Suppose a spaceship is moving at uniform speed of 0.5c relative to another inertial frame of reference such as earth, Frame E. From the frame of reference of spaceship, Frame S, the clock of Frame E is running slow. For someone in Frame E, the clock of Frame S is running slow. In terms of the special relativity both are correct and equally valid.
Frame S decelerates and starts co-moving with the Frame E; I think we can say that after the deceleration both frames become a single inertial frame. If a person who was aboard the spaceship compared his clock with that of earth, he would find that spaceship's clock was running slow assuming the clocks were synchronized before the spaceship started its journey. I'm ignoring the effects of gravity.
Before the deceleration, according to Frame S, the clock of Frame E was running slow. Likewise, according to Frame E, the clock of Frame S was running slow. After the deceleration, it became 'physically' clear that which clock was really running slow and which frame was actually valid. Was it the deceleration which affected the time, or was it really that Frame S's clock was running slow? Does the special theory of relativity assume that the 'rule' of validity is only applicable as long as both inertial frames of reference are moving relative to each other? Could you please help me with it?
