I stumbled upon this question: Can we really not tell if we are moving? and it made me start thinking (probably a bad idea for a non-physics guy).
To my knowledge, moving at relativistic speed means that time passes slower than for a non-moving observer. My question is, can't this be used to determine whether we are moving?
Say, we have people 1, 2 and 3 and we know they move along a certain vector at the same relativistic speed (say, they are oriented along a line in space, they know, one of them is "front" and one is "back" but not who is what, they also know the speed $v$ they are going).
All three synchronize their clocks and now 1 and 3 accelerate in opposite directions until they reach $v$ relative to 2. After some time, they accelerate again until they match speed with 2 again. We know, one of them has somehow doubled his absolute speed, the other one came temporary to a standstill.
As I know, we cannot tell, we are moving, I am certain, that re-synchronizing their watches will give the same deviation for 1 and 3 relative to 2. But why, as one of them stood still for a certain amount of time, while the other was almost at twice $v$ velocity.