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Are there any theories that might explain the result?
If the result is proved correct – and that is still a big if – you have to go into some relatively uncharted areas of theoretical physics to start explaining it. One idea is that the neutrinos are able to access some new, hidden dimension of space, which means they can take shortcuts. Joe Lykken of Fermilab told the New York Times: "Special relativity only holds in flat space, so if there is a warped fifth dimension, it is possible that on other slices of it, the speed of light is different."

Alan Kostelecky, an expert in the possibility of faster-than-light processes at Indiana University, put forward an idea in 1985 predicting that neutrinos could travel faster than the speed of light by interacting with an unknown field that lurks in the vacuum. "With this kind of background, it is not necessarily the case that the limiting speed in nature is the speed of light," he told the Guardian. "It might actually be the speed of neutrinos and light goes more slowly."

Does this mean that time travel is possible?
Don't hold your breath, we won't be routinely jumping into the past in DeLoreans any time soon. If particles could travel faster than light, special relativity suggests that travelling backwards through time is a possibility, but how anyone harnesses that ability to do anything useful is way beyond the reach of any technology or material we have today.

Physicists have postulated a hypothetical particle, known as a tachyon, that can travel faster than light and that can therefore move backwards in time. But they also think that tachyons, if they exist, would have no way of interacting with normal matter.