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It’s now been three weeks since the extraordinary news that neutrinos travelling between France and Italy had been clocked moving faster than light. The experiment, known as OPERA, found that the particles produced at CERN near Geneva arrived at the Gran Sasso Laboratory in Italy some 60 nanoseconds earlier than the speed of light allows.

The result has sent a ripple of excitement through the physics community. Since then, more than 80 papers have appeared on the arXiv attempting to debunk or explain the effect. It’s fair to say, however, that the general feeling is that the OPERA team must have overlooked something.

Today, Ronald van Elburg at the University of Groningen in the Netherlands makes a convincing argument that he has found the error.

First, let’s review the experiment, which is simple in concept: a measurement of distance and time.

The distance is straightforward. The location of neutrino production at CERN is fairly easy to measure using GPS. The position of the Gran Sasso Laboratory is harder to pin down because it sits under a kilometre-high mountain. Nevertheless, the OPERA team says it has nailed the distance of 730 km to within 20 cm or so.

The time of neutrino flight is harder to measure. The OPERA team says it can accurately gauge the instant when the neutrinos are created and the instant they are detected using clocks at each end.

But the tricky part is keeping the clocks at either end exactly synchronised. The team does this using GPS satellites, which each broadcast a highly accurate time signal from orbit some 20,000km overhead. That introduces a number of extra complications which the team has to take into account, such as the time of travel of the GPS signals to the ground.

But van Elburg says there is one effect that the OPERA team seems to have overlooked: the relativistic motion of the GPS clocks.

It’s easy to think that the motion of the satellites is irrelevant. After all, the radio waves carrying the time signal must travel at the speed of light, regardless of the satellites’ speed.

But there is an additional subtlety. Although the speed of light is does not depend on the the frame of reference, the time of flight does. In this case, there are two frames of reference: the experiment on the ground and the clocks in orbit. If these are moving relative to each other, then this needs to be factored in.

So what is the satellites’ motion with respect to the OPERA experiment? These probes orbit from West to East in a plane inclined at 55 degrees to the equator. Significantly, that’s roughly in line with the neutrino flight path. Their relative motion is then easy to calculate.

So from the point of view of a clock on board a GPS satellite, the positions of the neutrino source and detector are changing. “From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter,” says van Elburg.

By this he means shorter than the distance measured in the reference frame on the ground.

The OPERA team overlooks this because it thinks of the clocks as on the ground not in orbit.

How big is this effect? Van Elburg calculates that it should cause the neutrinos to arrive 32 nanoseconds early. But this must be doubled because the same error occurs at each end of the experiment. So the total correction is 64 nanoseconds, almost exactly what the OPERA team observes.

That’s impressive but it’s not to say the problem is done and dusted. Peer review is an essential part of the scientific process and this argument must hold its own under scrutiny from the community at large and the OPERA team in particular.

If it stands up, this episode will be laden with irony. Far from breaking Einstein’s theory of relatively, the faster-than-light measurement will turn out to be another confirmation of it.

Ref: arxiv.org/abs/1110.2685: Times Of Flight Between A Source And A Detector Observed From A GPS Satellite.

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