### What a start: my own bad math

Wow, but I'm off to a bad start here. Three posts on the blog, and I've already made my first huge math blunder.

Two objects, one stationary, one moving .9c are

Time dilation is tricky stuff, and a great example of why intuition about math can often lead you wrong - you can't just rely on the intuition (which is what crackpots often do) - you've got to take the time and

Here's an example of why it goes wrong (still going with just the intuition, but this time using it to show why the straightforward intuition is wrong.): Take our two objects - one stationary, one moving at .9c. Now, take the stationary one, and accelerate it to .9c in the opposite direction. How fast is it going relative to an object that is stationary at its original position? .9c. How fast is it going relative to the other object? According to what I said in the original post: 1.8c.

It's fun to play with the real equations a bit, to get a sense of how damn wierd reality is. You can find the equations along with a reasonably well-written explanation at wikipedia. Brian Greene's book, "The Elegant Universe" also has a beautiful description of relativity that manages to avoid explicitly talking in terms of the equations, which is really quite an amazing feat.

Alas, I'm not Brian Greene.

Two objects, one stationary, one moving .9c are

*not*equivalent to two objects moving at .45c. You need to do the relativistic adjustment. Which I didn't.Time dilation is tricky stuff, and a great example of why intuition about math can often lead you wrong - you can't just rely on the intuition (which is what crackpots often do) - you've got to take the time and

**do the math**.Here's an example of why it goes wrong (still going with just the intuition, but this time using it to show why the straightforward intuition is wrong.): Take our two objects - one stationary, one moving at .9c. Now, take the stationary one, and accelerate it to .9c in the opposite direction. How fast is it going relative to an object that is stationary at its original position? .9c. How fast is it going relative to the other object? According to what I said in the original post: 1.8c.

**Bzzzzt**. Impossible!It's fun to play with the real equations a bit, to get a sense of how damn wierd reality is. You can find the equations along with a reasonably well-written explanation at wikipedia. Brian Greene's book, "The Elegant Universe" also has a beautiful description of relativity that manages to avoid explicitly talking in terms of the equations, which is really quite an amazing feat.

Alas, I'm not Brian Greene.

## 3 Comments:

First of all, welcome to the blogosphere!

I wasn't going to nitpick, but since you started it... What if you had to objects going .45c but not in opposite directions. IE, the same direction. The speed between them would be 0. English is such an imprecise language...

By DouglasG, at 4:57 PM

Dammit, I didn't spot the relativistic correction either. I'm slipping :(

I make the actual value about 0.63c rather than 0.45c. That sound about right?

Good blog idea btw

By Lifewish, at 8:39 PM

lifewish:

Yeah, .63c is about right.

By MarkCC, at 8:48 PM

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