As someone who worked in neutrino physics for thirty years before retiring from research in 2000, I should be more excited than most by the report from CERN that neutrinos have been observed moving faster than light. And I am. The experiment looks very well done and the scientists involved are saying all the right things -- that their result is very preliminary and must be independently replicated before accepting it as scientific fact. If the observation is confirmed, it may be the most important discovery in science in the last 100 years.
However, a big fly in the ointment is the supernova in the Large Magellanic Cloud, which sits just outside our galaxy 168,000 light-years from Earth. It was first seen by the naked eye on February 24, 1987. Three hours before the visible light reached Earth, a handful of neutrinos were detected in three independent underground detectors. If the CERN result is correct, they should have arrived in 1982. So, if I were a wagering man, I would bet the effect will go away because of some systematic error no one has yet been able to think of.
Nevertheless, the enormous attention currently being given to this result affords us the opportunity to delve into to implications of faster-than-light travel should it ever be observed, which are profound. To begin, it needs to be made crystal clear that despite what has been reported in the media, superluminal motion in no way contradicts Einstein's theory of special relativity published in 1905. Einstein's equations fully allow for particles to travel faster than light -- provided they never travel slower. Physicists have speculated about such objects for years. They are called tachyons. Many searches have been conducted, with no significant signals until now.
Einstein showed that it was impossible to accelerate a particle moving less than the speed of light (in a vacuum) to the speed of light or higher. Similarly, a tachyon cannot be decelerated to or below the speed of light. Only massless particles, such as photons, travel at exactly the speed of light.
However, there is a problem with tachyons. They imply that cause and effect are interchangeable. Consider the famous duel between Aaron Burr and Alexander Hamilton on July 11, 1804. An observer moving by at less than the speed of light with respect to the participants would have seen the bullet from Burr's gun enter Hamilton's lower abdomen. However, another observer moving faster than light would have seen the bullet emerge from Hamilton's abdomen and enter Burr's gun. Did Burr kill Hamilton or did Hamilton kill Burr?
When you read, "Einstein proved that particles cannot go faster than the speed of light" you have to understand that this was not a consequence of the basic axioms of the theory of special relativity. To prove this he introduced an additional assumption now called the "principle of Einstein causality": cause must always precede effect. In that case, it then follows that we can't have superluminal motion.
Einstein causality certainly seems reasonable based on normal experience. Cause and effect are deeply embedded in our thinking, in both everyday life as well as virtually all of science. Causality is one of those commonsense notions, such as the world is flat, that hangs in there as a "self-evident truth" until some very bright person come along and says: "Maybe not."
A very bright Scottish philosopher named David Hume (d. 1776) said "Maybe not" when he pointed out over two hundred years ago that just because one event precedes another in our experience, we cannot conclude the first event necessarily was the cause of the second.
In modern chemistry and physics today, no distinction is made between cause and effect on the atomic and subatomic scales. Time is completely reversible. A carbon atom and oxygen molecule will combine to give carbon dioxide and energy. You can just as well have energy plus carbon dioxide give a carbon atom and oxygen molecule.
In 1948 Richard Feynman showed that, assuming our conventional direction of time an antielectron ("positron") going forward in time is indistinguishable from an electron going backward in time. Clearly when you reverse time, cause and effect are reversed. But it doesn't matter. The phenomena that are observed in submicroscopic chemistry and physics can be described either way.
Furthermore, many events on the quantum scale are described without even introducing cause and effect. For example, the theories that successfully describe atomic transitions and the decay of nuclei treat these phenomena as occurring spontaneously, without cause.
So, if confirmed, the reported result from CERN or any future observation of superluminal motion will not lead to the overthrow of Einstein's theory of relativity. Its significance will be to overthrow the distinction between cause and effect. At the worst, Einstein might be faulted for taking causality a little too seriously.
Finally, you might want to ponder what effect the demise of causality would have on the notion of God as the ultimate cause of all there is.