Fern, it isn't theoretically impossible for a mass to exist that always moves faster than the speed of light.
Yes, I believe it is. It is theoretically impossible for a an object with mass to exist that moves at hyper light speed according to Einstein's theory (as I understand it from a laymen's pov).
First, please spend a moment or two dwelling on the concept of "infinity". Whether it be infinite energy or mass.....
In the first place I contend that there is no such thing as "infinite" in our known laws of physics/science. The universe is finite, as such it's 'potential' energy is finite.
If, in accordance with Einstein's theory of relativity, it requires an infinite amount of energy to accelerate an object to hyper light speed then you're suggesting an infinite amount of energy was applied to a (infinite) mass to accelerate it to hyper-light speeds at some point in time. An infinite quantity of, well anything, has never been postulated, much less theorized or proven, AFAIK therefore you are suggesting an equally radical occurrence to explain away this possibility. Which is more unlikely, or unproven?
There is already a "god particle', or you suggesting another one? (I joke here, but what you are suggesting opens discussion for any number of incredulous claims. The claim of infinity is mostly in the theological realm as best as I can tell.)
Look up "tachyons." Note: the actual existence of such things has never been proven. However, the point is that the existence of such a thing isn't theoretically impossible. I don't know the physics any better than you do, but this seems to come up every time this issue is discussed.
http://en.wikipedia.org/wiki/Tachyon
Dig a little deeper. If I understand correctly, a tachyon is theorized to have a
negative mass. (A negative square root in the formula). If so, it would be irrelevant here. Also, being only theoretical, as opposed to an observed neutrino, it is of little-to-no use here.
Personally, (and disappointedly) I suspect we may find this phenomenon is attributable to an error in measurement. OTOH.....
Fern