Einstein's Theory: All Frames Equally Important for Time

[HarryDaniels]

Einstein said that all frames are equally important.
Now, assume that I (or body A) was moving at a velocity of V. If body B was considered to be stationary and I was traveling away from it at a high speed then my time would slow down. This I understand.

But...
If body A was the inertial frame and taken to be stationary then body B is traveling away from body B. This is true if one subscribes to Einsteins theory. If this is true then body B's time is slowing down at an equal amount to body B (assuming that both B and A have an equal mass). So in theory (according to what I am asking and along with Einsteins) they are both slowing down in time at the same rate.

So, even though body A is moving away, according to Einstein body B is equally moving away, so they are going at the same speed through time as there velocity is the same depending on the frame. So nothing slows down in time if all frames are equally important.

Am I right?

 

[JesseM]

It's true that if two observers are moving apart inertially, each one will say the other is aging slower in their own frame, and in relativity neither frame is more correct than the other. However, if one of the observers changes velocities in order to turn around and catch up with the other, then when they reunite, the one that changed velocities will have aged less (since the moment they departed from one another) than the one that didn't, and all inertial frames will agree on this prediction.