General Relativity Lecture 4

(October 15, 2012) Leonard Susskind moves the course into discussions of gravity and basic gravitational fields.

The Fall 2012 quarter of the Modern Physics series concentrates on Einstein's theory of gravity and geometry: the General Theory of Relativity. This course is the fourth of a six-quarter sequence of classes that explores the essential theoretical foundations of modern physics.
Originally presented in the Stanford Continuing Studies Program
Stanford University:

Stanford Continuing Studies:

Stanford University Channel on YouTube:

[NothingMaster]

Strictly speaking, Susskind is more of a String theorist and a QFT specialist than a General Relativist. But I’m absolutely amazed at his incredible abilities and insightful approach in teaching GR. He is a gifted lecturer who has a special knack for communicating the heart of the matter behind the seemingly hairy-intimidating equations. By the time he is done teaching a subject you feel like you’ve always had an intuitive feel for it; and that’s the trait of a supremely gifted professor.

[kaustuvregmi]

1:05 Covariant derivatives of vectors with covariant components
8:05 Covariant derivatives of vectors with contravariant components
14:44 Parallel Transport
24:37 The curve with all of its tangent vector parallel to each other is geodesic curve
29:44 Notion of the tangent vectors
31:35 Parallel transport of tangent vectors of geodesic curve is constant. This gives equation of motion of geodesics.
36:43 Trajectories in Space-Time (Minkowski geometry and Riemannian geometry together)
40:58 In general relativity metric becomes a function of space and time.
41:15 The metric of space time always has one negative eigen value and three positive eigen values.
46:23 Problems with special theory of Relativity
48:55 Polar coordinates as the analog of uniformly accelerated coordinate system.
1:05:44 Our aim is to introduce an arbitrary set of coordinates and write the equation of motion of geodesic in it and see if it looks like the particle falling in a uniform gravitational field.
1:06:47 Metric in polar coordinates, its analogy to uniformly accelerated coordinate system.
1:09:12 Expressing Metric of uniformly accelerated coordinate systems interms of ‘g’
1:22:10 Finding how the particle moves in this obtained metric (Equation of motion in geodesics) which is Newton’s equation.
1:33:49 Equation of motion in real gravitational field
1:35:25 The metric for the horizon of black hole

[maryvaughan]

I studied physics in college for a few years 55 years ago and then moved on to other things. The last few years I’ve been returning to physics through these lectures. It’s been a real gift. I hope these lectures stay around for me to return to as I move on to books and other sources of study. Just want it known they don’t grow old.

[AkamiChannel]

Congrats everyone! We made it to lecture 4!

[klgamit]

If you're a newcomer to GR wanting to really get into it, and watching this series: after going through this route myself, I can definitely tell you Susskind's presentation is very accessible on the one hand, but *extremely* dated on the other hand. There is a much more geometrical approach to GR today that sure, requires developing some familiarity with differential geometry, but boy after you know this stuff all those indices don't look so arbitrary and unmotivated. The simplest example is the "A tensor is a thing that transforms like a tensor" line is one that really bothered me for a long time. Just my own opinion. Nevertheless, coming to his lectures after some additional familiarity with the background math is very refreshing and anyone can learn something new from it, because after all... it's Susskind :)

[huonghuongnuquy]

My dream is one day I can master the general relativity. Thank you so much Mr. Leonard Susskind for these lectures, you help me to make my dream come true.

[zaclaplant]

Anyone else severely under-qualified and still following along to his GR lectures? I'm watching these, reading through Einstein's works, and starting a journal of the whole derivation of GR. To be honest, i kinda want to write it out building up from high school algebra to GR like you would normally, but then expand GR and represent it in a way that only uses notations from a high school algebra level. See how many pages that takes up... lol

[benjaminnachumi]

The (really good!) exposition about "fictitious" gravity in an "accelerated elevator" complements a discussion of a "uniformly accelerated rocket" in Hartle's giant introductory GR tome. It was very useful to have thoroughly understood how a constant proper acceleration appears in a "rest" frame in SR--how each one of the coordinate hyperbolas happens.

[pmassio]

Thank you so much for sharing these lectures

[Algebrodadio]

@23:00 Vector fields are not parallel transported, elements of the tangent space are. Generally, if you have a path from the point p to the point q, then parallel transport gives you a map from the tangent space at p to the tangent space at q. 

[AkamiChannel]

2:14 dude jumps at a quick opportunity to ask a question

[cybermoose]

7:57 gives me fits of laughter. "G blah blah with respect to X flah flah" poetic.

Great lectures though, currently on number 5.

[cheeheifoo]

It's such a privilege being able to learn from Leonard Susskind. I could not have been able to follow along this subject otherwise

[Algebrodadio]

@1:10:00"3 times 3 is ten, so c squared is 10 to the 17th."

HA! Physicists like estimates...

[tehyonglip]

i am happy this professor is working in metric, i cant stand US customary units

[christianfarina]

Lecture 1, 324k views, Lecture 2, 108k, Lecture 3, 88k, Lecture 4, 64k, Lecture 5, 52K, Lecture 6, 46K, Lecture 7 34K, ... :)

[brainstormingsharing]

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍👍

[phildurre]

Its just disgusting how easy he makes GR look lol. Good Work!

[maazadnan]

now i get it, what Einstein said:
‘If you can’t explain it simply, you don’t understand it well enough’.
(great job done sir!)

[PetraAxolotl]

Funny that the professor did not understand the question at 1:39:45.

You don't need a big R for a small A in general. You can certainly translate the world line with a big R left along the x-axis and make it go through the origin.

The professor chose a big R only because he insisted, for mathematical simplicity, that the equations have the form x = R coshω and x = R sinhω.