
Re: Is there a compact form for ntuple relativistic additions of velocities?
Posted:
Jun 4, 2010 3:47 AM


Hi, and several googols of thanks for your help. When I tried your
vsum(n copies of x) = 12/(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 counterintuitive, 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.

