- #1
leonmate
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Homework Statement
In the inertial frame of observer A two events occur at the same position a time 10 ns apart. In the frame of the observer B moving with respect to RA, one event occurs 1m away from the other. What is the difference in time between the two events in B's frame.
Solve by finding the Lorentz boost speed v that connects the two frames.
Homework Equations
Lorentz transformations:
T = γT'
L = L' / γ
[t] = [vγ γ][t']
[x] [γ vγ][x'] <--- supposed to be the Lorentz transform matrix
The Attempt at a Solution
I've attempted this a couple of different ways:
First, in B's frame:
T' = 10^-8 , X' = 0m
T = ? , X = 1m
If I attempt to use the length contraction formula to find γ, I find γ = 0 as X' = 0
So then I don't have enough info to find T. So i figured this can't be right!
Next, I tried using the transformation matrix
[t] = [vγ γ][t']
[x] [γ vγ][x']
Plug values above, and I find I get stuck with an equation with loads of v's that i can't simplify.
Any help??
Thanks
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