Thought experiment on relative motion Imagine two persons (A and B) in a vacuum in outer space that are in front of each other and are not in motion.
Say that suddenly A starts moving away with a constant velocity from B.
In this case, would A or B be able to determine themselves in any way that A is the one who is actually moving and B is stationary?
I think they can reach only one of the following conclusions but never know who was actually moving:


*

*A is moving and B is stationary.

*B is moving and A is stationary.

*A and B are both moving with some velocity from each other that could be equal or not.

 A: If A changes their velocity then you can say absolutely that A has accelerated, since acceleration is not a relative effect. That said, you still cannot say in any absolute sense who is moving, since all movement is relative. A is moving relative to B and B is moving relative to A - both statements hold true at the same time.
Likewise, the concept of 'being stationary' only makes sense if you specify a reference frame relative to which something is motionless.
A: I have the first of your statements.
Imagine two persons (A and B) in a vacuum in outer space that are in front of each other and are not in motion relative to one another.
Say that suddenly A starts moving away with a constant velocity from B.
Introducing an acceleration changes things.
(1) A pushes B hence B pushes A ( Newton’s third law).
Velocities relative to their original position (centre of mass) could be found as well as the relative velocity between them.
(2) A throws a ball.
B will not move relative to the original position and the ball and A will be moving relative to each other and relative to B whose position is also the original position of A and the ball.
A: To come from rest v=0 to v=const you would need a force acting on the body, hence de/acceleration, which you would detect if you allow some kind of instrumentations, unless you do it infinite slowly.
A: 
suddenly A starts moving

Things don't just start moving. Something had to give A a shove. (I.e., something applied force to A to make them start moving.) That's called "acceleration," and it can be measured. Even though, from A's point of view, it may look like B was the one who started moving, It's A who feels the shove. B does not feel it.

After the acceleration stops...

I think they can reach only one of the following conclusions...

Not true. Once the acceleration stops, all three of your "conclusions" are equally valid. What you are comparing there are three different inertial frames of reference. One may be more convenient than another (e.g., it sometimes makes more sense for me to think of myself as "stationary",) but experiments done and described in any inertial coordinate frame obey all the same laws of physics as experiments done on the same subjects in any other inertial coordinate frame.
A: This can't be done. It's the essence of the principle of relativity that there is no experiment that can distinguish between A's and B's constant velocity reference frames.
However, if A was also there when they start accelerating (which they must have experienced, because they were originally at rest) then A will be able to tell that A is the one that moved.
