The Maths of General Relativity (4/8) - Metric tensor
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- Опубліковано 13 гру 2020
- 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,
For more info: www.alessandroroussel.com/en - Наука та технологія
How is it that you are able to explain this so clearly?
I am genuinely amazed. And somewhat smarter now.
Ahah thanks I am glad you like it !
I feel the same...I took a GR course last semester and I'm still struggling to come to terms with it entirely..watching this and revisiting it will bridge the barrier.
That backround music keeps me charmed all along the story...
interstellar theme would have taken it to the whole new level.
Yeah bt 3blue1brown bg musics are better for this kind of things.
This is the song!
ua-cam.com/video/3OCqSLc5J-c/v-deo.htmlsi=xUr2N2x6729qd77x
I wish people taught not just general relativity, but also special relativity this way
that might be the future
We definitely see some higher quality educational videos since the Covid-19 outbreak.
special relativity is "relatively" simple. proper courses with deep explanation are better.
@Bhavesh sinha Personally I find minutephysics' videos too simplified. They use analogies that make it easier for the layman to understand, but aren't very accurate for people who know more math
You may search for sl in youtube.There are a lot of info about sl, esp in MIT .
13:34... I lost it! I literally spilled my drink all over me, this was mindblowing!!
Yep that's when I went 100% crazy :D
One of the MOST UNDER-RATED Science channel on UA-cam.
This is why I love UA-cam. Content creator like you makes this platform amazing.
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!
Exactly ! What we call "proper time" is actually simply the measure of distances along the worldlines of objects
It isnt Minkowsky Metric but Minskowsy MATRIX
@@ibmmbi2317 Minkowski metric is the function which determines the distance between two points in the Minkowski space-time which is defined/calculated using this matrix
@@AndrewStarostin Oh ok.
So within this Universe is made up of space(s). What is beyond the universe made of then?
Fantastic! I never seen GR explained so succinctly
Just want to say that your last video which mentioned the geodesic equation sent me down a UA-cam rabbithole which resulted in my learning a lot about variational calculus and Langrangian mechanics, which is was really interesting, so thank you for that. :)
Mind sharing your rabbit hole? I had some confusion surrounding the Christoffel symbols. Specifically, when we obtain the vector de1/dx0, and resolve them into their components, what components exactly are they?
@@hrithikravi8117 Sheesh, I don't remember the specific videos at this point and they're way too far back in my watch history to find them that way, but I just searched "Christoffel symbols" to see if any of the results showed up something I'd watched and I found this one: ua-cam.com/video/1CuTNveXJRc/v-deo.html
I don't remember if it was any good, but it's worth a try.
Edit: Just realized there's a search tool got watch history. I think the above is the only video I watched on Christoffel symbols, but I remember this one on Langrangian mechanics being really good: ua-cam.com/video/SQLxrr9N8zM/v-deo.html
and this one on variational calculus: ua-cam.com/video/SQLxrr9N8zM/v-deo.html
I too went down a rabbit hole of trying to learn general relativity. Eigenchris has a good playlist on tensor calculus and general relativity now I understand it extremely well.
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!!!
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.
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.
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.
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!
This channel is too underrated!
Probably, the only video on UA-cam 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. 👍
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.
Oh man, I never thought I'd be able to discuss general relativity with people. This channel is crazy!
“This is more commonly called ... light.” :D
Exactly, it seems so weird to talk about something crossing no distance/time between two points, but that's exactly what light does all the "time".
*head explodes*
Goosebumps
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
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.
The less I understand, the more excited I get. Damn it! can't stop watching!!!
Thanks! This youtube channel is beyond this world!
Blown away by the quality of these videos. They raise the bar extremely high.
These are insanely complex topics from physics and mathematics perspective... and yet you managed to put them in amazingly simple terms that everyone is available to understand, so well done my friend well done 🤓😁👏👏👌
You're going to make me have a good grade in GR this semester! Thank you so much
Hi friend how are you i hope you will get a better note in general relativity but can i ask you wich Studie in high school are studing i understand all about relativity
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!
This is such an amazing video.. It deeply extends your understanding of the reality with such an ease.
Glad you liked it !
This course is absolutely amazing, it describes the theory very intuitively and precise. Keeping moving forward.
These videos are excellent, thank you so much for them.
