Einstein's General Theory of Relativity | Lecture 3
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- เผยแพร่เมื่อ 4 ก.พ. 2009
- In this lecture, Leonard Susskind continues his discussion of Einstein's theory of general relativity. He also gives a broad overview of the field of tensor calculus and it's relation to the curvature and geometry of space-time.
This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on classical mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.
Stanford Continuing Studies:
continuingstudies.stanford.edu/
About Leonard Susskind:
www.stanford.edu/dept/physics/...
Stanford University Channel on TH-cam:
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Thank you, Stanford, for sharing Susskind's lectures. Thank you, Susskind, for being a brilliant educator.
Same here. Thank you very much.
And thank you for that $20 you loaned me...
No worries
Lies again? Extra Time
Hahahahah sissy among us word hahahahhahaha among us 😞🙁🧐😞😣🤬😥😰🥶🤯
Doppler effect; Differential Geometry 19:00; Tensors and Contravarient vectors 39:00; Covariant vector 1:02:30; Metric Tensor 1:12:00; Flat space 1:31:00; Examples: Polar coordinates 1:37:00;
Stanford really are blessed with some of the best lecturers in the world, this guy and Robert Sapolski are 2 of the greatest minds of our time and their delivery is so good
Exactly! These two professors have the most entertaining and informative lectures, even compared to my actual college professors. I’m on the hunt to find more lecture series on TH-cam that match the brilliance of these two guys.
Professor Susskind is making all this much easier to grasp. It just proves what I have always believed that only if one understands something deeply one can explain it simply.
Thát´s the point
For me, that's absolutely. I studied Einstein's theory at the university long time ago, in my youth. And I must say that my teachers never explained this so clear. Great respect!
I was once one of those relentless questioners midclass in my own university. I'm so sorry, folks. The frustration is understood. I'm writing them down for after class now.
I really think a question is not a question is not a question. There are questions that will help you understand what he's saying, and these, generally, will be beneficial to everyone even if the others didn't ask it. Then there are questions whose purpose is only to show the professor how much you already know. This guy is asking terrible questions. But it doesn't make all questions terrible.
love this guy .... and love the teacher more
I keep rewatching this lecture to grasp the importance of tensors for physics. Don’t know if it’s me but I find it very difficult to intuitively understand tensors and I constantly forget how they work as time goes on. But Prof. Susskind explains them very well here and shows their utility in the following lectures. I’m glad that these videos are accessible to the public to learn from!
For me, tensors are the one thing I keep relearning and forgetting, over and over😢
Watch the youtube canal of eigenchris. The best course about tensors and relativity on youtube.
Fantastic teacher!
colleges like Stanford and UC Berkley who put up there lectures and then making them available for download that is really awesome of them
1:11:02 helpful question/comment: Partial derivatives are like basis vectors. So varying like the basis vectors is co-varying.
Susskind: Yes, also where contra[variant] and norm came from as well.
Thank you . Both Prof. Susskind and Stanford University .
After getting beyond 1:02:40 I found it helpful to revise from 31:50 and from 47:30, mainly to keep the context of the formulae fresh in my memory. Likewise, after getting beyond 1:43:50 I found it helpful to revise from 1:24:35. On the whole, I felt I comprehended the lecture pretty well. Will see how well I comprehend the next one.
Adrian Morgan thanks for the idea
Susskind makes differential geometry more understandable than my differential geometry professor. Thank you Stanford.
keen observation, in fact there is no requirement that dyi/dxj is constant. We even have explicit examples in the lecture, for example dx/dr = cos(theta) is not constant. Strictly speaking, vectors and tensors only exist at a single point in space. What he is actually dealing with are vector fields and tensor fields which are not a collection of (constant) numbers, but rather collections of functions in space, but he just calls them vectors and tensors.
Prof: "I don't know what this rule is called"
Tool: "I must let the class know that I do!"
Prof: "For those of you familiar with linear algebra"
Tool: "I must let the class know that I am!"
Academia in a nutshell
One in every class
Well I don’t think it’s a big deal if the teacher asks, but bragging is pretty pointless.
That guy is constantly annoying throughout the lectures.
is incredible how able is prof susskind to respond to every question.... (i m accountant... so i can imagine how physiscists may be feeling about annoying questions...)
