so what is the response to this paradox?
You return on schedule, kill your own granddad, hence you're not conceived, consequently you can't return into time, subsequently your granddad isn't killed, so you are conceived, so you return on schedule to kill your own grandfather".
Meaning, both the possibilities are occurring, simultaneously. Your granddad is both alive and killed. You are, likewise, both conceived and unborn.
sub nuclear particles routinely do numerous things in equal. It's called Quantum Superposition. Your granddad is in the two states on the double, so there is no paradox.
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