Matt Strassler 11/19/11
Ok, here’s the latest, as I currently understand it, on the OPERA experiment’s measurement that suggests (if it is correct in all respects) that neutrinos might be traveling faster than the speed of light, which in the standard version of Einstein’s theory of special relativity should be the ultimate speed limit that no particles can exceed.
Warning: For the moment not all numbers are double-checked, and there might, in places, be a number that’s off by as much as a factor of 10. But there should be no major errors. Also, I’m going to be restructuring the website a little bit and will add more cross-links between this article and the various OPERA articles and posts that I’ve put up. Apologies if there’s a bit of construction going on while you’re here.
The Old and New OPERA measurements
Since I’m going to be talking about OPERA’s first measurement (the one they announced in September, which started the public hubbub) and also about this more recent OPERA measurement that serves as a cross-check and got all the press this weekend, I’m going to give them the names OPERA-1 and OPERA-2 so we don’t get confused about which one I’m referring to.
The only difference between OPERA-1 and OPERA-2 (as far as I am aware) is an alteration in the duration and scheduling of the pulses of neutrinos that are sent from their source at CERN (near Geneva) toward the Gran Sasso laboratory (in Italy) where OPERA is located. I’ll discuss the pulses in much more detail below. You should keep in mind that the distance measurements and the time calibrations for OPERA-1 and OPERA-2 are the same, so if there’s a mistake there, it will be present in both versions of the experiment.
Neutrinos Are Tough to Catch
Now, the whole story about OPERA starts with a basic fact about neutrinos. A high-energy electron or proton or neutron won’t get very far in ordinary matter; it will smash into some of the atoms in the material, and soon come to a stop. But neutrinos, which are not affected by the electromagnetic force or by the strong nuclear force, are very unlikely to hit anything when they pass through ordinary matter. Although the probability of hitting something increases for neutrinos that have higher energy, and the CERN beam has neutrinos that are much higher in energy than, say, the neutrinos from the sun, it is still true that the vast, vast majority of the neutrinos in CERN’s beam pass through the 730 kilometers of rock between CERN and the Gran Sasso laboratory, and out into space, without hitting a single atom. So rare are the interactions (and so broad is the beam by the it gets to Gran Sasso) that only 1 in about 1,000,000,000,000,000 neutrinos (one in a thousand million million, or a quadrillion in American counting) from CERN’s beam have a collision inside the OPERA experiment! Fortunately it is possible to make large numbers of neutrinos. If it weren’t, OPERA wouldn’t ever detect any neutrinos at all.
In OPERA-2, which ran from October 22nd to November 6th, the number of neutrinos sent from CERN toward Gran Sasso was about 40,000,000,000,000,000 or so. This required over 100,000 pulses of about 300,000,000,000 neutrinos each. Over this 16 day period, OPERA detected about 35 neutrinos, of which 20 were detected well enough to measure them in detail. What you learn from this is important: for most pulses of neutrinos sent from CERN to OPERA, not a single one of those neutrinos hit anything in (or near) OPERA at all.
Now we’re ready to understand why OPERA-1 was such a problematic experiment in which to measure neutrino speeds, and why OPERA-2 was such an improvement.
OPERA-1: A Convoluted Way To Measure Neutrino Speed
First, let’s recall that OPERA-1 was not intended primarily to measure the speed of neutrinos. It was intended to study neutrino oscillations, looking for a process in which the muon neutrinos in the CERN neutrino beam oscillate into tau neutrinos, hit something inside of OPERA, and turn into a tau particle, which only tau-type neutrinos can do. For this reason, the highest priority was to have as powerful a neutrino beam as possible, to make the detection of this process possible. The fact that such a powerful beam would have properties that would make a measurement of the neutrinos’ speed more complicated was not a primary concern. The speed measurement was “parasitic” — something that could be done, admittedly with some difficulty, as a side project that would not affect the main goals of the OPERA experiment. That’s why, as we’ll see, the methods used in OPERA-1 look a tad inelegant.
You may have read in the press that OPERA-1 measured the speed of over 15000 neutrinos. That sounds impressive, but this statement is fundamentally wrong. The OPERA-1 measurement is a single measurement; the speed of neutrinos is only measured once. The method used is very convoluted, to the point that it requires many thousands of neutrinos in order for it to work. And that’s what I’m going to explain now. Bear with me. I promise the explanation of OPERA-2 will be much, much simpler by comparison!
