Demystifying The Metric Tensor in General Relativity 

Thank you!

IM NOT A MATHEMATICIAN. And it is still totally wrong. Because I don’t understand the Accuracy. They still Don’t understand how to wORK out a CiRCLE.. 3.15… I would have EQUATOR LINES NORTH TO SOUTH..

If you are a mathematican and probably a nacissist then what is the shape of a point in space using the metric tensor?

@@dialectphilosophy The metric tensor is used for - to simplify the meaning - dimensions of space. So, what is the shape of a point in space in metric tensor? Also, how can you apply this tensor to ''time''?

@@user-ky5dy5hl4d Ask a flat earther they will give an accurate answer

Wow -- first off, we absolutely love your videos! They're a complete inspiration, and so thank you very much for gracing our channel, we're very honored! And secondly, you're absolutely correct to point out that imprecision. In fact, you would only need one ratio/number to describe how your distance element changes in a small region of the map, since as long as you are confined to that small region, it does not matter what direction you are moving, the distance element remains the same. This holds true for any metric on a manifold technically, including the spacetime manifold. The components of your tensor more describe the changing relationships between old and new axes/bases. In that altitude scene we technically cheated by using an extrinsic geometric component (since the vertical component does not lie in the manifold but in the exterior space) -- something which we felt guilty about doing. However, we felt it was a more intuitive, easily visualized approach to introducing the idea of components, and technically speaking, the correct metric components could be recovered from that information. We'll probably try to clarify that issue in our follow-up video -- we hope you'll stay tuned!

@@dialectphilosophy Glad you like our videos! I understand. It was just nitpicking, it doesn't affect the quality of the video at all. I've definitely subscribed, cannot wait to see the next videos!

@@dialectphilosophy I was a bit perturbed by that extrinsic axis as well, but only a bit. Some amount of hand waving is to be expected, and as long as the general idea comes across, we're good. We're already going along with the grid analogy, after all.

happy to c u sir

Today I learned the politically correct terms to call out errors. "Precision" and "Imprecision". How's that for pedantry?

Thank you for watching! We'd be happy to know you are sharing this in the classroom or in texts, and no need to credit us, we're just doing this for the betterment of the RU-vid learning community as well as our own understanding. What textbook did you write? It sounds intriguing. Indeed, our goal with this video - and the ones that will follow it - was to try to explain an advanced mathematical/physics concept to a lay person. Hopefully we can keep it up!

@@dialectphilosophy our textbook is "The Beautility of Math." It's a portmanteau of the words beauty and utility to emphasize that we want students not only enjoy mathematics for its own sake, but appreciate how we use it in the real world.

You're right, i just finished my school and when i had read the title, i had not understood anything and thought it would go above my head.. and now i have got what metric tensor is 90%+

@@everythingisalllies2141 and your take is BS. "You have become the very thing you swore to destroy."

@@jmcsquared18 I love the term "Beautility" as a description for mathematics, really hits the nail on the head.

We can promise you no butter bar LTs were involved in the making of this video

If you can quantify a crap ton, we can add it to the tensor! Thank you for serving, soldier.

We're glad it could help! We didn't give a general definition of a tensor in this video since it is a much more abstract, broad mathematical tool, but will touch on it in later videos.

Dang, _yes!_ It's freaking ingenious.

Appreciate the kind words, thank you. Glad to hear it helped your understanding, and if you liked it, make sure to check out the sequels!

After watching the video I understand what the metric tensor is how it works. What I still don‘t understand: What is the function of the metric tensor?? What does it have to do with the map conversions??

Thank you for watching! We're planning a series of highly-visual GR videos (on the metric tensor, connection coefficients, curvature tensor, etc.) for this spring & summer, so stay tuned!

Gosh thank you! We're just glad it's been helping as many people as it has so far!

Thank you! Riemann tensor is planned as the next one in this series, though we might have to do an intermediate one with the connection coefficients first.

PS: back in college we didn’t know why the heck we’re deriving the field equations. Lol

Thank you! We're glad it helped!

We're glad you found the channel :-)

Thank you very much, we're excited to hear it!

Why thank you! Our music is composed in-house, so we appreciated that compliment :-)