Symmetric Time Dilation in Uniform Relative Motion

I feel (and hope) this is an easily answerable question among physicists versed in GR. I promise that I searched for other answers on the forum. Here goes:

Observer 1 starts at X distance from observer 2, moves at 99% the speed of light towards observer 2 and then stops to interact with observer 2.

My questions are:

1. Since each observer sees the other as moving slower/faster due to the interchangeability of reference frames, do the slower/faster speeds cancel one another out?

2. If so, does time dilation really matter for observers?

1 Answer

Both observers see the other approaching at 99% of light but since observer 1 is the reference frame that accelerated, and changed it's behavior of motion, it is the reference frame that will have experienced less time than observer 2 during the duration of it's travel. The change in motion (acceleration/deceleration) is what changes the rate at which a reference frame progresses through time. When observer 1 stops, and it's behavior of motion matches observer 2 they will progress through time at the same rate again.