Visualization of tensors - part 2B
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- Опубликовано: 1 янв 2024
- This part continues with the electromagnetic tensor. It explains about space-time diagrams, then visualizes how the electromagnetic tensor can represent magnetic fields, electric fields, or both together.
![Visualization of Einstein's special relativity [HD]](http://i.ytimg.com/vi/CS7aLVHpeTs/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
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!
Perfect, can't wait to the next episode!
The goat posted!!!!!
I love your series on tensors, udiprod. I am making a series of videos on continuum mechanics and this is very inspirational ❤
Yo this guy is severely underrated when it comes to explaining tensor in terms of physical systems !
YOU GOT A SUB MY MAN!!!!!
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
Absolutely out of this world!
Thank you for the huge effort.
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'm very impressed by your ability to explain these things!
Can't wait to watch this with full dedication to something I have absolutely zero understanding of
I just love this and must watch again (and again, and again).
Please, keep doing these videos! You are making an wonderful job!!
Wow, we're really getting deep now.
Awesome series, thank you!
amazing video, thank you so much for doing this series!
amazing series. really impressive visualizations.
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]).
Thank you for making this video! Keep up the good work : )
Это прекрасно ! Спасибо
amazing explanation🤩🤩🤩 continue legend
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!
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
Thanks
Very cool
I was a bit confused in part 2A, but completely lost here
wake up, new udiprod video just dropped!
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?
I need more.
can you visualize cocktail shaker sort?
Finally
interesting video
bro holy shit this is an AMAZING explanation
me on my way to model anything I can metrize relativistically:
🧠
👁👄👁
I could follow it the first 8 minutes. :D
no way an upload
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.
Ow, my brain.
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.
Which tool u are using to visualize these phenomena
I'm using Maya.
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.
I think at 15:08 you incorrectly state the XZ plane for B-field, I think you meant YZ
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.