The "Illusion of Time" and distant observers In Brian Greene's "Illusion of Time" on NOVA, he cited a case where a distant alien rides a bicycle away from us at a constant speed and then looks back at the earth. She will see a slice of spacetime in our past. Similarly, if she rides towards us at a constant speed, she will see a slice of spacetime in our future. What happens if she accelerates instead of rides at a constant speed? I know this is the realm of GR so weird things might happen. But as she looks back at us, won't she see events on earth going backwards as her instantaneous speed increases? In other words, won't she see entropy decreasing, not only on the earth but also in our general area of the universe? And if she looks in her forward direction, won't she see events speeding up? But in both directions, if she looks out far enough will she still see the Big Bang?