The Spacetime Metric 

Far and away the best explanation of the spacetime metric tensor I’ve seen, over 40 years of doing this

Exceptional work. Definitely one of the best on youtube.

Subscribed. My favorite moment was when you artfully explained the geometry of the space time map …” is rather a map of world events which are merely ordered in space and time .” 🤯🤗Thank you.

Incredible video! Really gives me a precise intuitive roadmap should I want to deeply learn the mathematics of GR. I’ve been searching for something like this for awhile and seems like a first of its kind.

Please keep doing what you are doing. It is really wonderful✨

Great use of maps and globes to keep it grounded in something familiar. Cool to see how Einstein keeps company with people like Ptolemy and William Clark.

Dear Dyalect. You're work is one of the best on RU-vid and with this great quality it will grow very big without any doubt. Bravo 👏

Simply a great explanation for a very difficult topic.

Man, this should be shown in IMAX, the best sci fi movie ever made! Aaand.. I'm going to watch it again. Also I hope there's a sequel, with quaternions and stuff. Maybe even a trilogy!

This is the best explanation I've seen for the Metric Tensor. It acts as a translator that translates the language of the terms in the metric tensor that are in a mathematical language I previously didn't understand into a language I do understand.

Great series especially for someone like me who doesnt have all the underlying mathematics down to understand something like General relativity

Very nice work on the visuals and modelling!

WOW! That was a great journey. Thank you for explaining that so well...

Appreciating my first "ohhh...I get it" event at 3:18 -- nice lead-in to that.

I must ECHO the sentiments of all others - phenomenal presentation both the gestalt and production! Bravo!

Totally brilliant. I'm eagerly awaiting the next video in the series. But I can see you put a lot of work into these videos and it takes a long time to make them. One tiny improvement, the 'fun aside' that popped up was hard to read. Please make any fun asides in future videos easier to read. Of simply put them in the description.

Simply excellent. Thank you.

Phenomenal presentation. Specifically the great combination of beautiful visuals, slow dialogue and supporting mathematics. Other physics channels don't offer this level of indisputable truth of how our Universe works. Simply brilliant👏

This is the most incredible didactic effort ive ever seen. You guys have to be awarded for this.

Excellent work , Keep posting

That was absolutely brilliant. Thank you so much!!!

I watch so much universe and space / time stuff, and so rarely do I actually feel educated. This was amazing and gave me so much context to integrate into everything I had previously listened to. Instant subscribe.

That was a superb video, it gives a good intuitive understanding of what the space-time metric is all about.

Great job ..keep up the great work and release more videos more frequently 👍

Great Illustration.

Just subbed, So much hard work went into these videos, keep growing, love from India.

Always waiting for new India. Thanks for giving good insights.

Best vid of the SpaceTime metric on RU-vid

Fantastic video animations ! The intro I have seen yet. Would LOVE to see similar treatment of the Riemann tensor.

Thank you, Dialect!

Waiting for the next videos with the complicated stuff made simple!

The most intuition-compatible essay about this very important and complex issue I ever found ! Thanks a lot ! To me one didactic problem remains, in fact AFAIU the one that imposed the conflict in the highly controversial video on misunderstandings among multiple contributions on gravity that can be found: What exactly is meant by "locality" or specifically "locally flat". (This potential ambiguity lurks in some corners of this video, too, as Narfwhales explained me, personally.) The rather easy to see conflict is that the curvature of a sphere is the same everywhere (unequal zero i.e. the 2nd derivative never vanishes), while the (Euclidean) metric of the sphere needs to be considered "locally flat" (i.e. approximates that of the tangent plane, as you always can find coordinates such as the first derivative at that point vanishes). In curved Minkowsky space in GRT this results in the inability to find s shortest curve between two events and hence (other than in SRT) there is no well defined spacetime interval number, while the spacetime length of any curve is defined an independent of the observer. (BTW.: in SRT the spacetime interval is not calculated really differently than the length of a spacetime curve in ART, the algorithm just can be simplified a lot.) -Michael

Great explainatory video!

Absolutely amazing! 🤩🤩

Crystal, elegant, and enlightening! Thank you for educating and delighting so many with clear devotion to your craft here. So clear!! Also clearly so much precise and careful work, but so worth it for such a product we all truly appreciate in the end. Hoping you do many, many, many more! Amazing! 💗

Thank you for the video.

Very useful video!

Great job. Thank you

Outstanding video and superbly narrated. Well done!

What a great video! Thank you so much 😊🎉❤

Love your content and the quality it is presented in! Can't wait to see new stuff coming :)

My favorite channel now

I learned so much! What stunning visuals !

Loved it!

Thank you for posting!!

Amazing videos !! thank you sir !!🤗✌❤

Elegant, sophisticated, clear and classically modern . Bravo!

Guys, you put things SO brilliantly clear, that even a dumb nuclear physicist like me can understand. thx very much! 👍

A dialect video!!!! What a day !!!!

This is a very good presentation in the subject. Keep up the good work!

Brilliant Work!

Wow, excellent video!

Wow. Your videos are so well done. They are really brillant to get a visual intuition of one of the most fascinating theories of physics. Thanks a lot! I am really hoping you will produce more videos.

Thumbs up great video!

Good honest information is hard to come by these days. Thank you. It has been a pleasure watching your Uber biased videos.

Keep the great work up!

Just fantastic!

Thanks for your videos, especially the “why don’t we understand relativity”. Now you talk about the space-time “distance” between 2 observers to tell that their coordinates systems can be skewed between one another. But indeed I think that you should talk about their relative speed to talk about that, don’t you ? Hope you’ll continue to do this good job !

