They plan to run a similar experiment in a few months, though there are hints it may also take longer. They first need to upgrade their equipment, among other things.
Strangely, this article doesn't mention Fermilab's 2007 experiment. The article which TEG posted did mention it:
DailyTech - CERN Physicists Observe First Faster-Than-Light Long-Distance Travel
One indication the results may be correct, though, comes from Fermilab, a physics lab located just outside Batavia, Illinois. In its MINOS experiment, Femilab researchers have been sending neutrinos in a similar experiment to a detector at the bottom of the Soudan mine in Minnesota.
In 2007 they also seemed to observe faster-than-light travel of neutrinos, but unfortunately their lesser experimental equipment made it impossible to determine whether the measurement was legitimate or merely an artifact of the high level of statistical deviation in the measurements.
Professor Plunkett, who also serves as co-spokesperson for the MINOS experiment, is excited to find out if the results were authentic. He states, "There was something that could have been a fluctuation in the direction of things arriving early, but it didn't have enough significance for us to make such a claim. Obviously, the hunt is on and we'll be upgrading that previous measurement and also implementing something we already had in the works, which is a plan to make improvements so we can reduce our errors. One of our next objectives is going to be trying to verify or disprove this result as hard as we can."
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Interesting, yes, but just one of many more theoretical objections of the kind 'it can't be true'. (There are already plenty of theoretical reasons 'it can't be true'.)
I doesn't explain the measurements which have been made at CERN, or any mistake they might have made.
It's not really scientific, but does a good job of showing where the skepticism is coming from. However, it is quite biased, and summarizes only one side of the coin.
Worse, he writes things as this:
It seems strange to me that Einstein’s equations (both special and general relativity) need to be taken into account to measure something that is proving them wrong. It just doesn’t make sense.
Why would the experiment not take into account that which it proves wrong? It is a contradiction all the same.
Whereas his reasoning that faster-than-light speeds would make things appear to go backwards in time, which he even puts in bold across a whole paragraph, is based on relativity which would already been proven imperfect (of course not completely wrong) by faster-than-light speeds. So the reason to believe it would make things appear to go backwards in time is already gone. This seems a logical fallacy on his part, at least in the way he presents it.
Next: her argues that "Thus the mass of a fast moving object is much greater than its mass when stationary." and "To accelerate it up to the speed of light would require an infinite amount of energy, which is impossible."
But he appears to forget that there is a case where this doesn't apply: The creation of photons (for example simply when you light a candle). While they don't have a rest-mass as photons (though even photons have a relativistic mass), the corresponding energy does exist in a form with rest-mass before the candle is lit. Particles which move at the speed of light are quite exceptional, and saying that they have no rest-mass is not an explanation but just a further description of that fact.
EDIT: Even if the experiment showed that just the GPS method of synchronizing clocks is flawed, that would be an important result since top-experts believe so far it was done with correct methods.