So, remember about three weeks ago, when some neutrinos traveling between Geneva and the Gran Sasso Lab in Italy arrived about sixty nanoseconds quicker than the speed of light? That was weird. However, on the 14th, Ronald van Elburg at the University of Groningen at the Netherlands seems to have figured it out. His team calculated the distance between the two stations, then factored in the relativistic motion of the GPS satellites involved.
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.
Cool! Well done, Van Elburg!