- #1
George Plousos
- 11
- 2
- TL;DR Summary
- The classic twin paradox is "explained" because there is acceleration, but in the following version of the twin paradox there is no acceleration and I do not see how the dilation of time could be explained.
Bob is standing on Earth and Alice is on a distant planet at a constant distance from Earth. Their watches are already synchronized in the following sense: Suppose Alice's planet is a light-year away from Earth. Bob emits a light signal to Alice at time t = 0 according to Bob's watch. When Alice catches the signal, she sets her watch to position t = 0. Bob sets his watch to t = 0 one year after the signal is sent. Now Bob and Alice's watches are synchronized.
Alex stands behind Bob, then accelerates and the moment he overtakes Bob his speed stabilizes. At that moment they are synchronizing their watches, and this marks the beginning of the experiment. It does not matter what Alex did before the clocks were synchronized, so his acceleration does not count in the experiment.
Alex continues his journey until he gets too close to Alice. At that moment, Alex photographs his watch and Alice's watch at the same time, and immediately after that, he slows down and stops. If at that moment Alex compares his watch with Alice's watch, he should not find a significant difference from the difference between the photographed watches. Because Alice and Bob's watches are synchronized, it is not necessary for Alex to return to Earth to compare his watch with Bob's watch.
In this experiment we can assume that Alex is motionless while Bob and Alice are on the move. However, both alternative reporting systems are different aspects of the same events. This means that the photographed watches will have the same difference in both reference systems. But these reference systems are equivalent, as there is no acceleration. Without acceleration we cannot justify the dilation of time for any observer of the experiment. So I conclude the photographed watches should not be different, ie they do not record any dilation of time. But despite these objections,
the question is
Comparing the photographed watches, did Alex's watch gain or lose time compared to Alice's watch?
Alex stands behind Bob, then accelerates and the moment he overtakes Bob his speed stabilizes. At that moment they are synchronizing their watches, and this marks the beginning of the experiment. It does not matter what Alex did before the clocks were synchronized, so his acceleration does not count in the experiment.
Alex continues his journey until he gets too close to Alice. At that moment, Alex photographs his watch and Alice's watch at the same time, and immediately after that, he slows down and stops. If at that moment Alex compares his watch with Alice's watch, he should not find a significant difference from the difference between the photographed watches. Because Alice and Bob's watches are synchronized, it is not necessary for Alex to return to Earth to compare his watch with Bob's watch.
In this experiment we can assume that Alex is motionless while Bob and Alice are on the move. However, both alternative reporting systems are different aspects of the same events. This means that the photographed watches will have the same difference in both reference systems. But these reference systems are equivalent, as there is no acceleration. Without acceleration we cannot justify the dilation of time for any observer of the experiment. So I conclude the photographed watches should not be different, ie they do not record any dilation of time. But despite these objections,
the question is
Comparing the photographed watches, did Alex's watch gain or lose time compared to Alice's watch?