# Special relativity and general relativity

## Main Question or Discussion Point

I have studied most of the concepts of Newtonian mechanics and understood the calculations and derivations involving the concerned formulae.

I have a basic knowledge of calculus (differentiation of products along with differentiation of trigonometric, logarithmic, exponential and implicit functions as well as how to integrate them by parts and reverse u substitution), and an understanding of 3d vectors and complex numbers (in polar forms as well).

Like most people, I'm experiencing moments of frustration very often nowadays because I frequently encounter questions which require a knowledge of relativity, which brings me to my question:
Should I start learning relativity? My knowledge in Maths is not very extensive(as you must've gathered by now) and I've heard that GR is mostly maths and SR is conceptual, so if I start learning relativity, what should I start with? Does anyone know any good websites where I can learn the essential concepts and practice questions?

Thanks, I'll look into it. Do you have any sources for GR though?

Eventually, there will be a GR course on there, too. I wouldn't worry about GR until you've done SR and maybe a little more math and other physics, but you might want to see if you can get the book General Relativity from A to B, which just explains some of the concepts. John Baez has some good GR tutorials on his website, but you'd probably want to look beyond the internet for the most part, except as a supplement. You could also start trying to learn differential geometry of surfaces because that's a good warm-up for the more advanced 4-d Lorentzian geometry of GR (first, you would want to do multi-variable calculus if you haven't done that). Also, electricity and magnetism is good to know, partly because it builds your math skills more.

I also like the book Spacetime Physics for SR.

Usually the next step from beginner Newtonian physics is electromagnetism.

jtbell
Mentor
so if I start learning relativity, what should I start with? Does anyone know any good websites where I can learn the essential concepts and practice questions?
You might find this site useful as a summary, although it's not a textbook and doesn't have exercises / practice questions:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html

WannabeNewton
...and I've heard that GR is mostly maths and SR is conceptual...
Neither of those statements are true in the slightest really.

Thanks for the responses, now I'm really pumped up for understanding these seemingly complex theories!

Fredrik
Staff Emeritus
Gold Member
I would recommend that you study some linear algebra (the most basic stuff about matrices and linear transformations) and then read the first 2-3 chapters of "A first course in general relativity" by Schutz. This is my recommendation for SR, not GR. I don't like the GR chapters of this book as much as the SR chapters. Chapters 1-2 are about SR. Chapter 3 is about tensors.

You're not ready for a mathematical presentation of GR yet. But that shouldn't stop you from reading the best non-mathematical book on GR, "Black holes and time warps: Einstein's outrageous legacy", by Kip Thorne. The problem with the mathematics of GR is that the best books on differential geometry (in particular Lee's "Introduction to smooth manfiolds" and "Riemannian manifolds: An introduction to curvature") require you to know topology, and it takes several months to learn topology well enough to follow the proofs that involve topology in a book like that. It is however possible to read Lee and just ignore everything that involves topology. You can still develop a pretty good understanding of the key concepts in differential geometry.

You asked specifically for what to start with. The short answer is spacetime diagrams. Schutz explains them right at the start. I think that "Spacetime physics" by Taylor & Wheeler (mentioned by homeomorphic above) does the same. I haven't read Taylor & Wheeler, but I think I read that Schutz based his presentation on theirs.

Definitely start with special relativity. General Relativity is hard, and very mathematical. It's usually taught at masters level. If you want to do anything interesting with it you need to know a lot of very difficult mathematics. If you're not familiar with tensors and that sort of thing you're going to struggle with any real GR text.

I'd suggest reading A.P. French Special Relativity - it's old but IMO the best intro to SR there is. It will give you enough grounding to tackle advanced physics. The only thing I'd fault it for is not covering enough relativistic electromagnetism, which in my opinion is very beautiful and really brings together classical EM.