Kae, that's what I tell my friends, that's gets us into a loop so we usually end it right there.
Well, here's another thought. Like what Kae said,it would result in a loop that would prevent time from getting anywhere, so let's say that the loop doesn't happen. You killed your grandfather, so then you are never born(that is, if he hasn't had your father/mother as his child yet) but, there is no loop, and he stays dead. You then do not exist anywhere in history, and are now just an object with no origin whatsoever, stuck in that time because you never existed to time travel.
Assuming the above happened, there are a few possibilities.
1- You're stuck, unless you somehow re-invent the time machine and stop yourself. And if you don't, you just live your life in that time, and most likely create your own fake backstory. Legally, I'm not sure how you'd exist though. Anyways, you'd live out your life in that time like it was your normal time, and die there as well.
2-You're still stuck, but since you were never born, then you never lived to the age you were when you time-traveled. Since you never grew up, you woudn't have any memories, and at the point in time that you kill your grandfather, your entire memory is gone. Then, you'd be a [insert your age here] new-born baby, with no knowledge whatsoever.
Those would either alter the timeline completely, or, as Ingemar stated, would result in an alternate timeline. But if it did indeed result in an alternate timeline, what would happen in your original timeline? Would your existence and that of your family disappear? or would it remain the same, with the exception of your absense?
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Here's my Dad's theory-- Since your father/mother has not been born yet, you have not been born either. ANd since you have not yet been born, the man you killed wasn't your grandfahter, he was simply some guy that you thought of as your grandfather. Then, what would happen if your possible-grandmother met another person, and had your father/mother? would that child still becmope your parent? or would you never exist, resulting in another paradoxial loop?
EDIT: Wow, Pascal, that's a bit confusing but I do think I get your point. Frrom the first standpoint, when you went back, there was no future from whence you came, you just simply, as you put it, *popped* into existence. So, you became just another person in that time, only with no existing backround other than that contained within your memories, which are now nothing more than that, memories, now not real at all, but somewhat like figments of your imagination even though they actually did happen to your physical self. Because now they never happened anywhere but your mind.
That is what you were saying, was it not? I want to try and understand this, becuase I did not believe there was actually an answer.
Edit Edit
(after all time is just like space only that we move forward in it at a constant velocity c!)
My dad just pointed this out to me after reading your post, Pascal. He said that we do not move forward in time at a constant velocity. There was that one instance in the Bible(not sure where exavtly in the Bible it is, but I do remember the story) where God stopped the progress of time for a while by stopping the movement of the earth. So, according to that, time is not constant, and can be changed. (Although in my opinion this was a supernatural act that could not, except by God's direct intervention, be replicated, and thus does not exactly show that time does not move at a constant velocity when not changed directly by God's hand.)