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This is a variation on the "Grandfather Paradox."

If you went back in time and killed one of your grandparents before your parent was born, it is theorized that you would never be born, then you would not be able to go back in time to kill your grandparent, so your parent would be born, and you would be born, then you would go back in time to kill your grandparent before your parent was born.

See? it loops. Paradoxes are anathema to nature and physics. Or are they. Quantum physics presents a different argument, the Multiverse. In a multiverse, for every possible action, a new branch or new universe is formed (this is a simplistic explanation). With the formation of each new branch, other new branches can be formed, and it continues outward from the big bang. There are an infinite number of universes then, so if you went back in time and killed grandma or grandpa before mom or dad were born, you would not be born in that universe, but you would not snap out of existence.

The Grandfather Paradox breaks down in another area too:

If you went back in time and killed one of your grandparents before your parent was born, it is theorized that you would never be born, then you would not be able to go back in time to kill your grandparent, so your parent would be born, and you would be born, then you would go back in time to kill your grandparent before your parent was born.

Would you? Would you be born? Would you continue with the same act that originally caused you not to be born? This presumes that the universe is set to rote time and cannot change no matter what happens, that every action is scripted. Fundamental Christianity's philosophy of Free Will doesn't even agree with this. There are way too many variables in play to be able to state categorically that this paradox is possible in more than a purely existential discussion.

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Q: If a girl went back in time and killed her grandmother wouldn't she have killed herself because her mother wasn't born?
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