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Relativity Weinberg's book vs undergraduate course

  1. Jun 12, 2017 #1
    I found the Weinberg's book on General Relativity the most complete book on the fundamentals of the theory.

    I would like to know (apart from laboratory clases and having a professor to guide you) what is the difference of self-learning General Relativity from that book, compared to a 4-5 years that it takes (in my country) to complete a undergraduate course on physics at uni? I mean how many knowledge one woud have at the end comparing the two cases?

    I hope you understand my question as English isn't my native language.
     
  2. jcsd
  3. Jun 12, 2017 #2
    Maybe it would be better to put my question in another way: what topics a undergraduate course covers that Weinberg's book does not cover?
     
  4. Jun 12, 2017 #3

    dextercioby

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    Weinberg is/was no specialist in GR, nor did he ever show that he knows the true mathematical modelation of General Relativity, hence specialists in GR would rather point you to the book by Robert Wald if GR is really what you want to learn. I think a more recent book by Hartle or Carroll would better and more appropriate for a lower degree of mathematical involvement.
     
  5. Jun 12, 2017 #4
    Thanks, dextercioby.
     
  6. Jun 13, 2017 #5

    Demystifier

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    Well, Weinberg's book is a very good work for a "non-specialist". :bow:
     
  7. Jun 13, 2017 #6

    vanhees71

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    Hm, if Weinberg is not a specialist in GR, I don't know, whom you'd consider to be a specialist?

    On the other hand, it might explain, why his book (and Landau&Lifshitz vol. II) appears to me (definitely not a specialist in GR, because I didn't research in this field) to be more readable than many other GR textbooks. It's emphasizing the physics rather than the differential geometry aspects.
     
  8. Jun 13, 2017 #7

    Demystifier

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    Perhaps Weinberg is not even a QFT expert, because his books do not exploit full mathematical rigor of functional analysis and differential geometry of gauge theories. o0)

    If that is criterion, then in some branches of theoretical physics (e.g. condensed matter QFT) experts do not exist at all. :H
     
  9. Jun 13, 2017 #8

    Demystifier

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    Zee, in his book "Einstein Gravity in a Nutshell", is particularly sarcastic about sophisticated mathematics in general relativity. Here are some quotes from the book:

    It might seem that the first approach is much more direct. One writes down (2) and that
    is that. The second approach appears more roundabout and involves some “fancy math.”
    It might even provoke an adherent of the first “more macho” approach to wisecrack, “Why,
    with a bit of higher education, sine and cosine are not good enough for you any more? You
    have to go around doing fancy math!” The point is that the second approach generalizes
    to higher dimensional spaces (and to other situations) much more readily than the first
    approach does, as we will see presently. Dear reader, in going through life, you would be
    well advised to always separate fancy but useful math from fancy but useless math.


    The set of D-by-D matrices R that satisfy these two conditions forms the simple orthogonal group SO(D),
    which is just a fancy way of saying the rotation group in D-dimensional space.

    Fancy people call the upper index contravariant and the lower index covariant—I can never
    remember which is which. If you like big words, go for it.

    I feel that it would be good for those readers seeing Riemannian geometry for the first time
    to work through some “classical” differential geometry dealing with curves and surfaces,
    “real” stuff that you could actually see and “hold in your hands.” Throughout this chapter,
    we will be living in good old 3-dimensional Euclidean space. I am going to tell you how the
    greats like Frenet and Gauss thought about curves and surfaces. None of the fancy tangent
    bundle talk for us; we will just do it. Action, not talk!

    Some sophisticated types favor a fancy-schmancy index-free notation.
    This is analogous to the vector notation v that you are fluent with, instead of the index
    notation v_i . But it takes considerable effort to learn the index-free notation, and when push comes to shove, in an
    actual calculation, even a sophisticate might have to descend to indices. Besides, you have to learn to walk before
    you can fly, and I think that for a first introduction to Einstein gravity, grappling with indices is an essential and
    ennobling experience.

    Unaccountably, some students are twisted out of shape by this trivial act of notational
    sloth. “What?” they say, “There are two kinds of vectors?” Yes, fancy people speak of
    contravariant vectors (p^μ for example) and covariant vectors (p_μ for example), but let
    me assure the beginners that there is nothing terribly profound going on here. Just a
    convenient notation.

