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I was wondering if (assuming it was possible to travel backwards in time) If someone traveled back in time and killed hid grandmother before his mother was born, What would happen? I have heard that time would split into one timeline where he does not exist and one other where he does. If he does exist in one timeline, then who killed his grandmother ?

You have stated a classic paradox about which a tremendous amount has been written. All answers to that paradox are highly speculative. The easy answer is - you cannot go back in time. If you cannot accept or do not believe that, then you must wrestle with this paradox. You will not find a satisfying answer in this forum, but you find a lot of literature. Very recently (Mar or Feb 94), Scientific American had a long article on this very thing. Even if that article is not not enough, at the end there is a list of further reading.

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