Time Dilation Problem

1. Sep 13, 2009

atarr3

Hey all, I'm having a bit of trouble with this problem.

Two events occur in an inertial system K at the same time but 4 km apart. What is the time difference measured in a system K' moving between these two events when the distance separation of the events is measured to be 5 km?

I though I could use the length contraction equation to find the speed the frame is traveling and use that in the time dilation equation, but I don't know the proper time. I found the speed of frame K' to be 0.6c with respect to K.

2. Sep 13, 2009

JesseM

Do you know how to use the Lorentz transformation? The position of the origin is arbitrary, so you can just say one of the two events occurs at the origin (x=0 and t=0 in system K), and then in the K frame the other must be at x=4 km, t=0 since they are simultaneous. Then you can use the Lorentz transform to get x' and t' for the second event in the K' frame...

3. Sep 13, 2009

atarr3

Yeah x' is given to us in the problem. It's 5 km. So when I use the equation t' = [t-(vx/c^2)]/0.8, I get t' = 1.25e^-5 s which would be the time difference, but the book says 1.0e^-5.

4. Sep 13, 2009

JesseM

I think you just made a math error somewhere. The math in these problems is always easier if you use units where c=1, so instead of x=4 km, plug in x=(4/299792.458)=1.334e^-5 light seconds, and since t=0 this gives t' = -0.6*(1.334e^-5)/0.8 = -1.0e^-5 seconds

5. Sep 13, 2009

atarr3

Ah yes I got it now. I had accidentally put in 5 instead of 4. Thank you so much for your help!