The bartender says, "We don't serve neutrinos here"

A neutrino walks into a bar.

The blogosphere is all abuzz about the CERN neutrino experiment that reported "faster than light" travel for the neutrinos. We all heard the news first from the blogs, and now the arXive pre-print server has the details. This immediate publication is already truly amazing, given the months before the paper copy appears in the library journal. The comments and consequences are flying so thick and fast, one hardly has time to absorb the impact. Einstein published his Special Theory of Relativity some 107 years ago, and this has been the first, contradictory laboratory evidence for "superluminal" transport.

But already, one day later, the first theorist has chimed in with an explanation. Not to miss any opportunities, the same theorist has a second explanation, with a different cast of secondary authors. Since both papers are written exclusively by Italians, it would appear that they had their theories ready to go as soon as the experimentalists were confident enough to publish. Other theorists weren't so fortunate to get advance notice, but they are quick with their theories too. Frank Close, an Oxford physicist who just published a book on the Neutrino, doesn't think his life's work was wasted quite yet.

 "Has Cern overthrown this paradigm? I doubt it. Light travels slower through water, glass, even air, than through a vacuum. Radio waves do, too. So light can be slowed down, but not sped up: the vacuum is nature's open road where light travels at the speed limit. We need to be careful when asking what exactly has the Cern experiment done, or, more pertinently, how did it do it?"

Looks like he hasn't read the arXive paper where they explain carefully how they did it, perhaps because his response like mine preceded the publication. Every physicists first question was--how can you measure +/- 10cm over 730km, GPS isn't that accurate! The article explains: with great difficulty. But apparently no expense was spared to get a geodesy model to measure the distance within 10 cm. Atomic clocks were carried into the tunnels to calibrate the timing. Lasers were used to measure the distances down the tunnels. A commercial firm was hired to produce an independent model. Earthquakes and continental drift were used to calibrate their model. If they did make a mistake, it won't be just scientist's reputations lost, there will probably be lawsuits too.

Let us first dispell the misconception of scientists clocking individual neutrinos starting at the Franco-Swiss border and arriving in Italy. No one can see an individual neutrino twice. In fact, you have about 100 million neutrinos from the Sun going through you each second and you don't even notice because their interactions are so very rare. Neutrinos can go through the entire Earth without much chance of interacting. That's why the neutrinos have to be detected statistically. Imagine a marathon that is so crowded that every 20 minutes, another 100 runners were allowed to start, and each runner's time was determined by subtracting off the start time. This is how the neutrinos were produced, in 10.7 microsecond long bunches, separated by 50 microseconds. Unlike a marathon, however, the experimenters assumed that every runner runs exactly the same speed, so the bunch at the end of the race should look just like the bunch at the start gate. Then by aligning the stop bunch with the start bunch will give the time of flight. The paper shows how the alignment looks if they use the speed of light, and how much better it looks if they use a very slightly faster speed. The difference is 60 nanoseconds, which when multiplied by the speed of light of 1 foot per nanosecond, gives 60 feet.

Is this within the error of their distance measurement?

This is the crux of the experiment. Over in Chicago, the scientists at Fermilab had done a similar experiment and likewise had found that neutrinos possibly travelled faster than the speed of light. But the Fermilab scientists didn't want to go through so much expense as the Italians and so they said "we probably made an error, since our uncertainties are bigger than the difference." That is why the Italians spared no expense to get their uncertainties as small as possible. And they got the same result as Fermilab, but this time the uncertainties were 1/6 of the offset, or a "six sigma" result. In experimental science, six sigmas is as close to certainty as you can ever wish for.

So let us assume that both the timing and the distance have been measured about as well as modern technology allows. How then does one explain the effect?

Well the measurement is a statistical measurement of a subatomic particle, which means it is a Quantum Mechanics measurement, and when it comes to QM, statistics are not what they first appear. For example, if you put one foot in ice water, and another in boiling water, you might statistically feel fine, but not in reality. Likewise, statistically the neutrinos might be going faster than light, but individually and in reality none of them are. For example, suppose that only the leading edge of the 10.7 microsecond pulse creates interactions, but the shape looks like the trailing edge of the protons, so that matching shapes gives a false impression of faster-than-light travel.

