Right so.
A ball dropped on earth 24 hours ago. This was in reference fram S. You're moving away from the Earth (or the earth is moving away from you) at near
c and so your frame of refernce is S' (that is, a second co-ordinate system, basically just means "everythings relative"
)
So you have two events, the ball been released, and the ball hitting the floor. Due to th Lorentz transformation, the time period between the two events in YOUR frame of references, S', will always be greater than the time period between the two events in the "proper" frame of reference, S.
Therefore you wouldn't see into the past ever, you would be observing the event in slow motion. (e.g. man on earth sees ball take 5 seconds to drop, you see it taking 5000 seconds to drop)
Time Dilation
IF it was theoretically possible for you to be travveling at above
c then the incorrect math (i.e. using my generalised principles) would indeed follow through that
(delta)T=(negative)(delta)T_proper
That is if the events occured 5 seconds apart, you would observe them -5 seconds apart.
HOWEVER someone far smarter than me took it back to first principles, fixed it, and once again showed that speed above c was impossible and therefore these negative numbers didn't occur.