The Terminator paradox

I want to use a variation on a story line in a particular film to
illustrate a time travel paradox. That film is the Terminator, in
which Arnold Schwartznegger is an indestructible android sent
back in time by the robots that rule the world in a violent future.
John Connor is the name of the rebel leader who is fighting for the
humans’ cause against the robots, and Arnie is supposed to kill
John’s mother before she has given birth to him. You see if John
had never been born in the first place then the rebels would be
easily defeated. So, by bumping off his mum, they get rid of him
too.
Of course not only doesArnie fail, but the hero of the film, who
is sent back in time to protect John’s mum, ends up falling in love
with her, gets her pregnant and she gives birth to . . . John Connor.
So this guy, who is the same age as John in his own (future) time,
is actually his father. He was sent back to make sure that John is
born, and ends up being the reason he is.
The question is whether it would have been possible for Arnie
to have altered the course of events so that the future could turn
out differently? What if he had succeeded in killing John’s mum?
Even though the story line in the film may sound rather silly if
you are not a sci-fi fan, it is nevertheless consistent. No paradox
arises because Arnie fails. Come to think of it the film is not at all
bad and the special effects are brilliant. (Yes, I know they are even
better in Terminator II.)
I wish here to retell the story in order to highlight the most
famous time travel paradox, known as the grandfather paradox. Stated in its original form, the paradox arises when you go
back in time and murder your grandfather before he meets your
grandmother. So your mother was never born and neither were
you. And if you were never born your grandfather could not have
been murdered by you, and so you would have been born, so he
was murdered, etc. This is the paradox. The argument keeps going
round in a self-contradicting circle.
Let us rewrite the script for the Terminator. Suppose that the
robots fromthe future decide that, instead of sending their musclebound
android back in time to do the biz onMum,they will capture
John Connor himself, and persuade him by whatever foul means
to go back in time himself and murder his mother.
What happens if he succeeds? I mean, if she is killed before
she gives birth to John then he never existed. Does he simply fade
away as she slumps to the ground? And if he never existed then
who killed his mother? It couldn’t have been John; he was never
born!
There are several ways out of this one. All have been aired in
many science fiction stories in one form or another. I will consider
three scenarios:
1. As John shoots his mother he ‘pops’ out of existence. This simply
won’t do. His mother will have a bullet imbedded in her
heart (doesn’t mess around does he, our John) that must have
been fired from a gun. Someone pulled the trigger. You can’t
say that John existed before he shot her because now that he
has altered history he was never born in the first place. The
past will have evolved differently (Johnlessly) and there will
have been no need for the robots to send someone—especially
someone who doesn’t exist—back in time to kill Mum. This
explanation implies that there arenowtwo versions of history:
one in which John was born and one in which he was not,
which cannot be right.
2. John cannot murder his mother because he is there to try. In other
words, the fact that he exists means that any attempt he makes
must fail. This is certainly better than the first option since it
ensures that there is only one version of history. However it
still leads to a problem, as we shall see. 3. When John goes back in time he slides into a parallel universe; one
in which he is allowed to alter the course of history. Thus, even
though he cannot change his own past he can change the past
in a neighbouring, yet almost identical, universe. So when he
kills his mother he will never have been born in that universe
but his mother would have continued to live in his own. This
type of explanation has, until recently, only been popular with
science fiction writers. But, believe it or not, it is now being
taken seriously by some physicists who would like parallel
universes to exist for quite different reasons. I will come back
to this later on and show that it is the only viable way out.
The simplest and, many would say most reasonable, of the
above options is the second one. Let us assume that there are no
parallel universes (since there is no evidence for them and, in the
absence of any time machines, no way we can check). There is
also only one version of history. We cannot go back and change its
course since we already remember events from our past. Basically,
what has happened has happened.
This is not the same as saying that we are unable to go back in
time and meddle with the past. It’s just that if we do, we must have
caused things to turn out the way they have. So a time traveller
can never go back and stop J F Kennedy from being murdered, but
could himself have been the murderer.
This way of explaining how we could go back and participate
in our own past is exploited wonderfully in the Back to the Future
films. There, certain events that happen are not explained at the
time. Only later do we learn that they were caused by characters
travelling back from the future. So we see certain scenes twice:
first from the point of view of the characters living in their own
time and then from the point of view of the time travellers (usually
older versions of the same characters).
Back to my version of the Terminator. John may well try to
shoot his mother but clearly something has to happen to stop him.
This may be due to any one of a number of reasons. Maybe he
comes to his senses in the nick of time. Maybe the gun wasn’t
loaded, or the trigger gets stuck. Maybe he is just a lousy shot. It
doesn’t really matter why he fails, simply that he must fail. His mother has to survive for him to be there in the first place. I will
refer to this sort of puzzle as a ‘no choice’ paradox, since it suggests
that time travellers do not have the freedom of will to do certain
things which will alter the course of history in such a way as to
make it impossible for them to have travelled back in the first place.
Once you start thinking about this you realize there is a real
problem. Does this mean that if John were to try again and again he
will always be doomed to failure? We can imagine that the robots
return John back to their time, give him a double dose of ‘kill your
mother’ serum, intensive shooting lessons and send him back to
the past with a well oiled, definitely loaded, foolproof, sawn-off
shotgun. He will still fail. The laws of physics are not required to
explain why he will always fail. All that matters is that paradoxes
are avoided.
Theoretical physicists have devised a thought experiment to
see what would happen in a real situation if something were to
travel back in time and meet itself. What would the mathematics
predict? To make the model sufficiently simple, they came up with
the billiard table time machine. The idea is that a ball enters one
pocket of a billiard table and emerges from an adjacent pocket in
the past. It can therefore collide with itself before it went in. In
this model, all paradoxes can be easily avoided if we allow only
those situations that do not lead to a paradox, called ‘consistent
solutions’. Thus a ball can go back in time, pop out of another
pocketanddeflect the earlier version of itself into the hole, enabling
it to travel back in time in the first place. But the situation in which
the ball emerges from the pocket and collides with its earlier self
such that it causes it to miss the pocket it would have rolled into,
would not be allowed mathematically since it leads to a paradox.
This is all very neat and means that supporters of time travel
can pat themselves on the back for proving mathematically that
paradoxes can be avoided if we are careful. The problem they try
to pretend does not exist is avoided because billiard balls do not
have free will. They have not exorcized the no choice paradox.
The rule is therefore that the past has happened and we are
allowed only the one version of it. We may do whatever we like
when we travel back in time as long as we remember that however much we meddle with history we will always cause it to turn out
the way it has. Even in the original story line, Arnie can never
succeed because he comes from a future where John is alive, and
therefore should not even bother trying so hard. But then I suppose
the film would not be anywhere near as enjoyable.