Just finished off Pawn (finally) and put it out on to the kindle thingie, and so since I had a little time on my hands (no pun intended), thought I'd return to my time travel theme.
This one is not a paradox so much as a simple logical incompatibility between two ideas. Time travel and true free will.
First, to set the scene a little, a short definition of true (or libertarian) free will. In essence this view of free will says that our decisions, what we choose to do are completely free, and that if we were somehow to rewind the universe a little bit and face the same choice again, we could legitimately make a different choice. In order to do this, libertarian free will requires that that part of our minds that makes some choices, exists outside of the bounds of the normal universe. (No I'm not talking about a drug induced state!) But in essence, it says that our decisions have to be based on something other then the chemicals in our brains, the atoms and molecules of the universe and all of those other physical things that we know exist. Because if our free will, our decision to choose was based in a part of our brain that was completely predicted by these things, then if we rewound and reran the universe all over again, we could only ever make the same choices. Thus our actions would be completely deterministic.
There is a model of free will that is compatible with a deterministic universe - oddly enough it's called compatibilism. And it says yes, our every decision, choice etc is based completely on physical things like brain chemistry and atoms and fields etc, but we still believe we can make free choices. The fact that if someone could somehow know the position and movement of every atom etc in the universe, they could predict with one hundred percent certainty our every choice, is irrelevant. (I tend to think of this as the illusion of free will. It's free in as much as we think it is.)
Anyway enough said about free will, and sorry for the lecture. Now to time travel and why it completely opposes true free will.
So let's say that a time traveller from the year three thousand goes back in time to three thousand BC, a short six thousand year romp. Sounds good doesn't it? But what our time traveller has done in taking this journey, is fixed every single possible action for the entire six thousand years. Absolutely everything that occurs during that time must be fixed exactly so that by the time the year three thousand AD arrives and we're at the point where he's ready to jump back in time, he must be at that point. Every change he made in the past, must have been made for him to be there.
Sounds confusing I know. But let's look at it in another way. Our time traveller goes back to three thousand BC. At that point we know that everything at three thousand AD must be as it was when he left. So if he makes a change in the past, it must already have been part of the universe that led to him being able to jump back in time.
So now he's back in three thousand BC, and as luck would have it, he stubs his toe on a rock. It hurts and he yells out, and a couple of people see him, and maybe laugh. That's the entirity of the change he makes. Sounds like nothing. But it's not. That tiny change would have profound consequences up the line. So say one of those people who laughs is a girl, and when she goes home that night she tells her hubby of it. He laughs too. Then they make love and start the baby factory rolling. Now because of that laugh, that one minute of story telling, they make love one minute later than they would have if he hadn't stubbed his toe. One minute, seems like nothing doesn't it? But this is the butterfly effect in action. One minute and one sperm out of fifty million swimming merrily away as it hunts down the egg. So what are the chances that the same sperm that fertilised that egg in the time line before the man arrived to stub his toe is the same one that arrived in the next version? One in fifty million more or less. Different sperm - different person being born. And of course that new baby grows up in the past to do different things to what the original person would do, and the changes multiply, until finally when the year three thousand AD arrives, the time traveller doesn't exist. That can't happen.
So the only way around this problem is to have the order of past events between the year three thousand BC and the year three thousand AD absolutely fixed. Not a single iota of variation can occur. This in turn means that every change the time traveller thought he made in the past wasn't a change at all. It always had to happen in order for the time traveller to be there at the right time ready to jump back six thousand years.
So stubbing his toe wasn't a change. It had to happen. The girl laughing wasn't a change. She had to laugh. The baby being concieved a minute later, actually had to be conceived at exactly that time after all. And the wrong sperm fertilising that egg was in fact the right one after all.
And as for the rest of us and the belief that we have true free will. If a time traveller could actually leave from our future and arrive in our past, then we simply can't have such a thing. Because every action we take, every choice we make, has to be the exact one necessary for that time traveller be there in the year three thousand ready to jump back. Even if we have no direct connection tothe time traveller.
Now imagine that someone from the very end of time, say forty billion years or so in the future, goes back to the very beginning. Now the entire span of the universe is fixed.
Anyway I think that covers the basic idea. Time travel does not allow for the possibility of true libertarian free will.
Feel free to ask questions or tell me I'm wrong.