12:21 this is after the question i'm replying to. the flaw in the logic is that the blue shift doesn't only occur at the moment when the light is emitted, it gets blue shifted all the way down, so the acceleration just factors into that as well as in the red shift, so then of course they cancel
GREAT LECTURE ON ELEVATOR REPAIR!
Damn video one had 6M views and were already down to 600k :). Love this series so far! I, unlike most, will be watching to the end. Thanks for this!
Superb lectures,
Thank you Stanford for uploading,
Susskind is a great lecturer.
@9:25 Shouldn't light be blue shifted because of gravitational field? Prof. mentions it as blue shift @10:17.
Stanford and Susskind being very very generous
Thank You! this video is priceless! You are doing a great Job! may God bless you above and beyond what you could ever imagine.
Such nice and clear lectures, it does not matter that a whiteboard becomes a blackboard and a 'super' becomes a 'sub'
Thank you prof susskind you inspire me a lot to love physics I love you may God protect you much 🙏🙏🙏🙏
It cut out early, but it looks like the metric tensor components for the surface of a sphere are: g_phi,phi = 1; g_phi,theta = g_theta,phi = 0; g_theta,theta = sin^2(phi)
Which book is recommended to get more in depth knowledge of these discussed concepts in the same order?
If you want a more geometric motivation and exploration of tensors as companion material, you can check out the lecture series from MathTheBeautiful.
So a light beam that comes from the Sun to the Earth is redshifted leaving the Sun, but then wouldn't it be blueshifted (though of less magnitude) due to this same effect via Earth gravity? So the Doppler shifts would be compounded?
Even though I cant understand the particulars, Einsteins field equations seem awesome.
Though I can appreciate the fact that art students generally don't tend to love mathematics, the generalization that they are all incompetent in the area is incorrect. I was a student of Political Science for two years before switching into Astrophysics. My head is in tact and my gpa is above average :)
I find those who need to belittle any major of any field is only doing so to make themselves feel special when they themselves are probably struggling students.
I'm glad you posted this comment.
110% correct
What do they teach you in Pol. Sci. ? Definitely not science.
Yes, and that's one of the tidal forces (gravity is stronger below than above), so susskin's response still explains the issue; you need more than a simple coord-transform to get the right answer. That's what I understood anyway; I'm also a layman.
Any great thinker in fields of work like science, philosophy have a genuine rich 'toolbox' or archive of references, and make antithesis or even synthesis (as do Freud, Kant, Hegel, Newton, Einstein and so on), creating something new out of bringing pieces together (and even formulating deductions from that new-lly found clarity).
@csmcmillion In Einstein Notation it is expressed as j, and is referred to as the Dummy Index.
The persistent questioning really breaks the flow of thought. I second the suggestion that they could have been taken at the end.
+Anirudh Gangadhar that's annoying!!!!!!!!!!!
dude, its not presentation, student cant follow if something is not clear. so questions are must at the spot rather at the end just like happens in presentation but its not
@@NaveedKhan-dg5bv 😷♓🐦,it will make sense guys.Even to me hopefully at some time.I learned a few things from Dr.Physics,a good guy too.
If a cone fails to flatten, what is the solution there? Do you tip off by some and create like honical geometry and then flatten it? Why does it fail? Is it because of singularity at the tip?
While I agree that Einstein is an extraordinary physicist and probably one of the most important, surely it doesn't matter at what age you make your important discoveries... Erwin Schrödinger was 39 before he formulated his famous and important equation but is still also one of the most important physicists.
There is one thing that's bugging me in his explanation. Do we know that dyi/dxj is constant irrespective of the point (which means that any y has constant derivative to any x and that y double derivate with respect to any x would be 0)? If not, shouldn't the vector translation to a different frame of reference be an integral over Vx?
If we could have a GR lecture both physics and its mathsmatical geometric structures together, that would be much more accepted when we talk about some concepts like the covarient or the invarient , which has its mathematical foundation on manifold theory
Thank you Doctor
24:10 Total differential
Ok so at around 35:00 minutes could I understand Phi as a function of x and then x as a function of y?
i just want to add something, sometimes its not always about the topic that youre learning, its about what youre learning.
Thank you...💫
Any "Einsteins" out there viewing this? Please identify yourself now.
Professor Susskind has the patience of a saint. I would have walked out on these arrogant students.
