On May 11, 8:10 pm, Igor wrote:
On May 9, 7:44 am, Albertito wrote:



Let us consider the simple case of addition of velocities
along a straight line. The incompleteness of SR resides
in the fact that a speed v can't currently be experimentally
distinguished from its rapidity r = arctanh(v/c), for values
of that beta = v/c below the third-order term approximation.
The power series expansion of r = arctanh(v/c) is

r = v/c + v*3/3c^3+ v^5/5c^5 + v^7/7c^7 + ...

Provide references of any experimental test of SR, showing
that the rapidity r can be distinguished from its beta v/c, beyond
its second-order approximation. Prove at least that the third-order
term v*3/3c^3 lives outside the error bars. Since, we can't still
perform such accurate experimental tests, we must conclude
the addition of velocities still remains within the euclidean sum
of vectors

w = u + v.

That sum can't still be experimentally distinguished from the sum
of rapidities

arctanh(w/c) = arctanh(u/c) + arctanh(v/c).

In addition, we must also conclude that the relativistic Doppler

f' = Exp(-r) f ,
where r = arctanh(v/c),

can't still be experimentally distinguished from this one

f' = Exp(-v/c) f

Uhh, you do understand that v/c = tanh r don't you? I didn't think
so.

is tanh hyperbolic tangent not asymptotic?