Since we are supposed to sum over all possible histories – not just those that satisfy some equations, the sum must include spacetimes that are warped enough for travel into the past. So the question is, why isn't time travel happening everywhere? The answer is that time travel is indeed taking place on a microscopic scale, we just don't notice it. If one applies the Feynman sum-over-path histories approach to a particle, one has to include histories in which the particle travels faster than light, and even backward in time. In particular, there will be histories in which the particle goes around and around on a closed loop in time and space. One cannot observe particles with such closed-loop histories directly with a particle detector. However, their indirect effects have been measured in a number of experiments. One is a small shift in light given out by hydrogen atoms, caused by electrons moving in closed loops. Another is a small force between parallel metal plates, caused by the fact that there are slightly fewer closed-loop histories that can fit between the plates compared to the region outside – another equivalent interpretation of the Casimir effect. Thus, the existence of closed loop histories is confirmed by experiment. One might dispute whether closed-loop particle histories have anything to do with the warping of spacetime, because they occur even in fixed backgrounds such as flat space. But in recent years we have found that phenomena in physics often have dual, equally valid descriptions. One can equally well say that a particle moves on a closed loop in a given fixed background, or that the particle stays fixed and space and time fluctuate around it. It is just a question of whether you do the sum-over particle paths first, and then the sum-over curved spacetimes, or vice versa. It seems, therefore that quantum theory allows time travel on a microscopic scale. However, this is not much use for science fiction purposes – such as going back and killing your grandfather. The question therefore is: can the probability in the sum-over histories be peaked around spacetimes with macroscopic time loops? Although time loops are allowed by sum-over histories, the probabilities are extremely small. Based on the duality arguments I mentioned earlier, I estimate the probability that Kip Thorne could go back and kill his grandfather as less than one in ten with a trillion trillion trillion zeroes after it. That's a pretty small probability. But if you look at the picture of Kip, you may see a slight fuzziness around the edges. That corresponds to the faint possibility that some bastard came back and killed his grandfather, so he's not really there! As gambling men, Kip and I would bet odds on that. The trouble is, we can't bet each other – because we are on the same side. On the other hand, I wouldn't take a bet with anyone else. He might be from the future, and know that time travel worked. You might wonder if this is part of a government coverup on time travel. You might be right.     – Stephen Hawking                The Universe in a Nutshell