(October 1, 2012) Leonard Susskind introduces some of the building blocks of general relativity including proper notation and tensor analysis. This series is…

(November 5, 2012) Leonard Susskind continues the discussion of black holes in depth using coordinate transformations and diagrams to develop an intuitive un…
Video Rating: 5 / 5

45 Responses to “General Relativity Lecture 2”

  • Waranle:


  • Richard Talcott:

    Thank YOU!

  • DFPercush:

    So, the metric tensor is formed by dotting basis vectors with each other? omg it makes sense now… i think.

  • Nick Bucheleres:

    i love that he’s always eating something…and talking with his mouth full :)

  • lsbrother:

    possibly the only lecturer who can be allowed to take a big mouthful of cake immediately prior to speaking!

  • timeisabsolute:

    General “theory” of relativity is a crackpot theory because it’s an outgrowth of the grotesque nonsense called Einstein’s special “theory” of relativity (cf. youtube.com/watch?v=mhG3R66wFpg). Einstein’s “theory” of relativity must be removed from physics urgently, to prevent further damage on science and society.

  • Ben Garside:

    The expression midway through the tinker toy analogy, when he realises the innuendo but cant turn back :)

  • drcooljoe:

    They are pseudo-tensors, which are a generalization of pseudo-vectors in the same what that tensors are of vectors.

  • Steven Hatton:

    This is better than his previous treatment of GR. I don’t like his choices of notation. I prefer using over-bars instead of primes, and whether I use over-bars or primes, I put the coordinate system designation symbol on the indices. It makes things much clearer. MTW use this technique.

    Nonetheless, his presentation is well done.

    I would do things differently; e.g., I would define partial differentiation in the context of arbitrary coordinates, and discuss the implicit function theorem.

  • BringerOfBloood:

    Short question: Pseudo-Scalars and Pseudo-Vectors aren’t Tensors, are they?

  • 1o618033988749894848:

    Ah, also on the wikipedia page when it talks about a ‘Field’ F, we’re usually talking about the real numbers (or complex numbers).

    So the dual space is the set of maps from the vector space to the real numbers, equipped with some fancy addition and scalar multiplication operations

  • 1o618033988749894848:

    Check out the wikipedia page on “Dual space” (at least the first few paragraphs) .. what it calls “co-vectors or one-forms” are covariant vectors.

    A covariant vector can be identified with a linear functional on the tangent space (the vector space where the contravariant vectors live) in the following way:
    Put the covariant vector next to the contravariant vector, using the same index. Since one is upper and one is lower, they contract to form a scalar. Probably oversimplifying, but meh

  • Ismail Steitiya:

    I thought I was sailing in the sea of relativity until I saw my self not even on the shores when Mr. Susskind grabbed me toughly to the bottom of the ocean without lightening the way

  • Christopher Manley:

    Oh hell yeah! Thanks interstellarmonkey! You just filled up all my free time for the next couple years.

  • interstellarmonkey:

    you should check out ocw.mit.edu

  • chinmay8045:

    thanks a lot for these lectures….man they are scintillating

  • interstellarmonkey:

    thank you!

  • 4815761:

    (4 of 3: Addendum!) …Ah, now I see the real problem–he uses a clunky, mechanistic method of teaching tensors that became obsolete 40 years ago (and doesn’t involve telling you what a tensor is!). Since MTW, most instructors have explained vectors, covectors, and higher tensors using familiar geometric concepts, giving you a fully explicit idea of just what they are. Prof. S’s more superficial strategy has enabled the confusion mentioned before.

  • 4815761:

    (3 of 3) …Misner Thorne Wheeler (usually called an advanced text but with a very geometric, intuitive treatment of the basics–using the “beginner” notation thru the whole book) explains the difference between “abstract” and “component coefficient” symbols especially carefully and explicitly. And definitely catch David Metzler’s awesome “differential forms” YT lectures for a great intro to the real significance of covariant vectors (another thing thus far absent from Prof. S’s presentation).

