In the news, there is a team at CERN stating that they have measured the speed of neutrinos to be greater than the speed of light. What's wrong with that?
One of the fundamental concept in physics is Lorentz invariance. What this means is that if I apply the Lorentz transformation laws to an equation that I think is valid in one frame of reference, this equation would not changed in another frame of reference.
Now, in the Lorentz transformation laws, we get this factor:
γ =(1 - (v/c)2)-½.
Should the speed of a particle be greater than the speed of light (v > c), then the γ factor becomes an imaginary number! This brings humongus headache to the theory. One way out is to postulate that the particle has an imaginary mass (tachyons) since this factor often multiplies the mass of the particle, and the product of two imaginary number is a real number. However in the real world, masses are real quantity, not imaginary, so particles with a mass must travel at a speed less than the speed of light, and only massless particles ( m = 0) can travel at the speed c.
In the case of the recent findings about the neutrinos traveling at a speed greater than light, that would contradict this theory which has been around for over 100 years. That's why the findings, if confirmed, would be disturbing, to say the least.