Other Problems With Superluminal Neutrinos
The laws of relativity produce a number of strong constraints on particle physics. They impose a very strong mathematical framework that allows for certain particle processes and denies the possibility of others through the application of energy and momentum conservation (kinematics). If it were possible that something could break the light speed limit imposed by relativity, for whatever reason, then it follows that those constraints would be different and previously kinematically forbidden processes would be observed.
One of those particle processes that would now be possible is:
ν → ν + e− + e+
That is, a neutrino gives up some of its energy to produce an electron/position pair and keeps trucking along. Please forgive my inability to put that into better notation with this interface. Normally, this is something that is kinematically forbidden, but, if they are going faster than light, this is now possible.
So what does this have to do with the OPERA measurement?
If there were superluminal neutrinos created by CERN, then those neutrinos would have been spitting out electron/positron pairs all over the place. This would have meant a loss of the highest energy neutrinos to be counted, because they would loose energy to make those electrons and positrons. The process would happen at a high rate.
OPERA did not loose those high energy neutrinos. There should not have been any. If they were going faster than light, they shouldn’t have been there. Worse, for OPERA, the longer neutrinos travel, the more depleted of those high energy neutrinos the signal would be. There is just more time to have these decays. Experiments that look at neutrinos produced by astrophysical phenomena put a very strong constraint on what OPERA could have seen.
Andrew G. Cohen and Sheldon L. Glashow
The OPERA collaboration has claimed that muon neutrinos with mean energy of 17.5 GeV travel 730 km from CERN to the Gran Sasso at a speed exceeding that of light by about 7.5 km/s or 25 ppm. However, we show that such superluminal neutrinos would lose energy rapidly via the bremsstrahlung of electron-positron pairs (ν → ν + e− + e+). For the claimed superluminal neutrino velocity and at the stated mean neutrino energy, we ﬁnd that most of the neutrinos would have suﬀered several pair emissions en route, causing the beam to be depleted of higher energy neutrinos. Thus we refute the superluminal interpretation of the OPERA result. Furthermore, we appeal to Super-Kamiokande and IceCube data to establish strong new limits on the superluminal propagation of high-energy neutrinos.
Lay person summary:
1. If the neutrinos were going faster than light, they would be spitting off electron/positron pairs as they went.
2. This would leave a lot of very low energy neutrinos.
3. OPERA has a lot of very high energy neutrinos.
4. Other experiments, where the neutrinos came from much further away (astronomically further) have a lot of high energy neutrinos also.
5. Therefore, the claim that the OPERA neutrinos are moving faster than light is not likely to obtain.
[UPDATE] with a hat tip to Bob Dillon
In my last post on this topic, Neutrino update: Einstein reaches from the grave… I had written about the need to account for General Relativistic effects on the synchronization of the OPERA clocks. This was something that the OPERA team did not do. According to this paper, they did not take Special Relativistic effects into account either. This is shocking to me, I had not thought that they would have missed this. If true, it’s a real bonehead mistake. So I didn’t think it was likely. We will have to hear from the OPERA people to see if they took this into account or not.
But, if they didn’t, just from calculating the relativistic shifts caused by the motion of the GPS satellites themselves, that were used to synchronize the clocks, a 64 nanosecond delay flops right out.
Ronald A.J. van Elburg
The Michelson-Morley experiment shows that the experimental outcome of an interference experiment does not depend on the constant velocity of the setup with respect to an inertial frame of reference. From this one can conclude the existence of an invariant velocity of light. However it does not follow from their experiment that a time-of-ﬂight is reference frame independent. In fact the theory of special relativity predicts that the distance between the production location of a particle and the detection location will be changed in all reference frames which have a velocity component parallel to the baseline separating source and detector in a foton time-of-ﬂight experiment. For the OPERA experiment we ﬁnd that the associated correction is in the order of 32 ns. Because, judging from the information provided, the correction needs to be applied twice in the OPERA experiment the total correction to the ﬁnal results is in the order of 64 ns. Thus bringing the apparent velocities of neutrino’s back to a value not signiﬁcantly diﬀerent from the speed of light. We end this short letter by suggesting an analysis of the experimental data which would illustrate the eﬀects described.
If the experimentalists at OPERA failed to take this relativistic shift from the satellites into account, then far from overturning Einstein’s relativity, they will have just stunningly confirmed it in yet another way.