I'm very sorry that I have not been able to describe clearly the problem. I fear your wrath by suggesting that you watch the video from 1:18:30
But I am using the video because as they say a picture is worth a thousand words, and this is difficult to describe.
I understand time dilation but this time difference is far more than simple time dilation can account for in a situation where relative speed difference is so small.
I will attempt once again to ask my question with words.
According to this video, if someone is a very long distance away and they reverse their direction of travel from away from me to toward me, their experience of time is supposed to switch from my past to my future.
I have been trying to understand why their direction of travel makes this much difference. How this is possible to switch from past to future. I get that there is a very small change in time dilation, but it seems that the Lorentz factor would have to switch from positive to negative and even if that happened why would the amount of time vary by so much between past and future? It has something to do with the very long distances. If you chose to watch the video you should only have to watch from 1:18:30 till about 1:27:00 to understand exactly what I'm asking.