YES! I wish they would STFU. They ask questions they already know the answer to, as an attempt to impress. I don't know who they hope to impress.
I feel for the guy around 10 mins asking that question about the difference between his previous admission about the dopler effect cancelation at v and at v', he says its freely falling but also accelerating, if it is accelerating it will see more shift than the other, how does velocity = acceleration.
The answer was that you have to introduce special relativity to explain why they are the same. I was with the guy asking the question on that one too. But when Susskind explained that SR accounted for why they were the same, I figured that I would need to understand SR to get it. Basically I guess the difference in velocity between the top and bottom was so small that it introduces the SR effect. Versus what we traditionally understand about the Doppler effect at the macro scale.
@unchained1978
a tensor is kind of a super vector.It contains atleast two vectors.
for example if A is a vector and B another vector
C is a tensor of rank two. C =A*B
i loke it
Has he done all his lower indices right? He says they're down stairs, but in the denominator it looks like they're upstairs. Or if you're in the denominator does it count as downstairs anyway?
BG
The guy at 10 minutes simply forgot that Susskind had been seeking to show that under "equivalence" , a gravitational field equated to an acceleration(accelerating frame) .
So in the (free falling) accelerating elevator , on the one hand we had a doppler ,red shift , but because we were in a gravitational field , we also had a (counter acting) blue shift .
@fermista thanks for that :)
well form the little i kno, if you can do a transformation on the metric tensor and turn it into the kronecker delta, then the space u used the metric from is considered as 'flat' because it can be transformed into normal cartesian coordinates.. some geometries can't, like the spherical geometry
@gumbilicious1 That's because classical mechanics is a system of four dimensions, as was known since as far back as Newton. That quote isn't indicative of what Einstein meant by space-time. Einstein's ideas about there being a fabric of space-time, which directly correlates to gravity, was not yet theorized. He didn't publish the paper until 1916, so whatever he was working out before that isn't relevant to the age that he made that contribution; which is what the comment that I replied to was
how does that coordinate transformation work .. ?
He mentions that g12 is not necessarily 0. Why? Kronecker delta when m is not equal to n will still be zero regardless of the functional relation between x and y.
i think its a matrix that encodes the geometry of a coordinate system.. cartesian coordinates have (1 0 .. 0 1) but if you find the matrix for polar coordinates its (1 0 ... 0 r^2) so the geomtry's different
Now I just play it loud while I sleep to make neighbours think I'm important:P
Great lecture, as always. Love'em.
I'm amazed he can still say blackboard while directly looking at something that white; I'd totally say whiteboard!
ah, so you were talking about spacetime in relation to gravity?
i see, it was a response to the 'age' of a scientist when he submits his most pertinent theories.
another very pertinent scientist who was quite advanced in age when submitting his most influential work was Maxwell Planck. I think he was in his early 40's when he submitted his solution for black body radiation.
His name was Max Planck
Excellent
If you watch lecture 4, you hear Susskind note that it would be impossible for Einstein to describe his own physical theory without the mathematical framework established by many others.
Great as Prof. Susskind is. I can't help wishing mathematics be taught with the physical insights as motivations to proofs. That is splicing his content into standard curricula. In fact the more I think about it. Mathematics and Science should be taught as a complete whole.
Hythloday71 The great mathematician arnol'd famously quipped that mathematics is a part of physics pauli.uni-muenster.de/~munsteg/arnold.html
+Hythloday71 But mathematics goes far far beyond what is used in science these days.
I don't know about this. Physicists and Mathematicians think about math in a completely different way. In my quantum mechanics course, the professor was constantly assuming things were zero at infinity. It drove me, with more of a mathematical background crazy. But for a physicist, it's just obvious--of course it's zero at infinity; we're talking about reality. Physicists make gigantic assumptions all the time that make their mathematics far simpler than real mathematics is.
greg55666 I don't even think this is the biggest problem with this idea, I mean physics is a science which uses deduction, and math is proof based and uses induction, the mathematical models used in physics are not really math, they're just using mathematical conclusions based on physical theories. I mean physicists do make a lot of weird simplifications but it's based on the idea of convergence to a solution to a problem, mainly because most problems in physics can't be solved analytically :/
greg55666 What they are assuming is that you are on a Hilbert space... Per definition it goes to zero at infinity.
that is what I thought. But how is it related to the Kroniker delta?
