# Faster than light! **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [October 13, 2002, 10:38pm UTC](https://boards.straightdope.com/t/faster-than-light/132139 "2002-10-13T22:38:20Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![Devil\_s\_Advocate](https://avatars.discourse-cdn.com/v4/letter/d/3d9bf3/32.png) [@Devil\_s\_Advocate](https://boards.straightdope.com/u/Devil_s_Advocate)\ **Post date:** [October 13, 2002, 10:38pm UTC](https://boards.straightdope.com/t/faster-than-light/132139/1 "2002-10-13T22:38:20Z")
The math in the following column – [http://www.straightdope.com/classics/a2\_095.html](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. ---
**Author:** ![Bob55](https://avatars.discourse-cdn.com/v4/letter/b/e9c0ed/32.png) [@Bob55](https://boards.straightdope.com/u/Bob55)\ **Post date:** [October 14, 2002, 12:16am UTC](https://boards.straightdope.com/t/faster-than-light/132139/2 "2002-10-14T00:16:54Z")
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 ---
**Author:** ![Devil\_s\_Advocate](https://avatars.discourse-cdn.com/v4/letter/d/3d9bf3/32.png) [@Devil\_s\_Advocate](https://boards.straightdope.com/u/Devil_s_Advocate)\ **Post date:** [October 14, 2002, 1:09am UTC](https://boards.straightdope.com/t/faster-than-light/132139/3 "2002-10-14T01:09:17Z")
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. 🙂 ---
**Author:** ![Some\_Guy](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Some\_Guy](https://boards.straightdope.com/u/Some_Guy)\ **Post date:** [October 14, 2002, 1:33am UTC](https://boards.straightdope.com/t/faster-than-light/132139/4 "2002-10-14T01:33:58Z")
> [@](#): > > \*Originally posted by Bob55 \* > \*\* > > w = (1.8c) / (1 + .81c^2 / c^2) cross out c^2’s > > w = (1.8c) / (1 + .81) > > \*\* Careful there, **Bob55**. You can’t just cancel the c[sup]2[/sup] out in that equation. ---
**Author:** ![Some\_Guy](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Some\_Guy](https://boards.straightdope.com/u/Some_Guy)\ **Post date:** [October 14, 2002, 1:35am UTC](https://boards.straightdope.com/t/faster-than-light/132139/5 "2002-10-14T01:35:08Z")
Erm, nevermind. I, too, read the damn equation wrong. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [October 14, 2002, 6:46am UTC](https://boards.straightdope.com/t/faster-than-light/132139/6 "2002-10-14T06:46:54Z")
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: > [@](#): > > w = (u + v) / (1 + uv) > > w = (.9 + .9) / (1 + .9 × .9) > > w = 1.8 / (1 + .81) > > w = 1.8 / 1.81 > > w = .994475 ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [October 21, 2002, 5:41pm UTC](https://boards.straightdope.com/t/faster-than-light/132139/7 "2002-10-21T17:41:59Z")
> [@](#): > > \*Originally posted by \*\*\*Some Guy \*\* > > > [@](#): > > > > \*Originally posted by Bob55 \* > > \*\* > > > > w = (1.8c) / (1 + .81c^2 / c^2) cross out c^2’s > > > > w = (1.8c) / (1 + .81) > > > > \*\* > > Careful there, **Bob55**. You can’t just cancel the c[sup]2[/sup] out in that equation. Sure you can. Why would you think that you can’t? ---
**Author:** ![Devil\_s\_Advocate](https://avatars.discourse-cdn.com/v4/letter/d/3d9bf3/32.png) [@Devil\_s\_Advocate](https://boards.straightdope.com/u/Devil_s_Advocate)\ **Post date:** [October 22, 2002, 3:36am UTC](https://boards.straightdope.com/t/faster-than-light/132139/8 "2002-10-22T03:36:47Z")
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! 😃 ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [October 22, 2002, 12:40pm UTC](https://boards.straightdope.com/t/faster-than-light/132139/9 "2002-10-22T12:40:08Z")
:smack: ---
**Author:** ![rampisad](https://avatars.discourse-cdn.com/v4/letter/r/858c86/32.png) [@rampisad](https://boards.straightdope.com/u/rampisad)\ **Post date:** [October 22, 2002, 2:08pm UTC](https://boards.straightdope.com/t/faster-than-light/132139/10 "2002-10-22T14:08:12Z")
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. ---
**Author:** ![Devil\_s\_Advocate](https://avatars.discourse-cdn.com/v4/letter/d/3d9bf3/32.png) [@Devil\_s\_Advocate](https://boards.straightdope.com/u/Devil_s_Advocate)\ **Post date:** [October 23, 2002, 4:28am UTC](https://boards.straightdope.com/t/faster-than-light/132139/11 "2002-10-23T04:28:56Z")
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.