Superb !

Wonderful videos. Thank you for them. Any suggestion of bibliography which follows the same lines of reasoning but showing all the detais? Regards from Brazil

Absolutely incredible

Wow nice great work

Great video glad this showed up in my feed, I'm trying to convince a friend of mine that spacetime exists, and is affected by gravitational potential, and speed of course. Just hard for me to describe when he won't watch videos detailing how it works.

Thank you! After so many books and videos finally somebody explained it perfectly clear and understandable! Impressive work! Better than at any A league university!

Thank you so much for your submission! (final video announcement with winners / runner ups out now, by the way)

These videos have been great! Getting an MS in EE I wish I had these descriptions back then. Instead of a pile of matrix equations with almost zero explanation.

Amazing content

Nice video.

At 1:42, I fell in love with you. This is an amazing video. Very high-quality, clear, and concise, graphical and mathematical projections. My goodness, with videos such as this one, you could teach the derivation of the General Theory of Relativity to 6th graders. I wish it were 3 hours long. Thank you!

This video is too good to be true, thanks!!!

Bravo👍👍👏👏

Excellent explanation and summary. In the end, it's all geometry. More or less easy to visualize, difficult to explain mathematically.

I honestly thought that I had to get abducted by aliens to get an explanation of the universe this good. Can you please do a video on the Schwarzchild metric? Some of the boring videos on RU-vid for that topic are destroying my soul.

Hadn't seen this. Really well explained. Will you maybe cover Christoffel symbols in a future video (like this)?

fantastic

Very very thankful for this matric tensor linked to GR videos. Since you have GR your units in light years & light second. But what is the limit in 4D surface matric tensor can be used. Smaller unit like plank length , is any deviation of geometric symmetry acts?

Thank you for sharing your understanding, very nice work. Now I wonder, what would be the unit of such spacetime distance ? Does the idea of "unit" even holds here ?

You are fantastic! This is the most amazing explanation video I have ever seen.

Fucking beautiful. Thank you so much. I did a General Relativity course at university and they never taught me this basic fact!

Hey, great Video as always :) I am interested in the name of the song that plays during the time period around 9:35. It reminds me of a game i used to play as a child.

Great video.May I know why space time is in hypobolic plane? ds^2=dt^2-dx^2? Why minus sign? Thx

Unrelated question, but what text-to-speech software are you using? It's really really good!

Wow I've spent the last month going through Special Relativity in developing the Big Bang Kilonova Hypothesis in order to find simple explanation about how the metric sign flips from negative to positive in the consideration of superluminal velocities. This before showing the importance of how inside a black hole the signs flip and why this so important in well defining the anatomy of a field. Nice one chaps.... don't mind if I do a bit of plagiarism?

How do you make the visuals for this series? Blender?

Quoting Stewiesaidthat - Space and Time are two separate frame of reference. Clocks are instruments that measure motion in space. Combining the two frame to believing that clock measures time is what creates the paradox. Space-Time diagram? That shows one person is experiencing more space in the same amount of time.

Best till now

@dialectphilosophy But why the minus sign? You said “so it’s hyperbolic” but why must it be hyperbolic? Amazingly clear video overall 👏 but I felt the minus sign explanation was hand wavy

I can't wait for you to describe a gravitational field with a metric tensor

Thanks!

How do you explain the difference between atomic clocks from the ground to the sky?

It reminds me of statistics, with the symmetric covariance matrices between coupled random variables. But why is it a symmetric 4x4 matrix? What is the significance and meaning of the off diagonal entries there? I would really expect it to just involve 4 partial derivatives, if gravitational potential is a level function and gravitational field experienced is just the gradient of that, why is there need of a 4x4 matrix in the first place? Though it isn't as crazy as the stress-strain tensor, that's a 4x4 matrix that I would have expected to just be maybe a mass density at that point and a velocity vector but I don't understand at all the role of a 4x4 matrix in describing it.

Great explanation! Just a little suggestion, I think you should make the background music a little louder, to the same level of your "Demystifying metric tensor" video. Then it would be perfect in my opinion.

Steppin up the game! Good job - if you need a narrator I am your man - I have a rare Irish DIALECT

Bruh, thanks 4 the grounding. I'm C, A, T, smart, but this isn't my field. Just a passion 2 entertaining myself since I gave up TV over 3 decades ago. I've been doing brute force calculations w/out. An understanding anchor points in reality. This series is phucking awesome. The meaning of what I have been studying for years has suddenly hit me like the hot kiss of wet fist. Groovy 2 dah MAX Dahbig Friendly Satanist, tommyj

In 1965 I was 14 and read a book on relativity. It had the Lorentz transform on every page. I understood nothing, but got an A on the book report. I still don't understand it.

Danke!

I recommend you look at eigenchris series on tensors and general relativity if you are interested in the mathematics involved in GR.

17:28 This the part in all of this that is problematic for me. It appears to take a 3 dimensional space and then tags a time dimension to it. I cant find this 3 dimensional space in space-time to begin with. Is this meant to convert space-time back to some kind of Newtonian representation? This appears wrong :( Is this some kind of Newtonian 3D + a time dimension? > Let me clarify what I mean here. This representation appears correct to the geometry that has been used in the std model for ~70 years. But the initial geometry used for relativity SR space-time seams to be incorrect. I am attempting to work out why...

How do you make your graphics?

Can you provide some examples for the spacetime metric? Something other than dx, ds, g?