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