>>11026783This is why they talk about that:
The unprimed observer is at rest with respect to a rod, and they measure a length L.
We say and
Where point 0 is the left side of the rod, and point 1 is the right side.
Applying the Lorentz transformations for an observer that sees the rod moving with speed v to the right:
We get and
So here's why they talk about synchronization of measurements:
We might naively assume the moving observer sees a rod length of
and since gamma is greater than 1, the rod should appear even longer for the moving observer.
However, notice that the times of the two primed events are different! This means these two events correspond to the moving observer measuring the position of the left side of the rod at one time, waiting a bit, and then measuring the position of the right side of the rod at a later time. But this doesn't make any sense as a measure of length, does it? If you wanted to measure the length of a moving car, would you measure the position of the left side, wait a few seconds, then measure the position of the right side and subtract the two positions? Of course not, you would measure the two sides of the car at the same time and subtract the positions.
To get the position of the right side of the rod at , we take
Which is the proper length contraction formula.
