The Meaning of the Metric Tensor

In the follow-up to our prior video, Demystifying the Metric Tensor, we continue to explore the physical and conceptual intuition behind the complex mathematical object known as The Metric Tensor, whose crucial role in the General Relativity, requisite to understanding the theory, tends to be easily obscured by abstract ideas and mathematics.

Contents:

00:00 - Introduction
00:54 - Spacetime Cartography
02:30 - Maps / Coordinate Systems
04:00 - Bar Scales / Metrics
06:03 - Spacetime Distance
07:30 - Topological Transformations
08:39 - The 2D Metric
13:58 - The 3D Metric
18:39 - Conclusion

[alemorita]

I did my undergraduate research and master’s on GR. Had I seen a video with this quality back then, I wonder how much faster I would have grasped concepts in GR. Fantastic video, explanatio, and animations!

[eigenchris]

Another great video on the metric. I've been through pages Schutz and MTW, desperately trying to understand things. It really helps to have a video like this to consult first.

[MrAguc]

This is a fantastic video, with well explained concepts and perfectly illustrated! I have a PhD in Physics and a master in Mathematics but despite all this, I have never seen the tensors concept so well explained. Other videos are always focused in the matematical operations and interpretations but here you can see the how it relates to real world. You make it so simple in this video that I will recommend this to my students!
Your series are a very welcome addition to explain the beuty of Physics and Math!
Please keep the excellent work and I will keep helping you as well.Thanks!

[jrv]

Wow! I rarely write any comments in Youtube but I must say the level of detail and simplicity with which you describe these concepts is astounding. Hope you get millions of subscribers soon, not only you deserve it but they would hugely benefit from this content.

[chyldstudios]

I'm astonished at the level of detail in this video. Well done!

[worldwithinadream]

I have bachelor degree in physics and I find this metric intuition as clear as it could be. Better than in any book I read.

[jmchez]

When Professor Goodstein of Caltech got a grant to film his lectures and use the latest 3d animation back in 1983, he created one of the greatest teaching tools in physics still fantastically useful to this day, "The mechanical World and Beyond". I've been wondering for a while how much better the animations could be done with today's technology. Frankly, not that much better. but your videos do fill in the gaps in some areas and are a worthy successor to Goodstein.

[nemvus_]

The amount of this video that is 3D animated is impressive. I imagine it takes a lot of clever work to get the 3D shapes to behave that way in the video. Excellent quality content. Needs more views.

[stevewhitt]

This was amazing. After years I finally get the intuition.

[HassaanFareed]

How can someone be so perfect in explaining such a difficult concept. Your order of explaining things is perfect for the proper understanding. And I can understand how much difficult it is to produce animations of this quality. Keep making such an amazing content for us ❤️

[mikegale]

Beyond brilliant. You really got it down to the brass tacks. Testify!

[nosnibor]

Thanks that was well described - my God the amount of work you put into the graphics. The 4th dimension adds time. Then we need to understand how mass causes tensor to change. Thanks

[flmbray]

What an amazingly simple and straightforward explanation. Although I not a physicist, I do watch a lot of these types of videos, and I've seen explanations of the metric tensor before. But this is the first (and only) one that really made it clear. The analogy to old maps and how they depict a curved space in a stretched fashion for our benefit was absolutely perfect. It all feels so natural now that I'm sure I will retain this new knowledge. Thanks! You earned a subscribe from me!

[elindauer]

The visualizations in these videos are amazing. The whole series is beautifully instructive. Great work.

[stevenschilizzi]

Fantastic presentation. I’m eager to see the sequel. Thanks for putting all this together for us.

[bofink]

Thank You for the very clearly and straight forward explained Metrics and mapping. This clears many problems for me, trying to really understand the General Relativity and Gravitation in a more visual way, than just the plain raw mathematics.

[Maderum]

Wow! The animations and simplicity of explanations on this video blew my mind! Well done sir, well done.

[jack.d]

Newly discovered your channel Dialect. And as someone who's familiar with Special Relativity wanting to understand General Relativity, your visual presentation along side clear, slowed foundational GR language is absolutely brilliant.
I feel it in your video's, your goal and target audience is too teach this subject to people who have zero knowledge of GR. And as someone who feels like your target audience, I must say again, the ways you teach are mindbogglingly sensational!
I'll give you a donation for your service to humanity. You've earned it.

[manymany]

I really like the pauses in narration at the right spots to give me a moment to think through what's just being said.

[MictheEagle]

Pure Gold! This is the school we all needed. Bravo! Keep it coming, and Thank you.