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On 2002-10-11 00:29, JS Princeton wrote:
Your math error is actually a very common one. You assume that the squareroot of the sum of two squares is equal to the sum. It is not.
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I don't see where he does that directly, but as you point out below, it is a consequence at non-relativistic velocities.
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Another way you to write your formula for v_3 is as follows
v_3=sqrt(v_1^2+v-2^2-(v_1*v_2/c)^2)
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Huh? Does that work out? Hey, that's right. It follows right from his equation:
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If this is nonrelativistic v_1*v_2 much less than c^2, we get from your equation that
v_3=sqrt(v_1^2+v_2^2)
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And, as you say, in order for that to be true, the right hand side would have to be also equal to v_1 + v_2
I think the basic error is his assumption that the dilations compound by multiplication. He assumes that if A sees B as twice as slow, and B sees C as twice as slow, then A will see C as four times as slow. That's obviously not true--just let C be the first observer A. A would see A as four times as slow?