  • 4815761:

    (3 of 3) …Misner Thorne Wheeler (usually called an advanced text but with a very geometric, intuitive treatment of the basics–using the older, “beginner” notation throughout) explains the difference between “abstract” and “component coefficient” symbols especially carefully and explicitly. And definitely catch David Metzler’s awesome “differential forms” YT lectures for a great intro to the real significance of covariant vectors (another thing thus far absent from Prof. S’s presentation).

  • 4815761:

    (2 of 3) …I think I know why: He’s conflating the notation used by modern working relativists with the older one that’s still better suited for teaching beginners. (Making the eventual switch is actually quite easy, almost nothing to it–hence, no doubt, his carelessness–but you do have to start out the right way.) Every quality book avoids this mistake; good intro choices include Hartle, the mindblowingly awesome Moore “workbook,” and the Carroll notes (the arXived ones) if you like them…

  • Gary H.:

    There are those of us watching, pausing, and transcribing every hen-scratch the Dr. makes. Often, Dr. Susskind will raise his hand above his head to touch and refer to to a term in another equation in order to clarify the current expression. The camera either remains focused on the current expression, or rotates azimuthally to follow Susskind. However, the camera never pans upwards to reveal the other equation…a minor inconvenience.
    Thank you Dr. Susskind,
    Respectfully – เสือ

  • SlashVe:

    Oppositely dragging in one direction, but dragging combined in the other direction. And when the photon is behind the horizon all its energy will be ‘dragged’ and it won’t get out.

  • HardBall212010:

    @therealijordiano; as alice asymtotically approaches the horizon, the amont of energy of each photon get fractionally lower in frequency; so the total amount of EMR energy emitted by A tends to some finite amount over time

  • TheCrappyaccount:

    Honestly Susskind really is not a world class lecturer. This is disappointing and I think that he needs to be more concise.

  • Tomislav Završki:

    Leonard is extremely patient with this dumb questions of who see what. Everything is on the diagram and some people are just plain stupid.

  • adam dicken:

    So if Bob throws Alice into a black hole he could never get charged for murder since in anyone outsides reference frame she never really dies..

  • billy jean:

    well the light is infinitely red-shifted until it is at some point not really a light wave.. so i would say no, but i could be wrong

  • therealjordiano:

    for an infinite amount of time* i hate typos >_>

  • therealjordiano:

    question lol.. i can’t resist
    from bobs perspective, alice never crosses the horizon but just slows down and takes an infinite time to touch the horizon… so does that mean that he’s receiving light from alice for an finite amount of time, hence.. infinite energy released by alice? :S

  • billy jean:

    why no? when it is passing between the two combined horizons they are equally dragging the light beam to them.. so there would be no slowing of the light beam because all of the forces would cancel, maybe the amplitude would increase or the wavelength would shift to higher energy?

  • SlashVe:

    simple: when the point in between is behind the combined horizon then no, otherwise yes.

  • billy jean:

    Well you could see the irritation on his face from all of the redundant questions and the frustration of not being able to cover all he wanted to… what does their questions have to do with his preparedness?

  • giovanibattini:

    Susskind wasted at least half this lecture hiding behind highly redundant questions about Bob and Alice perspectives and at the end he said he only covered a quarter of what he wanted to cover. Whose fault is that ? Sometimes Susskind gets on a role and is very informative. Other times he seems to rest on the oars and pacing time until class is over. Is it because he is unprepared ? Gets tired ? In any case, the attendees are getting ripped off during those lulls.

  • Markus Jaeger:

    oddly enough he had not as many unimaginative students in other lectures. for some reason general relativity gathered couple dense ones lol

  • billy jean:

    I actually have a question… i dont know if leonard looks on here, but what if something was at the point in between the merging black holes if say they were of equal size and create the dumbell shape if one was at the exact point in between where the forces of the horizons were competing with each other could light escape that if it was perpendicular to the two competing forces?

  • billy jean:

    I call it a Hawking hole…

  • silverstorm2:

    oh i think that is nice, still people should think before they say something

  • Seb Campbell:

    I think anyone can attend these lectures, regardless of qualification.

  • silverstorm2:

    some of these questions are really annoying, are these real university students??

  • silverstorm2:

    1.19 he is getting annoyed :P

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