Where can I find a proof for the mathematics of special relativity?

[gkalogeris]

Where can i find a proof for the mathematics of special relativity from a physics point of view?

 

[HallsofIvy]

?? What's wrong with any of the basic texts on relativity?

(For general relativity, the absolute best book is The Mathematical Theory of Relativity by Sir Arthur Eddington, first published in 1923.)

 

[chroot]

You cannot prove physical theories, so your question is meaningless.

Special relativity is a theory: a mathematical formalism which predicts the results of experiments. As it happens, it has correctly predicted the results of every experiment ever devised to test it, so it is a successful theory. It has a mountain of supporting evidence. It cannot be proved, however, because it is always possible that it will fail to correctly predict the results of some experiment in the future.

Proofs are in the domain of pure mathematics. The best you can hope to achieve for a physical theory is a mountain of supporting evidence.

- Warren

 

[gkalogeris]

Thanks for the general relativity book. Regarding my question on special relativity. I do not have any book about it and i was wondering if there are on the web any kind of notes with derivation of the special relativity formulation. Not from a mathematical point of view but from a physical point of view.

 

[Archduke]

I can't say I've read any of these books, but here is the http://www2.warwick.ac.uk/fac/sci/physics/teach/module_home/px109/reading_material.pdf" from my first year Physics degree Relativity module. Not sure if you'll be able to get hold of many of these books if you're from the U.S (I say that, because our core Text "University Physics" By Young and Friedman has "NOT FOR SALE IN AMERICA OR CANADA" in massive letters on that back! Not sure, why, really, but yeah...)

Hope those books are useful!

 

[neutrino]

Even the "physical points of view" will involve some amount of mathematics, but nothing more than high-school algebra and trigonometry, and in the extreme case, elementary calculus. A good introductory text is Spacetime Physics. You can download the first chapter of the first edition here. And a set of lecture notes
http://cosmo.nyu.edu/hogg/sr/

 

[maverick280857]

The books by Young/Friedman or Sears/Zemansky/Young are indeed available in the US, but in a different form. In India for example, most of these books have the "not for sale..." printed on the back covers, but that is (I believe) to prevent piracy and mass reproduction and sale at lower costs.

A very nice introduction to Special Relativity is the book by Robert Resnick. You don't need a lot of mathematics to get started with special relativity, although some amount of differential calculus would definitely be useful if you're interested in the derivations. As neutrino pointed out, the book Spacetime Physics by Wheeler/Taylor is also a good first book.

As for the "proofs", well, everything in special relativity (or at least everything I know about it) can be "derived" from the Lorentz transformation and the Minkowski metric as starting points. But as chroot pointed out, there are really no proofs: you start with axioms--which by the way, are all experimentally verifiable for SR--and deduce the outcomes in SR that you are probably seeking "proofs" for: length contraction, time dilation, to name two.

And yes, the physical point of view inevitably will require some mathematics, but it will be far less than what you can expect in the full blown formulation, and you can always figure out what you need to know more in mathematics from reading any of these books. Enjoy!

Nice links Neutrino

 

[gkalogeris]

I just ordered the books of Taylor proposed by neutrino. Thanks guys

 

[Friendlyel]

I'm just wondering, aren't there websites like Wikipedia and Eric Wolfram's Scienceworld that give basic descriptions of the material?

 

[nrqed]

I'm just wondering, aren't there websites like Wikipedia and Eric Wolfram's Scienceworld that give basic descriptions of the material?

Just an aside: It is Stephen Wolfram. A lot of the material on the Wolfram math site is written by Eric Weisstein.

 

[Friendlyel]

Thank you for clearing that out. I was just wondering exactly how useful those sites are for learning the question mentioned here and/or other subjects of modern physics.

 

[neutrino]

Thank you for clearing that out. I was just wondering exactly how useful those sites are for learning the question mentioned here and/or other subjects of modern physics.

Before anyone starts beating a dead horse again, I'll point you to the archived beating of one.
https://www.physicsforums.com/showthread.php?t=159967

Again, while places like Mathworld are useful as a reference, they're not places to learn things from scratch...not the most the effective way of learning. Mathworld is like a detailed dictionary of mathematics.