backwards in time. However, we will see that for a relativistic, Minkowski space, the particle will always move forward in time with the speed reaching a limit of c. It's a cool visual!
is this the way Maxwell figured it out? is this the way Albert Einstein formulated relativity theory?
@@kevinesh maxwell no, and synthesizing others' ideas without having this unifying perspective on the mathematics meant he was only able to make the essential contributions he is known for after doing a massive amount of work for which he isnt
einstein yes
this was amazing, i hope you continue the series!
The goat posted!!!!!
Yo this guy is severely underrated when it comes to explaining tensor in terms of physical systems !
YOU GOT A SUB MY MAN!!!!!
Dude thanks for these cool animations, I can finally understand it at least in principle. In fact, yesterday I even had a friend ask me about the general form of the electromagnetic tensor as a matrix and I could give him an answer I was satisfied with
I just love this and must watch again (and again, and again).
I'm very impressed by your ability to explain these things!
Please continue with the next episode, i NEED it i understood more by watching this series than at university
I think your method of displaying tensor is realy nice. Maybe you can make a video that explains the gradient of a vector field, which returns a tensor for each position. I think that would be a very helpful visualisation of the concept.
I love your series on tensors, udiprod. I am making a series of videos on continuum mechanics and this is very inspirational ❤
Please, keep doing these videos! You are making an wonderful job!!
Can't wait to watch this with full dedication to something I have absolutely zero understanding of
amazing explanation🤩🤩🤩 continue legend
amazing series. really impressive visualizations.
@6:40 I think units of each axis should be velocity (displacement/unit time). There cannot be time axis as these are not space time co-ordinates, but velocity co-ordinates. So, If you add a time axis, it would represent linear change in velocity (constant acceleration).
It might be confusing due to sphere that goes into the time component, it should probably be a cylinder with axis in t direction and x-y axis plane representing velocity magnitude and direction.
Coordinates after @7:44 with time component make sense as they represent actual spacetime.
Probably I am not getting it right. I will think more over it.
amazing video, thank you so much for doing this series!
Awesome series, thank you!
You cant set the standard för videos like these THIS high and then uppload this slow. I NEED your videos to complement my watching of standfords lecture series on general relativity
Thank you for making this video! Keep up the good work : )
Это прекрасно ! Спасибо
Wait, if you were to map out the acceleration of the particle by the electric field would it trace out a hyperbola?
That would be awesome, because it would sorta make sense that the tensor “rotates” the trajectory either way, but rotations in temporal directions are hyperbolic bc of the Minkowski metric?
Wow, we're really getting deep now.
Finally! thanks
I've been reading Schaum's Outline on tensors for fun, and I appreciated the more algebraic approach. I'll have to rewatch this series to get myself a fuller picture!
It didn't click for me that the difference in definitions of Contravariant and Covariant would make the tensors transform in literally opposite ways (at least as visualized here), despite seeing the algebra.
Nice stuff!
So, that's what it means for electric and magnetic forces to be a bivectorial (rotational) fields in spacetime algebra (Clifford Algebra w/ signature [1,3]).
wake up, new udiprod video just dropped!
Are these tensor concepts same as the one used in machine learning (TensorFlow) ?
There's some similarity. In machine learning a tensor is simply a multi-dimensional array.
I like to think of velocity vectors in terms of their homogenous coordinate vectors, since time is a dimension but is independent of space whereas space is dependent on time
Very cool
bro holy shit this is an AMAZING explanation
me on my way to model anything I can metrize relativistically:
🧠
👁👄👁
I was a bit confused in part 2A, but completely lost here
Watch it again. This time pause the video after each concept is explained and picture changing the valuse in your mind. That's what helped me
can you visualize cocktail shaker sort?
Which tool u are using to visualize these phenomena
I'm using Maya.
0:56 it looks to me like you incorrectly referred to particle's kinetic energy as "power", while power is energy per time and not necessarily proportional to speed squared.
The power shown in this scene is proportional to the velocity, not the velocity squared. The rectangle shows the velocity squared, but the value of the power shown follows the formula that power is the inner product of the force and the velocity. In this scene the velocity is either in the same direction or in the opposite direction as the force, so we get that the power is simply the velocity multiplied by the magnitude of the force.
I could follow it the first 8 minutes. :D
8 months later ,where is the next episode?
It should be ready in 1-2 months.
I think at 15:08 you incorrectly state the XZ plane for B-field, I think you meant YZ
interesting video
what does a particle that rotates through a magnetic field and passes through a hoop look like to the other observer?
The focus of animation was to plot the rotation (acceleration) of eletric force and deflection from a direction, but to plot helicoidal motion we'll need all three spatial directions, so we can't plot time. Therefore, it's a whole new visualization, showing lengths' contraction all that.
@@linuxp00 yeah that went completely over my head, maybe I should stop watching these videos
@@kylaxial they're fun to me, but yeah, maybe we should take a time, once a while.
I need more.
So why can't we "rotate" a tensor to create a gravity field? Why does this only work for electric and magnetic fields?
Thanks
Finally
I don't get why "time force" should be interpreted as power
It does a "work" pushing a particle over space, giving it a veleocity, and that push gets stronger or weaker over time. Work that changes over time is the definition of power.
no way an upload
Ow, my brain.