As far as we know, time only moves in one direction – forward – but if you could
loop back to visit the universe at an earlier point in time, a famous paradox arises.
What if you killed your grandfather when he was a child?
Then your father or mother wouldn't have been born, so you wouldn't have been born, so you
wouldn't have been able to go back in time to kill your grandfather in the first place.
Paradox.
The simplest resolution to the grandfather paradox is that when you go back in time,
you're actually not going back into your own history but to a copy, and everything you
do there influences the new alternate future of that universe, not your own past.
But that's boring, because it just avoids the paradox.
If what you do when you go back in time actually influences your own past, and the effects
of your time travel do loop back to the present...future...past – no problem.
Let's just follow the paradoxical timeline through BEYOND its paradoxical conclusion.
You go back in time, kill your grandfather, thus you aren't born so you can't go back
in time, thus your grandfather isn't killed, thus you are born, so you go back in time
and kill your grandfather, and so on...
I'm showing this as a linear series of events but really it's two entangled histories happening
in parallel.
Is that even possible?
Well, I don't know about the time travel part, but subatomic particles regularly do multiple
different things in parallel – it's called quantum superposition and is responsible for
the weirdness of the double slit experiment, many properties of atoms and molecules, fusion
in the sun's core, and so on.
So if the universe were to exist in a superposition of two states – your grandfather is alive
and your grandfather is dead – then the natural result is a superposition of two states:
you're born and able to go back in time to kill your grandfather, and you're not born.
And the natural result of these is a superposition of two states – your grandfather is dead
and your grandfather is alive – and so, at least from a logical perspective, this
looping timeline is entirely consistent and there's no paradox.
And a similar paradox-free solution can be obtained by viewing the problem as a steady-state
solution to a Markov chain – but I won't go into that here.
Now of course nothing about these solutions to the grandfather paradox suggests that closed
time loops are actually possible – in fact, some of the implications this kind of time
loop have in the study of complexity theory seem to suggest that time loops – and thus
time travel into the past – must be impossible.
But the main point is sometimes we think a situation creates a paradox when it doesn't,
and really the only paradox is how our thinking can be twisted enough to dream up time-traveling
murderous grandsons, but not twisted enough to think about twisting time.