A second issue is that the neutrino is describable by a wave-function in QM, which is not a single point but spread out over a region of space. One usually describes the wavefunction in terms of a "wave packet" that looks something like an American football, tapering to a point at the front and back. The speed of the football is the "group velocity" and this is the object that has to travel slower than the speed of light. But the interior of this football is full of waves, and those waves can move faster than the speed of light, which is called the "phase velocity". It is the phase velocity that gives the packet its interior shape, though it is the center-of-packet that gives the group velocity. Now the Italians are correlating to the shape of the packet, and if this means they are statistically sensitive to the phase-velocity, they may be fooling themselves thinking they are measuring simply the group velocity.

A third issue is related to the one above. If a wave-packet has a width, then a measurement of the leading edge of the packet and subtracting off the tail-edge of the packet will cause an offset of approximately the width of the packet. That is, when the proton makes the meson that decays into the neutrino, we time the proton and assume that the neutrino acts as if it were collocated with the proton. But perhaps the neutrino acts as a wave that is not collocated with the proton. It would be quite unusual for the wave packet to be 20 meters long, but perhaps it is QM entangled pairs of particles that have this length. Supposing that this entanglement is somehow energy related might account for the fact that MeV neutrinos don't seem to have anomalous offsets, 15GeV neutrinos have a 53ns offset, and 40 GeV neutrinos have a 67 ns offset.  

Having discarded all explanations that rely on errors in timing or distance, we are left with QM wave-particle effects which are not well developed for neutrinos. The closest cousin to a neutrino is an electron, and it weighs in at 511,000 eV/c^2, whereas these neutrinos are thought to weigh much much less, some putting this particular muon neutrino at a rest mass of only 0.003 eV/c^2. This means that the wavepacket size is almost entirely defined by its kinetic energy, which at GeV energies should be sub-atomic length, which is how it interacts with matter--through the weak force at the subatomic level. But no one is really sure, since it is quite difficult to do experiments on such slippery particles.

Let's play a few games with equations, and see what happens. Suppose the rest mass of the muon neutrino is 0.003eV/c^2 (as determined from flavor oscilations between 1 & 2). Then 40GeV/0.003eV = γ = 1.3 x 10¹³. Now events that happen in the rest frame of the neutrino will be multiplied by gamma in the experiment frame, so things that go quickly in the rest frame will appear to go very slowly in the experiment frame (e.g., the decay of muons from air showers). So let us estimate how long a virtual neutrino-antineutrino pair will last in the rest frame. From Heisenberg's Uncertainty, ΔE x Δt = h, or, 2(0.003eV) Δt = 4x10^-15eV-sec ==> 6x10^-13 sec. Now we multiply that by γ to get the experimenter's viewpoint, and find γΔt = Δt' = 8 seconds. Well it only takes 2 ms to go the 730 km from Switzerland to Italy, so in some bizarre fashion, the experiment in Italy is coherently coupled to Switzerland, and we should be using QM correlated statistics rather than uncorrelated statistics.

This experiment was first performed at Fermilab over about the same range, and the 2007 paper reported a speed just a tad slower than the speed-of-light for 3 GeV muon neutrinos. Unfortunately the dither in their GPS contributed 120ns error, and they could only say that the error bars included a possibility of faster-than-light travel as well.  The smallest error bars are for the Supernova 1987A neutrino detection, which found the speed of the 10 MeV electron neutrinos to be very very close to the speed of light. Not only does the smaller gamma for these supernova neutrinos shorten the correlation length, but the astronomical distances should uncorrelate the wavepackets as well. So on the surface, I would suggest that the mystery can be solved through proper attention to QM effects.

Does this result invalidate Einstein?

Not yet. But it does show the difficulty of making Einstein's relativity consistent with quantum mechanics. Einstein apparently despised QM as being "incomplete" so he didn't care about agreement, but the past 60 years have been spent trying to construct a unified theory. And while the weak force (which controls neutrinos) was thought to be well incorporated with photons/electrons into an "electroweak" theory, the discovery of the Higgs boson that was supposed to confirm the theory has proved elusive. So perhaps there remain mysteries in the electroweak formulation, mysteries compounded with these neutrino results.

No.

What about time travel?