Faster than the Speed of Light (literally)

My friend in NYC just sent me an article today about neutrinos (subatomic particles) that travel have tested repeated to be able to travel faster than the speed of light (which physically is impossible for matter to do), at Gran Sasso’s underground laboratories in Europe.

I’ve been watching a lot of  science fiction and a series about the universe with Stephen Hawking, in which I learned that he too is a Star Trek fan.  Some of the episodes have dealt with the ramifications of speed and time in different parts of the universe, such as close to a super black hole, like at the center of our galaxy (and presumably most).

So if matter cannot travel faster than the speed of light, my question, is:  Could we theoretically cover a spaceship with (fast-moving) neutrinos and then launch it to go ten times the speed of light (warp 10), for example?  I realize it would affect the time of the people inside, unless some kind of chronometer was able to adjust for that, but that would certainly alleviate the problem of our short lifespans in getting us to other solar systems, where there is bound to be other intelligent life.

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