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Say you went back in time intending to shoot your grandfather, the good old grandfather paradox. Well, instead, when you met him, you actually got along with the guy and changed your mind. You became best friends and when you eventually get back to your own time zone, you'll look through some old photo's and boom, you're in them; playing cards with grandad or something!
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"That's rich comming from you, Mr. 'I'm my own grandpa!'"'s best friend
Sorry had to be said
I think Time travel would be an interesting element from the rp point of view, especially with some of the things you guys can come up with. And i'm sure those player's who's characters who are effected by time travel will find a way of dealing with it.
As for dealing with altered timelines I like the multi-verse idea because it adds a lot of flare to character development. What if A goes back and kills B, the timeline spilts and A goes back to the wrong timeline, cue freak accedent and sch-daisy Quantam Leap-esque... A is in Bs body