For someone first getting into GR, the math and jargon can seem so daunting that learning might seem so complicated that people don't bother. These videos give insight with things most people are familiar with and no doubt motivate people to learn this beautiful theory.
Is this the same order in which mr. Einstein formulated the equations? what was going inside his mind?
This series is structured roughly in the same way we teach general relativity today, as a "finished" theory (no theory is ever "finished" though). But Einstein's journey in discovering all that was very much more cahotic and a lot less "linear". He was also greatly helped by many colleagues. Some of the things in this series were not discovered / studied by Einstein originally.
@@ScienceClicEN i have also thinked that
This is amazing! I am reviewing all the videos of this series because I am taking GR this semester and I am understanding it and loving it :) Thank you so much for providing a means for a simple student like myself to have an easier first approach to these concepts and mathematical tools. Well done :D
This is genuinely an amazing series. Thankyou so much for making it. I'm excited to see the rest of it :)
you are the best physics channel in UA-cam. thank you for your videos. can you make a series about the math of string theory?
I’m so lost, yet I keep coming back !!
I guess I enjoy knowing how did they reach their understanding. (In Theory, of course)
I never thought I'd understand GR, but you sir have done it. Also, the background music fits the mood absolutely perfectly. Keep at it mate.
Excellent. Now I want to know how to integrate the metric tensor over a trajectory on a sphere.
He gives the formula/components in the vid, I'd think it would just be a very simple integration of those
if it's a metric that doesn't depends on the position, its like a ∫ds, like in a circle, ds with constant radius is ds=rdθ => ∫rdθ
Bro, I legit have no idea how you only have 646K subs. Your work is very good, you deserve way more.
I need to pause this right now cause my mind is absolutely blown to bits, I don't usually watch youtube but for the past 3 or 4 days I've religously watched your channel, I have no idea how I found it. But these explanations are the exact thing I've been looking for to quench my thirst for knowledge in this feild of physics.
wow!! Amazing work my friend! Never thought that the math of general relativity would be this easy to understand, and that's because it isn't, yet you make it easy somehow! Thank you for this series.
The satellite example at the end was THE BEST explanation I've ever heard of why nothing moves faster than light and why no time passes when you move at the speed of light. Thank you.
This is just beautiful and brilliant. You are doing an amazing job!
You had my mind blown away at 13:35. I love you man, please keep your channel going.
Even though I will have to watch this multiple times to get an actual grasp, I am a huge fan of these videos. It is brilliantly made. Thanks!
A wonderfully simple explanation for a beautifully complex Theory
Again, thank you so much for this series!
Thank you for color coding the various symbols, it helped me keep track! 🙌
The physics is amazing, but the way information is layed out here is even more amazing. Anyone who wants to teach anything to anyone should strive for this level of clarity.
I thought the previous videos were amazing and the math will only get harder. But damn, this is amazing.
I don't remember the last time I've binge watched a science channel woahh
I’m watching this all the way from Afghanistan 🇦🇫 and I’m loving it.. don’t stop making these and also when could we expect the next video in this series?
Brilliant. What a great way to explain concepts.
Great work! I'm excited to see the next video.
This was amazing. I can't wait for more :)
As usual very well explained!
This is the GREATEST video on UA-cam hands down.
I'm from Houston tx and I started getting interested in science while listening science vids while driving as a way to escape politics and other useless trash.
It's been 5 years since then and I've learned deep concepts on relativety, quantum physics, electromagnetism and more.
I thank you from the bottom of my heart for the gift of knowledge and a continued love of learning.
I never thought that I would be able to learn this stuff.
That's a brilliant way to illustrate metric tensor...👏
13:55 "Nothing moves faster than light."
We hear this everywhere, but hearing it after being shown the reason has a different feeling to it, a stronger impact 😁.
I've actually watched the whole series in French many times and I'm in school to learn about GR and QM/QFT so I was already familiar with that concept, but that line still gave me goosebumps 😁.
I'm so happy you are making those videos...
Very BEST explanation of the Metric Tensor on You Tube.
Love these type of explaination ♥️
Applaud this systematic approach! Sharing with my friend circle
Wow, your videos really are something else. This made the intimidating equations and concepts really intuitive, thank you
Thanks ! Glad you liked it ! For the moment it's not planned but maybe in the future. Quantum physics is a really broad subject compared to General relativity, so I might do videos in this format but about specific subjects.
