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Mathematical treatment of Special Relativity

  1. May 15, 2010 #1
    Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.
     
  2. jcsd
  3. May 15, 2010 #2

    Landau

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    Last edited by a moderator: Apr 25, 2017
  4. May 17, 2010 #3
    I looked through that book. Can't make out just by browsing whether I will like it or not. Will give it a read and get back to you. Have you read it? What is your opinion on it?
     
  5. May 17, 2010 #4

    Landau

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    I'm sorry, I haven't read it myself, only browsed though it. Are you a mathematics/physics student? Do you know SR from a phycisists' point of view?
     
  6. May 17, 2010 #5
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  7. May 17, 2010 #6

    Landau

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  8. May 17, 2010 #7

    George Jones

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    There also is

    https://www.amazon.com/Geometry-Min...=sr_1_1?ie=UTF8&s=books&qid=1274105134&sr=1-1.
    I echo what Landau wrote. By "mathematical," do you mean "quantitative, but still from a physics point of view," or do you mean "written in a style suitable for a mathematics course?"
     
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  9. May 17, 2010 #8
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  10. May 17, 2010 #9

    Thanks guys. I'm looking for a math treatment, from the perspective of linear algebra, geometry and the like.
    Naber's book looks a little too advanced for the present.
     
    Last edited by a moderator: Apr 25, 2017
  11. May 17, 2010 #10

    Fredrik

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  12. May 17, 2010 #11

    Landau

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    @Fredrik: I already mentioned that book in post #6 ;) Haven't read it either, but looks promising (based on Google preview).
     
  13. May 17, 2010 #12

    Fredrik

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    I thought I had clicked all the links, but I must have missed that one. Naber's book looks really nice, especially the stuff about spinors. I might have to get that one myself.
     
  14. May 17, 2010 #13

    Fredrik

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    I just noticed what exactly you're asking here. Schutz's GR book contains one of the best introductions to SR, so I think you should probably start with that one.
     
  15. May 18, 2010 #14

    Fredrik

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    Does anyone know a book that includes a statement and proof of the Currie-Jordan-Sudarshan no-interaction theorem?
     
  16. May 18, 2010 #15
    Okay. I shall look through it. I'm going through Woodhouse's book now. It's okay. Not to my taste. I'm going to have to use Schutz anyway.
     
    Last edited: May 18, 2010
  17. May 20, 2010 #16
    Schutz is okay, but I'd like to know if there are better. Schutz isn't a math oriented style. Does anyone have any other suggestions?
     
  18. May 20, 2010 #17

    Fredrik

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    I'm thinking very seriously about writing one, but if you don't have a time machine...

    If you do, then please bring back a copy for me too so I don't have to write it. :smile:
     
  19. May 20, 2010 #18
    See, what I find out of place is that after reading Linear Algebra, Analysis etc. from math textbooks, I find the treatment given in most physics books quite odd. Instead of simply calling vectors as part of some vector space, they have all these round-about definitions like "a vector is something that transforms properly". Why go into linear transformations and other mappings just to define the same thing??
    They have all these weird connotations. A simple 4-D space that you might encounter all the time in an Algebra book is given some funny hokey name, "spacetime". Yeesh. They'll add "spacetime is curved" to sound more fancy. It's just a different metric, dammit! I'd find it so much easier if I could avoid all this weird stuff. This is why I'm looking for a book written on the math side.
     
  20. May 21, 2010 #19

    Landau

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    I think Naber is the way to go. He says
    etc. so he clearly defines his math, and then explains how physicists (intuitively) think about them.
     
  21. May 21, 2010 #20

    Fredrik

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    I agree. In fact, I don't think anyone hates that "definition" as passionately as I do. It's been about 15 years since I took classes where that definition was used, and I still get angry when I think about it. It's not just that it's a stupid and obsolete definition. It's also that the books I had to read back then as well as all the teachers I had always stated the definition in a way that doesn't make sense. Would it have killed them to say e.g. "an assignment of four functions [itex]v^\mu:M\rightarrow\mathbb R[/itex] to each coordinate system..." instead of "something"??

    But I have some good news for you. Schutz explains tensors really well, if I remember correctly. He defines them as multilinear functions, defines their components in a basis for the vector space (and it's dual space), and derives the formula for how the components associated with one basis are related to the components associated with another basis, i.e. how the components "transform".

    So I still recommend that you read that part. When you get to the GR part, where he starts talking about differential geometry (manifolds, tangent spaces, and tensor fields), you will probably want to study a math text instead. (I know I did). This one is probably the best.


    This is actually very natural. I mean, it's the mathematical structure that we use to represent real-world concepts "space" and "time", so I think the name is very appropriate. Also, it's not just "a simple 4-D space", because even though the vector space structure is defined exactly the way we would do it for a Euclidean space, it doesn't have an inner product, and is equipped with a bilinear form that isn't positive definite instead.

    There's a very good reason why the word "curved" is used, and you'll find the same terminology as well as an explanation of the terms in the best math books. (This one has to be the best).
     
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