Proof by Picture
basic stuff
Site History
Some Physics Insights logo and title
There are already many fine websites which treat physics in general and relativity in particular.  Some of them are mentioned on the links page for this site, and some you no doubt already know about (Wolfram, Wikipedia, etc...).  So what do I think I can add to such a wealth of material?  My own explanations and my own derivations of things, in which I try to discuss the results as I go and generally provide explanations of points that are often glossed over.  I've also provided visual proofs of a few items which are typically demonstrated only algebraically; I hope to increase the number of such proof-by-picture items as time goes by.

In these pages, I present a few of the insights which I found helpful, surprising, or just pleasing.  I expect most visitors will be to be amateurs, who are studying relativity for fun, just as I am; I found these things useful, so perhaps you will too.  Some things here are obscure items or things which most authors just assume you know (which you might not), and some may be things everybody talks about but which I think I have a slightly different slant on.  Of course, I have my own view of time dilation and the best "intuitive" way to view it, and I talk about that.  And some of the things here are just tricky problems or derivations which I worked out, and which I just wanted to show off somewhere.  No doubt most of this material is available (somewhere!) in textbooks and journal articles, but I did not find it there in an accessible form.

I have made little effort to separate "special relativity" and "general relativity".  They are cut from the same cloth; the former is just a special case of the latter, and there is not even clear agreement today on where to draw the line between them.   Most people seem to treat the "special" theory as dealing with flat spaces and coordinates in which the metric is Minkowski's (either diag(-1,1,1,1) or diag(1,-1-1-1) depending on your taste), and call anything that addresses nonzero curvature or uses a different metric tensor "general relativity".  Examples of both cases appear here.

Finally, if you've come this far, don't leave without checking out the links page.

(For general information on conventions used on this website, as well as general advice about learning relativity, please see the About page.)

Additions planned for the future (a long, long future, at the rate I'm going):
Write up the Lie derivative of a vector, for which I've finally got a good picture
Something on parallel-accelerating rods
Translate more of the site into French (including the front page)
Add a page introducing relativity
Reorganize and split up Accelerating Twins page, which is too big
Linear twins, porthole view
The Relativistic Albatross
Brachistochrone and a little on applications of calculus of variations
A discussion of 1-forms and rank 2 tensors from the algebraic POV

And for an unrelated view of Albert Einstein, here's a quote from Bob Dylan, which I've included solely because I'm amused by it and enjoy the song from which it comes.

These pages have been optimized for viewing with Firefox or Seamonkey at a resolution of 100 DPI which is really just a fancy way of saying that's what I use to browse the web so that's what I tested them with.  I may eventually test these pages with Mozilla 1.7, Netscape 4, AOL 7, Apple Safari, Opera, Lynx, Mosaic, Neoplanet, Cyberdog, and MSIE but don't hold your breath.   If you encounter any problems of any sort when viewing any of these pages, please email the webmaster who would be tickled pink to hear from anyone who's actually browsed this site.  By the way, I already know some buttons don't look right in MSIE; that is because Microsoft refuses to fully implement png file support.  You should bug them about it if you use MSIE.  MSIE 7 may do better on this score.

Page last updated on 11/16/06; typo corrected on 26 Apr 2010