The Maths of General Relativity (4/8) - Metric tensor

In this series, we build together the theory of general relativity. This fourth video focuses on the notion of metric tensor, its relations to the Christoffel symbols, and physical distances.

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Alessandro Roussel,

[Murtaskegg]

How is it that you are able to explain this so clearly?
I am genuinely amazed. And somewhat smarter now.

[injeel_ahmed]

One of the MOST UNDER-RATED Science channel on Youtube.
This is why I love YouTube. Content creator like you makes this platform amazing.

[twinkyfarmr]

Fantastic! I never seen GR explained so succinctly

[robertkesselring]

I've been struggling for years to understand the math of GR. This video series is filling in most of the gaps and making it make sense for the first time in 25 years of trying. Thank you so much!!!

[alexeecs]

I wish people taught not just general relativity, but also special relativity this way

[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.

[pythondemonstrationen]

13:34... I lost it! I literally spilled my drink all over me, this was mindblowing!!

[true_xander]

That backround music keeps me charmed all along the story...

[anupamupadhyay]

Probably, the only video on YouTube to have this clear and precise presentation of mathematical foundation of GR.
This is like a visual supplement to courses on Relativity from scientists like Suskind and Carol .

Awesome work. 👍

[AndrewStarostin]

Took me awhile to understand the meaning of distance by Minkowski metric at the end, but then I finally got that this distance actually represents the rate of proper time. And it is not the same in every direction of the space-time. I feel enlightened now. Your videos are amazing!

[prityy]

In my opinion everybody should see this, truly, a remarkable video! The way it gradually connects all the dots and filling gaps between concepts, bringing them together, astonishing! Thank you very much for sharing this, sometimes I get lost in the formulas, this is eye-opening!

[kshitishp]

Bro I don't know how to thank you..I'm in lack of words to express to you my support..u are the best teacher I have seen so far

[ΠΡΟΔΡΟΜΟΣΠΑΠΑΔΟΠΟΥΛΟΣ-ζρ]

Congratulations!
The correlation (at the end of video) of proper time dτ = ds of movment obsarvator O' with the "external time" dt of a relatively motionless observer O by use only a single square root is astonishing. And the distinction between distances between imaginary, complex and real, in the end is wonderful, because it leads to conclusions of significant natural significance.

[csikel]

Blown away by the quality of these videos. They raise the bar extremely high.

[Lucky]

Just want to say that your last video which mentioned the geodesic equation sent me down a YouTube rabbithole which resulted in my learning a lot about variational calculus and Langrangian mechanics, which is was really interesting, so thank you for that. :)

[rvmishra]

I wanted to know GTR but always hated and feared maths.
But you not only explained GTR perfectly but made me love maths as well.

[nemurerumaboroshi]

This is such an amazing video.. It deeply extends your understanding of the reality with such an ease.

[vasundarakrishnan]

Initially I couldn't understand much of what was going on this series and I was honestly baffled most of the time. I gave up. But after watching the some introductory lectures and gaining somewhat of a theoretical understanding, I came back. Honestly, this series makes a world of difference when it comes to intuitively understanding the theoretical concepts. The animations and the examples you choose to explain new ideas are great. It is amazing I could actually understand after struggling for so long, trying to grasp what the matric tensor is. Thank you for your time and energy in making these videos. I really appreciate it.

[racm]

I am hooked to your videos beyond measure. Been watching them on repeat (and once again a new comes out) in the hopes that I catch something I had previously missed!

Please keep them coming!

[pythagorasaurusrex]

Problem with most lectures about ART (or other complex subjects) is, that they dive deep into the subject without simplifying it. When you read scripts from university professors about that, you get "beaten" by most abstract multi-dimensional tensor analysis (immediate brain death).

But in these videos you get a general glimpse step-by-step without overloading you.
I am looking forward for the rest of this series.