Assuming time travel is in fact possible in a form that allowed you to kill your own grandfather,
I believe in the alternate universe theory, where the universe you had left in your time machine still exists and continues onwards but when you change something in your past it splits off an alternative universe based on that change you made, creating a world where you never existed.
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"Asking a bomb squad if an old bomb is still "real" is not the best thing to do if you want to save it." - denim
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