Imagine two rocket ships that are some distance (let’s say 500 meters) apart. An observer sees them both at rest.
Suddenly, they simultaneously start accelerating. Accelerometers in each ship measure the same value. Once they reach a velocity of .8c, they stop accelerating. From the perspective of the passengers, there is still 500 m between the two ships.
Presumably, the distance between the two ships is contracted to 300 m in the observer’s frame.
How and when does this length contraction happen? If the distance between the two ships is reduced to 300 m, they couldn’t have had equal acceleration paths despite the fact that they began with matching accelerometer measurements.