Indeed, the need for 15000 neutrinos sounds a little odd. If you’re just trying to figure out if neutrinos travel faster than light does, wouldn’t even one speeding neutrino be enough?! I mean, if I’m an alien trying to find out whether human airplanes can travel faster than the speed of sound, wouldn’t I just need to see one example of a supersonic jet in action, and I’d know the answer was “yes”?
Well, that’s right: a single example of a super-fast neutrino (or perhaps a handful, just to make sure you didn’t make a mistake) ought to be enough. And in fact that’s how OPERA-2 works. But not OPERA-1. OPERA-1 uses a much more complicated method.
In my blog post on OPERA-2 from Nagoya, Japan, I described OPERA-1 as being done with neutrino pulses that were like a long blast on a horn, while OPERA-2 uses pulses like short clicks. The analogy has now been widely quoted in the press, but there is something important missing from the analogy, and that’s what I want to fill in now.
OPERA-1 claimed the neutrinos from CERN arrived about 60 nanoseconds earlier than expected — 60 nanoseconds before light would have been expected to arrive, assuming all measurements of the times and distances were right. (Nanosecond = 1 billionth of a second = 0.000000001 seconds.) But the tricky part is that in OPERA-1, each pulse of neutrinos sent from CERN was 10,000 nanoseconds long. That still doesn’t sound so bad — if you were to blow your car horn for a minute starting at exactly noon, and I was a kilometer (0.6 miles) away, I could still figure out how fast sound travels by noticing that I first heard the horn blast at 12:00:03. But with neutrinos it doesn’t work that way. OPERA doesn’t detect the whole neutrino pulse. In fact, it’s a lucky pulse that leaves any trace at all! Most of the time, when CERN sent a pulse during OPERA-1, its arrival at OPERA, 2.4 milliseconds later, was greeted with dead silence. Only very occasionally — only about 15,000 times over three years, which is a few times per hour when the experiment is running — a single neutrino from that giant pulse hit something in OPERA (Figure 1), allowing OPERA to detect it.
What can we say about the speed of this neutrino? Answer: not so much. We know it was produced somewhere within that long pulse, but we don’t have any way of knowing if this particular detected neutrino came from the start of the pulse that contained it, or the end of that pulse, or somewhere in the middle. In other words, we know when the pulse started to leave CERN, but we don’t know exactly when the detected neutrino left CERN! So we can’t measure its speed with much accuracy at all! And certainly there’s no way to tell that it arrived 60 nanoseconds early.
So how does the OPERA-1 measurement work, then? Roughly (and inaccurately) speaking — the actual methods used were more sophisticated than this, but that’s a level of complexity and confusion that we can safely skip since OPERA-2 makes them unnecessary — what was done is something like the following. Combine all the data together; imagine taking all the neutrino pulses from CERN and piling them (figuratively) on top of each other, lining up their start and end times. Then take all the neutrinos observed at OPERA-1 and figuratively pile them on top of each other, lining up the window of expected arrivals for every pulse. What you get is shown in Figure 2; a distribution that shows most of the neutrinos arriving in the expected window. But a few of them arrived early! None arrived late, and there seems to be a little gap at the end of the window. It is as if the whole pulse was shifted early by 60 nanoseconds. Notice that of the more than 15000 detected neutrinos, most of them don’t matter much; the most important neutrinos are the tiny fraction — much less than 1 percent of them — that arrived early. Also important are the very last neutrinos to arrive, which help indicate that the pulse isn’t wider than expected, but is just shifted early. So only a few of the 15000+ neutrinos really matter. Experts: what is really done is roughly a fit of the time distribution of the detected neutrinos to the time distribution of the protons that produced the neutrino pulses. Even that’s not quite as sophisticated as what they actually did, which was to assign a probability distribution for the departure time of each neutrino… etc.etc.etc.
But wow — especially since the reality was actually a bit more intricate than my simplified version of it — is this ever a complicated way to measure the speed of neutrinos, when all you have to do, in principle, is measure the speed of a handful of them really well! And doing it in this complicated way opens the door to all sorts of issues. If, for example, there’s a problem that crops up in your understanding of the shape of the pulses — exactly how they start, and exactly how they end — or with the fact that you measure the shape of the pulses of neutrinos by studying the protons with which you create them — subtleties with the method I’ve described might introduce errors that would create a fake shift. Maybe.
