The math in the following column –
http://www.straightdope.com/classics/a2_095.html
– is wrong. In the example given, the result would be 3.258c, not 0.994c. In fact, the given formula predicts that the “addition” of two velocities always gives a result greater than their mathematical sum. That’s clearly not the case. If it were true, it would indeed allow faster-than-light travel.
I’m guessing this is a case of poor editing, as I can’t imagine Cecil himself would make such a blatant mistake.
I get .994c, in agreement with Cecil.
w = (u + v) / (1 + uv/c^2)
w = (.9c + .9c) / (1 + .9c*.9c / c^2)
w = (1.8c) / (1 + .81c^2 / c^2) cross out c^2’s
w = (1.8c) / (1 + .81)
w = (1.8c) / (1.81)
w = .994475c
Ugh. I missed the "/"s, and though the quantities were being multiplied instead of divided. How did I make a mistake like that? :smack:
I can be such an idiot sometimes. Worst of all, when I challenge something, I often make these bold declarative statements, without adding qualifiers like “I think”, because I’m so sure I’m right. Then later it turns out I missed something obvious.
Ah well. Better that I should be wrong than a Straight Dope column, anyway. 
Careful there, Bob55. You can’t just cancel the c[sup]2[/sup] out in that equation.
Erm, nevermind. I, too, read the damn equation wrong.
There’s a neat little trick that relativistic physicists do to make the math a little easier, and that is let c = 1. That is, when you say that something is moving at a speed of 0.6, it’s implicit that it’s 0.6 times the speed of light.
Then the velocity addition formula becomes w = (u + v) / (1 + uv), and the problem reworked is one or two steps shorter:
Sure you can. Why would you think that you can’t?
Um, DrMatrix, did you notice that Some Guy said in the very next post that he misread the equation? He does realize now that he made a mistake. Perhaps you just wanted to know what mistake he made. If not, you’re the third person in this thread to say something stupid as a result of missing something pretty obvious. Perhaps we should start a club! 
:smack:
Score zero for the Devil.
(0.9c + 0.9c)/(1 + [0.9]^2) = 1.8 / (1.0 + .81)
in other words
1.8 / 1.81 = 0.99447513812154696132596685082873
QED.
Yup. I knew from the start that it wasn’t Cecil who actually made the mistake. I just didn’t realize that it was me (duh).
If you read the whole thread, you know that it’s already been established that I made a dumb mistake, so that doesn’t really need pointing out anymore. If you didn’t… well, read my reply to DrMatrix above.