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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A problem in special relativity with a surprising result

**Physics Forums | Science Articles, Homework Help, Discussion**