"Tom Roberts" escreveu na mensagem
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El Enrrabadore-mor wrote:
"Tom Roberts" escreveu na mensagem
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Do you have an equation, dimensionally consistent, where one
could see what you are talking about?

Consider an object moving relative to an inertial frame with a velocity
v(t) (= dr/dt where r is its position 3-vector relative to that frame, and
t is the time coordinate of the frame); v(t) can be an arbitrary function
of time. Its elapsed proper time between t=T1 and t=T2 is:

\tau = \integral_T1^T2 sqrt(1-v(t)^2/c^2) dt

You mean that "T1^T2" is T1 exponential to T2?
Or else, is it "T1 times T2"?

Meanwhile:
integral_sqrt(1-v(t)^2/c^2) dt =
= 1/2*(v(t)^2/c^2)*sqrt(1-v(t)^2/c^2) + 1/2*arcsin(v(t)^2/c^2)

Something of the form:
1/2*x*sqrt(1-x^2) + 1/2*arcsin(x^2)
being: x = v(t)^2/c^2
v(t) = r omega = r w
w - angular velocity

Let me see where this leads, thanks.