Well sure, I'd be thrilled to see this finding get verified because it certainly would require a profound reworking of theory, but just like Nuke said I'm not holding my breath.
Let me put it this way. If this result is validated, then we need to explain why our understanding of relativistic kinetic energy is so wrong -- to accelerate a particle of nonzero mass to c requires
infinite kinetic energy to be imparted to it. Yet if this was wrong, then we should have had absolutely no trouble accelerating things past c long ago.
Next you'd have to explain why the mathematics of relativity, particularly the Lorentz transformations, are so wrong, because they show that a particle moving at speeds greater than c is functionally the same as a particle moving backward in time from some reference frames -- this violates causality. And yet this mathematics works for everything from cars to satellites to space probes to relativistic particles just like the ones we study at the LHC.
And what is so special about these neutrinos, I have to ask? We've observed neutrinos from supernova SN1987A and their arrival time exactly coincided with what you'd expect from neutrinos produced from the core collapse of the star and radiating outward at exactly the speed of light. What is it that's making these LHC neutrinos go FTL? How did they measure this? What were they doing to cause such a result in the first place?
I have no idea, because I can't even find their data. Nevermind,
here it is.
And I'm really not buying the Newtonian vs. Relativity argument either. Newtonian physics wasn't based on experiments involving things moving at near light-speed. Relativity
was. That's why Newtonian physics works well for every day speeds while relativity works for everything. As you've both mentioned, it's not so much a replacement, but a modification to describe a bigger picture.
This discovery on the other hand -- I can't see how it'd be a modification like Relativity was for Newton. Rather it would require essentially going back to the drawing board, because as described above, it is completely at odds with what we've already established with relativity. It would be like finding fossils of homo-sapiens in a precambrian formation. That would be one hell of an observation to have to work into your theory.