Brilliant explanations and I now finally understand concepts I have tried to read elsewhere
I watch this video through concentrated mode and diffused mode. It helps !-)
Best playlist of all time on GR😍
I'm waiting for all the 8 videos to come out so that I can share them indefinitely with all the souls who've expressed interest in understanding GR to me
Relativity.
I get older, they stay the same age.
-Albert Einstein
Space travel - The women get older I stay the same age (cries in Mathew McConaughey)
I love this channel it's brilliant
This series has been a great introduction to GR for me. I haven't studies it properly before this, and now Im learning it on my Christmas break. Thank you to the people at @@UCWvq4kcdNI1r1jZKFw9TiUA.
Really nice presentation. The only thing that's a little strange to me is showing time horizontally and space vertically. Having worked with space-time diagrams before, that was a bit unexpected.
Hi!
I have no words to describe how cool your channel is.
Marvellous, deeply thoughtful with clear explanations of extremely sophisticated abstractions.
Would you excuse my poor knowledge of physics and explain, how GR metric tensor relates to a tensor in quantum physics / computing? Is it just the same concept of snapshotting the precise moment or there is something more?
Thank you.
Wow! I didn’t expect coming to realize why integrals are so important. Such a great video.
best GR video i have ever came across :') , thank you sir
Hope to get more videos from your channel love it
This channel must be on top list and it's our future ❤️❤️love from India, keep rocking
Excellent explanation. Thank you.
Thanks another very professional video!
now it makes sense, tahnk you, I had modern physics in college and my professor wasnt even close of explaining the tensors to us, I was so confused because I really didnt know why nothing could be faster than light, thank you
Subscribed. Wish my physics lecturers in uni had explained things so well for then I would have understood it back then.
Originally, I only just wand to learn something about Reimann Manifold, but this fantastic explain of GR addicted me instantaneously when I started the video, after which let me had to firmly believe that we are living in a virtual word.
This concept of tensors and how they need to be integrated along the path is phenomenal. I was concerned as to how to compute things on a non Euclidean space with our math and coordinate systems that are flat. But thinking of the tensors as a "field", in which each point is the error between the actual coordinates and our (which is actually the one who's curved in comparison to the real world) is brilliant.
I am currently following this series by programming on an implementation of non euclidean spaces. Right now I have a "black hole" that you can orbit!
I may show you in twitter oncr I'm finished playing
yeah non euclidean geometry as well as riemannian geometry and conics are a bit hard to visualise on a regular cartesian plane
Great class, thank you.
Brilliant description of the Metric Tensor. Please do videos on how a constant speed of light = a block timed Universe.
Best advanced physics UA-cam videos ever.
This man is great
Rien à dire 👐👌
What the hell .... this is so awesome .... really really simple while packed with all the details ... thank you very very much ....
Wow...!!!! Excellent....helped me understand the physical significance of metric tensor...thanks..highly appreciated..
This is some great content
Excelente vídeo! 👍
I wish you had shown the derivations from minutes 2:00 and 5:50
For 2:00 check out quadratic forms. Basically the idea is that we can choose a grid such that it *is* the Pythagorean theorem. And therefore with another grid it must be the Pythagorean theorem but with a linear change of coordinates (so for example instead of x²+y², a change of grid gives you (ax+by)²+(cx+dy)², which is a sum of terms containing x², y², and xy)
For 5:50... the proof is left to the viewer :p Otherwise check out covariant derivatives. The idea is that the metric tensor should have a 0 covariant derivative (roughly speaking geometry must stay coherent along the surface), which forces the Christoffel symbols to take this form. The calculation is a bit painful but it's quite straight forward and its a good exercise to do. Try it !
@@ScienceClicEN alright; thanks for the video and the explanations
That last point you made blew my mind :OOO
Your channel is an inspiration of mine❤️
The fact that distance between two point gets smaller when they are when you take it away blows my mind
Thank you for visualisation. In next semester I'll learn GRT and it is really helpful. Respect from SPbAU RAS!)
Thank you so much
What a amazing video
This video gave me that lightbulb moment
Adjust the contrast and sit further away. :)
Gorgeous video
Very good! Congratulations!
Really love the videos! Ok if when you show the equations changing could you either keep up the old equation then introduce the new, or slow down the terms changing.