General Relativity Lecture 9

(November 26, 2012) Leonard Susskind derives the Einstein field equations of general relativity and demonstrates how they equate spacetime curvature as expressed by the Einstein tensor, with the energy and momentum within that spacetime as expressed by the stress-energy tensor.

This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In this quarter Susskind focuses on Einstein's General Theory of Relativity.

Originally presented in the Stanford Continuing Studies Program.

Stanford University:

Stanford Continuing Studies Program:

Stanford University Channel on YouTube:

[erwinmarschall]

Susskind is 73 years old. We all - except you - are very happy that he gives these lectures and make them public! If you should ever reach this age in mental vigor, you'll find that a sufficient energy supply to the brain is needed to accomplish such a great mental performance for 2 hours!

[danomicky]

Susskind is a fantastic professor. These lectures are epic! This is the internet at its full potential

[math.physics]

What I just feel like saying is thank you Stanford University. These lectures give me thrills

[Jipzorowns]

oh man, imagine drinking a beer with this fella

[johnmcevoy]

My knowledge of applied mathematics extends only to undergraduate level, however the manner in which these relativity lectures were structured & delivered, made it a pleasure to tune in & also learn as one lecture naturally followed it's predecessor!!. Brilliant course, bravo to the professor!! ...👍

[erwinmarschall]

Wheeler: spacetime tells matter how to move, matter tells spacetime how to curve

[drcooljoe]

Excellent explanation of the stress-energy tensor with the analogy of the 4-current! Thank you!

[justcrank]

wished someone did lectures like this for fluid dynamics also...fluid dynamics is as hard as GR

[Algebrodadio]

I don't mind at all that he's munching. In fact, it makes the setting a little more colloquial. It almost feels like he's just explaining some concept during the department tea.

[realcygnus]

hell is super if they had this when I was a kid....you'd prob be watching Lennys lecs are cool, but 7 & 8 from this series really took the cake...100X better then a typical 30 min Discovery channel is.exactly what the net is(should be) content/mind candy for the masses(only 7K views wtf !?") ....is 1 way 2 help fix the future 4 sure !

[ProCoderIO]

“Excuse me while I consult with Newton.”

*Crunch!*

[nurlatifahmohdnor]

Page 144-148





PRJ 370.152 MOH



It is belonged to MPKB library. Not returned. He donated to the library. Then he borrowed the book he authored.

[AntonGeraschenko]

1:25:00 - The following point confused me for a bit.
Q: shouldn't g^\mu_\mu be 2 rather than 4, since the signature of the curvature is (-1, 1, 1, 1)?
A: No. The curvature has that signature, but g^{\mu\nu} is the honest-to-goodness inverse, so g^\alpha_\nu = g^{\alpha\mu}g_{\mu\nu} is the identity matrix, which has trace 4.

[daujok]

I love these lectures, and the way that Dr. Susskind focuses on mathematics!!

[whovikrantsingh]

42:19 is the only definition you need on the energy-momentum tensor. Teaching at its absolute best.

[paulm]

43:30 The symmetry T0m=Tm0 can be easily demonstrated in a simple case. Imagine a cloud of particles with density n enclosed in a rectangular box and all moving at the same speed v in the positive x direction. Each particle has an enery gamma*m and a momentum gamma*m*v. The energy inside the box decreases by gamma*m with each particle leaving the box therefore the energy flux through the right box face is T01=gamma*m*v*n (because flux=density*speed). On the other hand since the momentum is gamma*m*v per particle the momentum density is T10=gamma*m*v*n and hence equal to T01. The whole thing holds because E=pv so that the energy fllux equals the momentum of particles carrying this flux.

[kevinmartin]

This lecture is sadly missing the contraction of the Riemann tensor to the Ricci tensor (alluded to at 59:59), and the covariant derivative of the Ricci tensor (skipped at 1:09:59). Would be nice to show how these two quantities help determine the Bianchi identity featured in the final field equations, which is analogous to the statement that "the divergence of the curl equals 0."

[exodus]

Ppl should be grateful that Susskind is kind enough to give these wonderful lectures. But no ppl are complaning about him eating during lectures. Well if you can't handle it just don't watch! 

No one is forcing you so go and watch Bieber instead, LOL

[therealjordiano]

that was incredibly tough to understand for me xD fascinating imo

[emekaasogwa]

what a wonderful lecture. Thanks very much, this really helped me in my further study of general relativity and cosmology.