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GR & SR for Dummies

  1. Sep 13, 2006 #1
    What book(s) would you all recommend for learning about these two theories?

    I have limited math knowledge; most of the equations I see look like a greek sentence to me. Is it even possible to really comprehend relativity without the math?

    I keep asking questions that turn out to be rather foolish, and I fear I'm trying the patience of those few here who can truly answer such questions.

    Efforts at reading online are proving to be problematic and even contradictory. For example, I read this statement:

    I believe Einstein gave up the ether concept and definitely opted for the physical relativity principle at least a couple of years before the final formulation of SRT, perhaps even earlier. At any rate, at some point well before the 1905 formulation of the theory, he made this choice and adhered to it thereafter.​

    in How Did Einstein Discover Relativity<. Admittedly, this article is focused on atempting to answer "how", but nevertheless it does state that Einstein "gave up" on the concept of "ether" by 1905.

    And yet, Ether and the Theory of Relativity, apparently given by Einstein in 1920 clearly shows he at the least "allows for" the existence of ether, or "aether" as they put it.

    Point is, material I've been reading can be (apparently) contradictory. I cannot find online versions of Einstein's theories (at least not in English).

    So, what book(s) might I look for?

    And if math is essential to understand the theories, what math do I ned to learn? I have merely basic algebra to work with. What's the shortest path through calculus or whatever to understand the math required?

    Thanks in advance.
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  3. Sep 13, 2006 #2


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  4. Sep 13, 2006 #3
    Thank you robphy.

    From reading that first thread, I get the impression that an absolute minimum math is vector calculus.

    Would you agree that is a workable starting point?

    And if so, where do I go from basic algebra to vector calculus? What should I look for next (I'm assuming there are intermediate topics to learn before being ready for vector calculus)?
  5. Sep 13, 2006 #4


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  6. Sep 13, 2006 #5
    I'm reading it now.

    Thank you for the link.
  7. Sep 13, 2006 #6
    With just a little algebra, you can have a fairly complete understanding of the core of SR. I recommend N. David Mermin's book for this.

    For a list of books graded by mathematical level, see this list of books.

    You can understand come of the concepts behind GR without math (i.e. gravity as an effect of curved spacetime), but a full working understanding requires some math. The Taylor and Wheeler black hole book tries to give you some understanding of at least the spherically symmetric case by just starting with the Schwarzschild solution. Hartle tries to get to as much phyiscs as possible before introducing tensor calculus.

    Math: Trig and "college algebra" (pre-calculus), Calculus & analytic geometry, vector analysis ("div, grad, curl and all that"), how to solve simple differential equations, linear algebra, tensor calculus (most GR books develop the needed tensor calculus). Some knowledge of Fourier analysis is helpful.

    Physics: classical mechanics (at the level of, say, French's book), E&M (Maxwell's Equations in differential form; at the level of Feynman v. 2).
    Last edited: Sep 14, 2006
  8. Sep 13, 2006 #7


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    It is not as "deep" as some of the other treatments, but I would recommend Bondi's book "Relativity and common sense". The only requirements are high school algebra.

    The treatment does not explain modern 4-vector notation, however. This could either be a plur or a minus, depending on your goals. Certainly, if you are serious about physics, you need to learn about relativity in 4-vector notation. If you are just casually interested, the approach without them might be more accessible.

    Being a Dover book, it is available fairly cheaply. Amazon lists it for 10 bucks.


    One vendor is currently selling a used copy for $.29 plus shipping. (which will be slightly over 10x the price of the book, if I'm reading the shipping rates correctly).
  9. Sep 14, 2006 #8
    You'll also need some linear algebra: how to solve systems of linear equations, manipulate matrices, calculate determinants; the idea of a change of basis and linear transformations.

    You might take a look at this book. I haven't looked at it in a couple decades, but I remember it as being pretty cool.

    Your standard big-ass "Calculus With Analytic Geometry" text will cover through vector calculus (which is usually the third semester). My old text, Swokowski 2nd ed., also has a final chapter on differential equations.

    To prepare for calculus, you'll need trig and "college algebra".

    The subject of self-taught calculus has come up here before. You might pick up a "Calculus Made Easy" type book and see how it goes. But that'll usually only get you in the door, and they don't usually cover things like Taylor series or partial differentation. Certainly less daunting, though. Some calculus primers I remember fondly include What Is Calculus About? by W. W. Sawyer and Prof. E. McSquared's Calculus Primer (if you're not offended by a comic book format.)

    By the way, Feynman Lectures v. 2 has a nice intuitive and physical intro to vector calc.

    EDIT: Looking around on Amazon, I found this monster, which seems like it covers just about everything in the undergraduate math curriculum needed for Physics. He reviews basic calculus, but I wouldn't want to start learning basic calculus from a book like this.

    Also, "Engineering Math" books, like this one have to start out at a really basic level given their audience (just kidding, engineers, just kidding!).
    Last edited: Sep 14, 2006
  10. Sep 14, 2006 #9
    Thank you all for the great references and advice.

    It appears I have a long row to hoe.
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