Some Pysics Insights


Proof by Picture
basic stuff
Update Log
As mentioned on the front page, the target audience for this website is amateurs -- people who are interested in physics, and are interested in relativity, but who are not professional physicists.

It is my fond hope that this site may help some visitors to better understand the subject of relativity, or at the least will provide some interesting reading.

About Relativity ... And Some Advice

The goal of relativity is to render all physical laws in a form which is relative to the observer:  the laws should be independent of any motion of the observer or (in the case of radiant energy) of the source.  Special relativity treats the special case of uniform motion; general relativity treats the more general case of accelerated motion.  General relativity also provides an answer to the question, "Why are inertial and gravitational mass always present in a fixed ratio?" or, equivalently, "Why does everything fall at the same rate?"

If you are setting out to learn relativity, then I have a bit of hard-won advice.  Start by asking yourself:

How's your algebra?  Pick one:
  1. Rock solid!  I invert matrices in my head for fun!
  2. OK, I guess.
  3. Boy I hated that subject -- skipped all the homework and just crammed for exams
  4. Algebra?  Huh?  You mean, like the quadratic formula 'n stuff?
If you answered (3) or (4), go find an algebra book and spend some time with it.  Artin's "Algebra" is pretty readable, if you haven't already got a good text lying around.  Ideally you should at least know what a symmetric bilinear form is before you tackle relativity.

GR requires tensor calculus, but introductory GR texts tend to cover it as they go, so it's not really a problem.  But they seem to assume you already know the algebra cold.

About Units and Conventions Used on This Website

Throughout this website, I use the convention that C = 1, and hence multiplication by C can be ignored.  If time is measured in seconds, then lengths are measured in light-seconds; if time is measured in years, then distances are measured in light-years.  This simplifies a number of formulas considerably, though at some occasional cost in clarity.

Except as noted, the Lorentz metric is assumed to be diag(-1,1,1,1).

About Me, and Contact Info

I'm a professional programmer with a long-time interest in math and physics.  I finally decided I wanted to understand something about general relativity.  So I blew a bunch of money on text books, and since then I've spent lots of my free time studying (or arguing with various people on sci.physics.relativity).

If you want to get in touch for any reason, please email me.  If you don't hear back, and the weeks roll by, you should assume I'm busy. I'll get back to you eventually, for sure...

About Errors

The derivations and proofs on this site are my own.  Though I have tried to be careful, the conclusions here have not, for the most part, been checked against published books or articles, so it's quite possible that there are errors either in the reasoning or in the conclusions.  If you happen to run across anything you think is incorrect, please let me know.

About Change

Most of the text on this page, along with most of the technical information on this website, was written a number of years ago. Since then things have changed, and I no longer have much time to spend in the pursuit of math and physics. Consequently the rate of change in the technical content has decreased to a crawl. That may change again in the future, but right now my free time is largely occupied by such pursuits as chopping potatoes and writing, with some fraction of the time spent writing being devoted to this site.

Consequently, most of the updates these days are to the Iemy section of the site. While I find it amusing, I'm afraid most visitors here will probably give it a yawn and walk off. So it goes. And even that section has been lagging badly; in fact, the first volume of the Iemy Papers (there's more than one volume of that drivel?? OMG!) was completed over a year ago, but continues to exist only on paper (written with a fountain pen no less).

About the Website:  Technical Details

Most of the original pages on this site were authored using Mozilla (which was capable of producing far more sophisticated websites than anything I ever asked it to do -- the simple site design and primitive formatting are by choice, not by necessity).  After Mozilla got canned, a number of pages were authored with a mix of Kompozer (a variant on NVU) and Seamonkey, depending on whose bugs I found the most annoying on any particular day.  The illustrations were done with Gimp.  Most of the equations were edited with OpenOffice, but recently I've gotten sick of the never-fixed bugs and limitations in OO Math and have switched to LaTex (which has a completely different set of problems).  Graphs were either drawn with splines in Gimp (when the curves were not critical) or were produced by Gnuplot.  The inline Greek text uses a mix of pictures and HTML Unicode characters, which may be unreadable in some browsers.

More recently, Kompozer stopped being maintained, and Seamonkey's updates come so slowly (aside from the bits and pieces that are pulled from the Firefox source tree) that it's hard to tell whether maintenance is still ongoing or not. The "follow-on" project to Kompozer seemed to be BlueGriffon, so I switched to that, and some of the pages here were authored using it.

BlueGriffon, unfortunately, has had an erratic update rate also, and most recently the updates have taken the form of removing features in order to improve the user experience (or so it appears). I.e., it seems to have caught Gnome disease. Furthermore, its spell checker, which I need desperately when I'm writing English text (or anything else except pure equations) works really badly in recent releases; it apparently loses interest in what I'm typing after a while and stops flagging misspellings (or maybe I just tire it out with the volume of them).

Consequently, I've switched again, and I'm currently using Bluefish. It's not WYSIWIG (shades of Runoff!) which is a major step backwards but none the less it seems to be OK for straight text entry. We'll see whether I can deal with the awkwardness when and if I get back into heavy equation entry. (And though I used it for several hours the other day without a hitch, it's crashed three times in the course of updating this About page, which gives me a really bad feeling.)

Anyway, updates to some part of the website will no doubt continue, though at a relatively slow pace. And this About page is likely to lag an awful lot -- the bits I'm adding to it today are the first time it's been touched in about 7 years. To see what's really going on the site as a whole, you need to check the Updates page, which is nearly always up to date.

Links and image dimensions continue to be checked with home-brew Perl scripts before uploading, and most pages have been validated using the W3C validator.  If you have problems with anything on the site please email me.  The pages are served by Apache running on a Linux box, on space owned by the good folks at (In fact, as of 2014, they've been out of the web hosting business for perhaps 3 years. They keep a few servers around running on virtual machines just for their old customers who haven't moved off. So, one of these days I should probably change to something faster, and more current...)

Why don't I use Dreamweaver?

$$$$, in short. After I decided BlueGriffon was losing, I once again looked into switching to Dreamweaver on a VMWare box (I've used it that way -- it's nice). I took a tight grip on my wallet and looked around to see what I would have to pay to buy a copy. Well it turns out you can't buy a copy, not any more -- nowadays you can only rent a copy from Adobe. And, I suppose, you can just forget editing while totally offline. Maybe that's a great idea but it creeps me out; I want the software on the disk, right here, and yes, I even want it on my backup tapes. So, no Dreamweaver here.

What about MathML?

I don't know if I've said this anywhere else on the site. I don't plan to use MathML until it's so mainstream every browser supports it, and I can predict exactly how the result will look when it's rendered by Joe Random Browser. Until then, I'll stick with little pictures for the equations.

On the other hand, if blatting pictures in with Bluefish turns out to be too cumbersome I may change my mind on that.

Except for photographs of Einstein, all text, images, and computer code on this site, unless otherwise noted on the individual pages, are copyright © 2004-2012 (or whenever) by Stephen A. Lawrence.  If you copy anything from this site at least have the good grace to send me email telling me about it.  (In any case my employer probably is the legal owner, since like most of us I signed away my rights when I took a job.  Whatever.)

It's hard for me to imagine how anyone who studies the general theory of relativity could fail to conclude that Einstein, Hilbert, and Riemann were brilliant.  Einstein, obviously, also had a sense of humor.

Albert Einstein acting silly

Page last updated 4 June 2014 ... and the update before that was 11/16/06 ...