23:41 is called differential of a vector valued function
I think it was very interesting that he wasn't rigorous mathematically which was unexpected (before I skimmed through some of his work).
Gah, unfortunate place for the video to cut out.
I didn't catch the difference between covarient & contravarient transformations, except they are like mirror images of each other in some way I think; but that doesn't make sense to me because & can't see different ways to do the same job (i.e., transform from coord-a to coord-b).
BTW, latitude looks like a "ladder"; that's how to remember them. (He got them backwards).
I like the way Leonard Susskind has adapted to those questions, he seems to have developed the ability to ignore the annoying guy lol. 18:06
He really is a genius. I respect the man the the utmost.
To clarify these lectures were actually part of a continuing studies program at Stanford for people who have graduated college a long time ago but want to go back to learn some physics and they may be rusty on their math. They are not all Stanford undergrad or grad students.
Thanks for clarifying. So this is sub 1st year university level...roughly speaking?
Einstein originated the idea that spacetime is curved as a result of its matter content. The mathematics to describe it was already in place.
Einstein's friend actually figured out the G.R. equations first, but he said Einstein was clearly the originator of the theory.
I love how somehow Bernie Madoff is being discussed in the context of a general relativity lecture (sarcasm).
Watching these classes is a real pleasure. Learning QM and relativity from someone as brilliant as Leonard is an honor.
Now you all may continue duscussing Madoff and watch out for the US congress & 'Chairman BO', they are doing the same thing on a much bigger scale.
Hi everyone, I tried to solve the problem at the end of the lecture: "why it is not possible to find a flat coordinate system for the sphere metric", but I failed.
I wrote the equations, implied by the flat metric sensor, but then I do not know how to prove that the function x and y are impossible.
Any clue?
Thanks
Marco
You compute an non zero scalar (so a number) that's 0 in flat space, but in the sphere is non zero. For example the curvature scalar do the trick. In every flat space is zero, but in the sphere is not. Since it's an scalar, it remains the same in every coordinate system, hence we cannot transform the sphere in Cartesian coordinates, because it would transform a non zero quantity into zero.
So if light is shot down a gravitational field, how can it possibly accelerate and create red shift if light cant accelerate past c?? Am I not comprehending the concept here or is this just another twist in relativity?
Dr. Susskind says over and over again that curvature is the obstruction to flattening out space and tidal effects are the obstruction to eliminating the effect of gravity by a coordinate transformation, therefore the curvature of space-time is actually what causes tidal forces. But this leaves me wondering the following: If curvature of space-time is just causing the minor tidal effects, then what is it that's causing the acceleration?
Tidal forces are caused by both the divergence of the field and the change in field by distance. I.E. in a field the field on your left side is at a different angle from the field vector at your right side. And every point in between the field vector changes. The field intensity changes from head to toe and as you move towards the mass point. If the field vectors were parallel and constant WRT position then there would be no tidal forces.
292 000 views of an general relativity lecture!...this fact is real revolution!
again this guy is great I've never taken the corse and I can understand him quite well. Funny how his students asks so many question on eazy special relativity ideas and they are near silent when there should be more questions. Hum...
These are some really great lectures. I do consider myself to be more of a mathematician than a physicist though. I don’t think I need to explain any further.
how does it work ?;s
@jimmayl1 yes, it would look much "better" - maybe it's because Einstein used superscripts in writing down GR?
Oh, I see. This lecture is in four parts; I only saw two and thought it was moving too slowly. Good video ;)
Well done. This is the most fire remix of the alphabet of all time.
Not! He wouldn't have called "chain rule" the expression for the multivariable differential
Why the last moments of the lecture is truncated?! :(
bro i fell asleep with my computer on and woke up to this
Maje aa gye is lecture mein😁😁
So I just came from the page this was produced from. Why are you the only educational person on there for more than 20 minutes worth of scrolling what is up with all of those 3-minute videos talking about how they feel I wish for more education like this amazing video maybe make a playlist because I tried that search as well within the page and it's still all about how we feel where are all the educational videos I want education and stuff in my ear to teach me new things that I may have not have remembered please and thank you please do have a good day
lol at 10:40 susskind was like "nigga, for the nth time it's freely falling"
What is the text-book used?
