Date: Jun 4, 2010 3:47 AM
Author: stargene@sbcglobal.net
Subject: Re: Is there a compact form for n-tuple relativistic additions of <br> velocities?

Hi, and several googols of thanks for your help. When I tried your

vsum(n copies of x) = 1-2/(2*AT(x))^n

it did not work for me, probably due to a misunderstanding on my

part. But your

vsum(n copies of x) = T(n*AT(x))

worked perfectly on my Haxial calculator, reproducing results

identical to my own tedious calculations, eg: with n = 5, 10 and 50,

using recursive versions of SR's original relation. Using your

relation and pushing n to 10^7 and then 10^9, it also shows that

vsum(n copies of x) converges quickly to

v = .761594155... Co,

instead of Co itself. This is unexpected, though I already knew

that for n = 2, 3, 5 and 10 (with v = Co/2 , Co/3 , Co/5 and Co/10 ),

the resultant velocities <decreased>, ie:

0.8 , 0.777 , 0..7672 and 0.76299 times Co ,

respectively (where Co = unity). This bothered me, especially since

initially it seemed conceivable that the sum might even converge to

0.0 as n --> infinity and v --> 0.0 Co! Nevertheless, the actual con-

vergence is still counter-intuitive, having expected the sum to rise

eventually to Co, as I'm guessing you did too.

Interesting...though what it might mean physically is anybody's guess,

without a ouiji board and Prof. Einstein.