I actually just need help with an explanation rather than equations (I hope this is OK).
In my essay I need to explain why the length contraction in Special Relativity is the inverse of the time dilation factor. My explanation is below, but I'm not convinced that I have totally understood it. Could someone please check that I have the correct understanding?
The Attempt at a Solution
''Imagine the pilot on the spaceship flying past the stationary observer on the space station. After a short distance there a two satellites, a large distance apart hovering in space. The stationary observer on the space station watches the rocket fly past the first satellite, and then travel towards the second satellite at velocity v, passing it at time t. The pilot however, sitting still in her rocket passes the first satellite and then watches the second satellite move towards her at velocity v, passing it at time t’.
From the observer on the space station’s point of view, the distance between the two satellites is L = vt, but the distance from the pilot’s point of view is L’ = vt’.
The time from the pilot’s reference frame is less than the time from the observer on the space station’s reference frame, but as they both agree on the length of time it takes to get from one place to another, the distance travelled must also be different to compensate. The distance between the two satellites appears shorter to the pilot.
L=vt = L'=vt'
L'/L = vt'/vt
These ratios are equivalent but L and L’ are different, and t and t’ are different, and so to make the equations equivalent one must be the inverse of the other.''
Thanks in advance