0

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.

Fascheue
  • 13
  • Imagine a variant of the experiment in which the ships remain at rest and the observer accelerates to 0.8c. The gap between the ships shrinks to 300m even though the ships have not moved. Does that tell you anything? – Marco Ocram Aug 07 '23 at 21:04
  • https://physics.stackexchange.com/questions/244315/is-this-a-fundamentally-relativistic-phenomenon – BowlOfRed Aug 07 '23 at 21:11
  • What does "simultaneously" mean? If the accelerations (and decelerations) of the two ships are simultaneous in the ground frame, then of course the distance between them remains 500m in the ground frame. If they are simultaneous in the frame of the ships (after they've gotten up to speed), then in the ground frame, the rear ship accelerated first, reducing the distance between the ships. – WillO Aug 07 '23 at 21:29
  • In the scenario I’m thinking of, the distance remains constant in the ship frame. Since the observer and ships are initially in the same frame, they would presumably have to accelerate simultaneously for everybody. Would all of the distance change then only appear during the deceleration period? – Fascheue Aug 07 '23 at 21:52
  • If the distance remains constant in the ship frame, then the rear ship accelerates first in the ground frame. The distance in the ground frame continues to shrink as the rear ship moves forward until the front ship starts to move. Once they are both moving at the same speed there is (obviously) no more shrinkage. – WillO Aug 08 '23 at 00:57

0 Answers0