This would seem like a likely explanation. We feel pretty confident that extra dimensions exist, but I don't know enough bout physics to understand the rules that govern the use of these dimensions.

I like to frame it in terms of the difference between 2D and 3D. Imagine you could only perceive 2 dimensions. As far as you're concerned, the shortest distance between two points is always a flat line contained within a plane. Now, imagine someone curled your plane. You can only perceive 2 dimensions, so this warping of the plane is transparent to you. The shortest distance is still a straight line in your eyes, but in the 3D realm, the path you'd travel is an arc. The 3 dimensional "straight-line" path is actually shorter.

When you measure speed in terms of the time taken to make it from point A to point B, the number of available dimensions becomes incredibly important. The more dimensions available to you, the greater the likelihood that you'll find a better optimized path, resulting in less travel time.

> In 2007, the MINOS experiment searched for faster-than-light neutrinos but didn't see anything statistically significant

So people have been looking for faster-than-light neutrinos? Is there some specific theory that predicts them that they were trying to check, or what?