    Meanwhile, a mathematician friend of yours—could have been James Joseph Sylvester,
    a rather astute fellow, since he demanded that his salary from Johns Hopkins University
    be paid in gold before accepting its invitation to move from England to a scientifically
    impoverished but economically upstart country called the United States—told you about
    some fancy-pants math called matrix theory.

    Because of general coordinate invariance, we have considerable freedom in choosing
    the coordinates. This corresponds to picking a gauge in electromagnetism. At this point,
    the rich man with his or her wealth of fancy terms starts talking about Killing vectors, and
    possibly even foliation. We will get to all that later. But for the moment, it is pedagogically
    more transparent to follow the poor man’s way,∗ using explicit nuts and bolts, wearing no
    fancy pants.

    You get the idea before I run out of Greek letters! As before, fancy people who like big
    words call the upper indices contravariant and the lower indices covariant.

    At this point, our friend the rich man could start spouting fancy talk about the covariant
    derivative, presumably without writing down a single index and disdaining such “quaint
    old-fashioned notions” as transformation, and thus cause our other friend the Jargon Guy
    to become flush with joy. Instead, let’s be more modest and, together with our friend the
    poor man, try to understand what the covariant derivative really means by working out a
    simple example. Again, a tale best told through a fable.

    ... we see that speaking of Killing vectors is just an extra fancy way of saying
    that the static isotropic metric in chapter V.4 does not depend on the coordinates t and φ.

    But at the level of this book, it is
    a small price to pay to avoid going into fiber bundles and other fancy mathematical topics.

    No need to take a fancy course in partial differential equations!
    Beginning students often snicker at this sort of getting an answer by “winging it,” compared to solving a
    partial differential equation in all its glory, complete with factors of 2π and what not. But in fact, in cutting edge
    research, the ability to do the former is often much more prized than the ability to do the latter. On the cutting
    edge, the analog of the partial differential equation is typically not known, but the truly great theorists are often
    able to grope for what they want in the dark “by the seat of their pants.”
     
  10. Jun 13, 2017 #9

    vanhees71

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    Well, don't cry. Feynman was proud of being not "an expert", and he had a point!:smile:
     
  11. Jun 13, 2017 #10

    martinbn

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    I also don't like Zee's book.
     
  12. Jun 13, 2017 #11

    vanhees71

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    Why? I'm prejudiced against Zee since I've seen his QFT book. Is the GR book as bad?
     
  13. Jun 13, 2017 #12

    dextercioby

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    It's funny how A. Zee wrote that passage in his GR book against "fancy mathematics", however, just at the same time, he was writing a book on group theory for physicists. True, the mathematical level of his group theory book is not like Barut & Raczka, but nonetheless it's funny how he advocates for the proper math methods in physics, but not "fancy ones".

    OTOH, Weinberg's QFT book has some advanced group theory results in his chapter 2, but discarding differential geometry in his GR text would still be be a no-no in my book.
     
  14. Jun 13, 2017 #13

    martinbn

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    I didn't say it was bad. I said I didn't like it.
     
  15. Jun 13, 2017 #14
    I think Zee's GR book is much better than his QFT book, which seemed too handwavy to me.
     
  16. Jun 13, 2017 #15

    atyy

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    Do you like Wald's coordinate-dependent tensors? :smile:
     
  17. Jun 14, 2017 #16

    dextercioby

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    I like all tensors, as soon as one first explains what a manifold is, what a tangent space is, what a cotangent space is, etc. Coordinates or not it won't matter, as soon as the math is right.
     
  18. Jun 14, 2017 #17

    Demystifier

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    Someone should open a thread "Theoretical Physics vs Mathematical Physics". :devil:
    Or perhaps "Physics First vs Math First".
     
  19. Jun 14, 2017 #18

    Demystifier

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    Do you like Christoffel symbols? Or would you prefer to avoid them whenever possible? :wink:
     
  20. Jun 14, 2017 #19

    Demystifier

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    I like them both, but for different reasons. The styles of writing are very different, as if they were not written by the same person.
     
  21. Jun 14, 2017 #20

    vanhees71

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