Here is a neat article from the Telegraph about a scientist named Itzhak Bars who claims to have discovered two new dimensions, one in space and one in time. He claims that the second dimension of time would resolve the grandfather paradox:

Bars first found hints of an extra time dimension in M-theory in 1995 and, when he looked into it, discovered the grandfather paradox and other fears could be overcome by using a new kind of symmetry - a mathematical property to work out the relationship between the quantities of position and momentum. It is this symmetry that might help reconcile the two mighty pillars of 20th-century physics, quantum mechanics and relativity.

For those who don’t know, the grandfather paradox is a time-travel problem that seems to allow you to go back in time and kill your own grandfather, thereby preventing your own birth. I would really like to hear the explanation of how he resolves the paradox.

Later in the article, the reporter wonders if this is all just hypothetical:

The work poses a question: is his proposal a mathematical fix, rather than a real physical entity?

Bars insists his extra dimensions are more than mathematical sleight of hand. “Absolutely not,” he told New Scientist. “These extra dimensions are out there, as real as the three dimensions of space and one of time we experience directly.”

There are some very interesting points in the comments from the article:

There’s a saying: You can’t step in the same river twice. You can try to step in at a specific point that you think you know, but water has passed between your previous ‘knowledge’ of that spot and now. No two attempts will ever produce the same result. So if you went back to shoot your grandfather, you may not even find him because you’ll already be in an alternate universe. And if you do shoot him you are only possibly preventing another version of ‘you’ from being born.

I liked this guy’s point. I have no idea if it has any scientific merit, but it make sense to me. For the scientists out there, here is a link to Itzhak Bars’ paper, which was over my head. If you can explain it to me, I would appreciate it.