@jimmayl1 yes, it would look much "better"
I like Susskind's way of introducing tensors. But he was sloppy at 57:10-20 when he "magically" moved $A^r_{(x)}$ to the right of the equation, without acknowledging that it was a property of the product of finite sums (or product of absolutely converging series). I'm surprised that nobody in the audience noticed this, given that the lecture was given at Stanford.
+Michael Chen I noticed the same thing and was wondering how he did it, since it was part of a sum. That's precisely the reason why I'm uncomfortable with Einstein's convention for sums. Without the Summation sign, it becomes easy to do sloppy maths. It's correct, no doubt, but poorly done
Indeed, what a horrible convention.
I disagree with that. Einstein's convention is a very powerful tool with respect to proofs. So long as one makes a clear distinction between free and dummy indices, it makes several proofs much simpler that they would have been had they been done otherwise
Ahh this was driving me crazy, thank you for affirming my suspicions!
I use this Principle when I let out my baby chickens to play however, it does not really work when putting them to bed I find that fastanating must have something to do with a change in mass.
Damn. Why did we miss the example about spherical metric in the end?
With mathematical signs it seems double duch to me, but thinking about what he really does - and I see the drawing example - I come to the conclusion that I don't know if I understand it or not.
It would be better if they could put the questions toons asked by students at the end of the video. It would save a lot of time.
I don't understand why you'd see the doppler effect in the experiment he suggested (a laser beem shot down toward the earth in a very tall building turning slightly blue)...
Wouldn't it matter where on the earth you are? How is the earth an elevator in this context? It's orbit? But then like I said wouldn't it matter where on the earth you are... or at least WHEN on the earth you are?
Edit: so.... I'm thinking that the gravity itself is acting as the elevator? Is this right? I'm having a hard time wrapping my head around that though. I can kinda see it making sense, until I really try to picture how it works.... then everything breaks down for me worse than information at time 0
What is the text book for this course ?
The universe
I've learned when you do things stuff happens, but it's kinda different in space
@ThatAustralianBloke If that's the case, then Einstein's equivalence principle must be wrong. In an inertial frame in zero gravity, it's obvious that there is no Doppler shift, and the equivalence principle says that the laws of physics are exactly the same for a frame in free fall. Have you gone through the maths yourself?
Dr. L. Susskind, exelente presentations, easy to understand and well organized. My comment is about the Subtitles/closed captions, in which the person that do the transcript of your presentation do not write what you are saying, he or she confused the pronounsation of the words with the actual word. For example, in Lecture 3, about the 3:13 minutes into the lecture he or she wrote "Adams" in stead of "atoms". Also in the 3:54 minute into the lecture he or she wrote "my new" in stead of "minute". This is consistence in other of your lectures. This kind of writing errors will confuse a person that cannot hear the presentation and relied in the Subtitles / closed captioned.
The subtitles here are auto-generated (the language name is 'English (auto-generated)'), you can only expect so much from them.
This is the third time that I try to get this comment, but I do not get it through. The transcripts of the lectures must be what the Professor Susskind is saying, and not confused when he say "Kronecker Delta", not to be transcript to "chronicle" delta, and many other errors. The transcripts of the lectures must be done by a professional in the field, like the professionals that make the transcriptions in the courts. This is my understanding and my opinion. Thank you.
These transcripts are not made by humans. The subtitles you can turn on in this video are provided by TH-cam and are generated automatically by their voice recognition algorithms. These algorithms aren't perfect and they know nothing about physics, so naturally the subtitles contain mistakes. That sucks but it's better than nothing (as no official transcripts are provided).
Notice that when you turn the subtitles on, a title briefly appears at the top left which says 'English (auto-generated)'. It indicates that the subtitles are machine-generated, not human-written.
Thank you Mr. artliss for the explanation, now I understand the errors given by the machine. Excellent explanation of the situation. I hope that TH-cam can do something about this critical situation on the education of the people. I am very greatfull for the explanation.
The "Eton" principle?
@HomemadeBanjo Incorrect. Space-time in physics didn't exist until Einstein formulated General Relativity, and he didn't publish that paper until 1916. He was born in 1879. Simple calculation, I'd wager. Einstein's biggest contributions came far, far after the age of 16. So mathematicians, who in the 1600s would submit papers at ages as low as 14, are more important than Einstein? The significance of the work has no value? Ridiculous, and utterly so.
1:25 Metric tensor