On this BBC article, BBC NEWS | Science/Nature | New model ‚permits time travel‘, a certain Prof Greenberger explains quantum mechanically why time travel could not just be possible, but shouldn’t be a logical problem, too.
He namely addresses and claims to resolve the „grandfather paradoxon“. And this is how it goes:
„Quantum mechanics distinguishes between something that might happen and something that did happen,“ Professor Dan Greenberger, of the City University of New York, US, told the BBC News website. „If we don’t know your father is alive right now – if there is only a 90% chance that he is alive right now, then there is a chance that you can go back and kill him. But if you know he is alive, there is no chance you can kill him.“
In other words, according to the good Prof, the present state of your father (alive|dead|unknown) determines whether or not we can kill him somewhen in the past. But, that does not address the actual paradoxon at all. The paradoxon is not about whether or not you can go back anywhen in time and kill your father, it is about whether you can go back to before he conceived you to do so. The question of whether your father is alive at present, or in fact was alive as early as at your birthday, or died in a train wreck the morning after the one night stand that brought you on, is totally irrelevant to the paradox situation.
Which is why it is actually called a grandfather paradoxon rather than a father one. Look at it the other way round: For safety sake, let’s look at your great-great-grandfather. Born in, say, 1811. Present state? „He’s dead, Jim.“ Check. In marches Prof Greenberger and tells us in his logic that we can happily go back to 1817 and smash the head of the poor innocent six-year-old with a stone. But wait, oops, what happened to our little paradoxon? Better not think about it…
I admit that the paper Prof Greenberger published takes a completely different view than the interview he gave to the BBC. The paper explains the situation by a series of formulae I hardly dared look at, much less understand. It is not very verbose at all. So his actual proof may well be right, I just say his verbal arguing is poor.