OK, here is the problem formulation, I won't give the "surprsing" answer for a few days.(adsbygoogle = window.adsbygoogle || []).push({});

In an inertial frame, we have

an observer at the origin

a particle moving at a velocity of .9c in the positive x direction at a postion of x = 10 light years.

We also have an observe acclerating at 1 light year/year^2 (approximately one gravity) at x=1 light year. This accelerating observer is stationary at t=0 in the inertial frame, and is accelerating in the positive x direction.

The question is:

In the local coordinate system of the accelerating observer, what is the velocity of the moving particle?

hint: it may be helpful to know that if [tex]\mbox{(\tau,\xi)}[/tex] are the coordinates of an object in the local frame of the accelerated observer with acceleration 'a' an inertial observer will assign the coordinates (t,x) as follows:

[tex]

t = (1/a + \xi) sinh(a \, \tau)

[/tex]

[tex]

x = (1/a + \xi) cosh(a \, \tau)

[/tex]

Note that [tex]\tau=0,\xi=0 -> t=0, x=1/a[/tex]

In this problem, a=1.

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# A problem in special relativity with a surprising result

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