The Maths of General Relativity (5/8) - Curvature

In this series, we build together the theory of general relativity. This fifth video focuses on the notion of curvature, and the different tensors that are used to characterize it.

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Alessandro Roussel,

[mathdash]

This is such a great channel, I hope to see you guys grow

[mikip]

3 totally different concepts that make General Relativity a difficult subject:
1) We work in 4 dimensions.
2) The dimension of time has a totally different behavior than the spatial ones you learn geometry on.
3) This 4D space-time is not always flat but can be curved, and the curvature might be intrinsic (no need for a 5th dimension where the 4D space-time is embedded and curves).

On top of all of this, you have to choose coordinates systems that might be as weird all the above concepts.
These are all different ideas and all work together at the same time in General Relativity. Awesome work explaining some of this mind fuckery! You are an incredible educator.

[jeanduplessis]

An important point is that the formula at 7:55 is only valid for orthogonal coordinates(as stated), but the formula at 8:01 is true for any coordinate system and is the general definition.

[roccofitel]

*Sees Premire Time.* This is an active Series! My mind was being blown and absolved all at the same time.
I sincerely WISH this was available 15 years ago. It makes much sense.
I can't stand it I'm ready to jump out of my own skin so many conceptual walls were being knocked down!
I feel so tingly!

[prabha-t]

You are doing a great work. The intuition behind the mathematics is really important.

[guanxi]

Best series on GR ever. Logically sequemced and concise explaination of key princples.
I suddenly understood GR which I failed to do for decades. Many thx for that wonderful Christmas present!

[kshitishp]

Bro u are the only teacher I found in my whole life who can teach relativity to even a 10 std student..ur my favourite and love you bro...👍

[dritemolawzbks]

It took years to understand General Relativity. I wish this was available a decade ago. I wonder if this type of material would be available if there were no lockdowns.

[stevenschilizzi]

Absolutely brilliant! Richard Feynman himself would have applauded, he who was so apt at explaining complex concepts in a clear and engaging way. It really makes you want to go back and listen to it again to make sure you understand every bit of it - at least, every bit of what’s presented.
Thanks again for taking the trouble to make this effort - it sure isn’t wasted.
Btw, The University of Western Australia has a program to bring Einstein’s Relativity to school kids (in high school), which seems to be quite successful. I am sure they will find these videos very useful.

[gncollaz]

2:14 Note that the upper arrow moved to the right keeps pointing to the same "who knows what" direction, and the lower arrow moved to the right does not have the same behavior.

[ismaelcastillo]

The quality of the Video is simply gorgeous. You've made such a good work

[antonios]

I consider these videos a great gift and I would like to express my gratitude.

THANK YOU!

[imagine.o.universo]

Hello I am a bachelor and this was the first time I formally study general relativity. I can say that your work helped me a lot! It was brilliant! I believe this is the best material on the internet to explore the concepts behind this subject.

[seanspartan]

Oh wow. I've never really understood curvature until now. Thank you!

[tornadospin]

As a high school student watching this, I don't necessarily understand the math. I understand the math and notation in small pieces of equations but when woven together, it is beyond my current understanding due to my limited knowledge in math. However, though I may not see the fine details in the mathematics, I understand how each piece of the equations (like the metric tensor and the Ricci tensor) plays a role in the motion of objects and the general ideas being set forwards. It is very hard to craft lessons and explanations in that way, where both experts and novices get something out of it, but you have done it perfectly. You are incredible and I can't wait to see more! Have a great day and keep up the fantastic work!

[mxk]

Even though it's so hard to grasp and understand... I didn't skip evn one second throughout this series.... Just because of your way of teaching!!!!

[dgareandro]

This gets Crazy complex but exponentially more interesting 🧐🤔
Thanks for simplifying and explaining to us so well such a fundamental topic.👏👏👌🤓😁

[angelan]

just wanted to say great job with this series! i'm in high school and find your explanations amazingly clear and cohesive. keep doing what you're doing, we really appreciate it!

[MyNameIsToGoHereNo]

I LOVE this video series so much! Can wait for the next installment. The visuals with your fantastic explanations help to demystify one of the most intimidating topics in all of physics.

[michaelsatkevich]

So clearly explained, it feels like I’m cheating somehow. I’m just starting to learn GR and I seem to have landed on the big ladder square of Chutes and Ladders. Thank you for making these videos!
If anyone wants the curvature tensor deep dive, eigenchris does a great job also.