It was obvious after OPERA-1’s public presentation of its results that a much better measurement would ensue if very short pulses were used instead. In fact many physicists had this thought immediately (and one even asked about it during the question/answer session following the presentation.) But it wasn’t widely known (until I heard about it in Nagoya and reported it here) that there would be an OPERA-2, using short pulses.
OPERA-2: A Simpler Way to Measure Neutrino Speed
So — why are short pulses so much better?
Look at Figure 3. This is an entirely different technique: pulses only 3 nanoseconds long, and separated by hundreds of nanoseconds. That makes the pulses much shorter than, and the gaps between them much longer than, the 60 nanosecond early-arrival that OPERA-1 observed. So if OPERA-1 were correct, what would we expect? Instead of a window of expected arrival 10000 nanoseconds long for each pulse, OPERA would now have a window of expected arrival only 3 nanoseconds long. If neutrinos were to travel fast enough to arrive 60 nanoseconds early, then each pulse from CERN would enter and entirely exit OPERA long before the window of expected arrival even opened up. In short, if any speeding neutrino from the pulse were to be detected in OPERA, it would inevitably arrive early compared to the window of expectation, rather than, as in OPERA-1, typically inside the window.
This is exactly what OPERA-2 has observed (Figure 4). All 20 of the neutrinos they detected over the two weeks from October 22nd to November 6th arrived early, from as little as 40 nanoseconds to as much as 90 nanoseconds early, with an average of 62. It’s unambiguous. Every neutrino is arriving early. And since we know the departure time of each neutrino to within 3 nanoseconds (the length of the pulse that contained it), and its arrival time to within about 10 nanoseconds or so (the measurement isn’t perfect; see below), we can estimate the speed of each neutrino separately. That wasn’t possible in OPERA-1.
Avoiding a Jump to Unwarranted Conclusions
Now, two comments to prevent us from misinterpreting this observation.
First, what we have learned is that there was no mistake in OPERA-1’s technique of combining lots of data from many long neutrino pulses. We have not yet learned that OPERA-1 or OPERA-2 have correctly measured the speed of the neutrinos. For all we know right now, OPERA-1 and OPERA-2 are making the same mistake in their measure of distance or of time, or making some other subtle mistake common to both experiments. OPERA-2 is less open to criticisms of various types than OPERA-1, but the story is not over. Every experiment with a radical claim must successfully clear an obstacle course of objections. OPERA has now passed a very important test, but more tests lie ahead.
Second, the fact that not every neutrino arrives at the same time to within the 3 nanoseconds pulse duration — the spread of the observed arrival times is, as I mentioned, much wider — does not imply that the neutrinos are traveling at different speeds from one another. We have to remember that every experiment has intrinsic imperfections, which translate into imperfect measurements. It is OPERA’s job to tell us how imperfect their measurements are, and what they say is this: when they combine everything they know about the imperfections (“uncertainties”, we call them) in their measurements — uncertainties in the measurement of the moment when a neutrino interacts inside their experiment, and in the timing measurement on the pulse of neutrinos when it leaves CERN, and in lots of other subtle sources of imperfections — the result of OPERA-2 is consistent with all of the neutrinos traveling at the same speed, with all of the different arrival times due to imperfect measurements. That doesn’t prove the neutrinos are all traveling at the same speed, only that OPERA-2’s result does not prove that the neutrinos are not traveling at the same speed.
Looking Back, and Ahead
Now why, you may ask, didn’t OPERA just run with OPERA-2’s short pulses from the very beginning? Once they decided to run OPERA-2, it only took them about two weeks to gather 20 neutrinos, and make a more convincing measurement than they made with all three years of OPERA-1! Well, that’s my question too. I think it’s because, again, OPERA-1’s measurement, unlike OPERA-2, was a parasitic measurement off of an experiment that was trying to measure neutrino oscillations. Meanwhile, OPERA-2 is great as a dedicated measurement of neutrino speed, but because the total number of neutrinos passing through the detector in a given month is 60 times less than with the long pulses of OPERA-1, it is impossible to do the neutrino oscillations measurements while running OPERA-2. Since it means temporarily giving up the original goal of the OPERA experiment, it wasn’t until OPERA-1 saw a strong sign of faster-than-light neutrinos that there was enough justification to run with the short pulses of OPERA-2. But the whole thing only took two weeks! I’m not sure why they didn’t run OPERA-2 for a couple of months back in September, before they made any public announcement about OPERA-1; if it was that quick for them to check it…
What’s next for OPERA? I don’t know, but I know what I would like. Of course they need to think of other ways to cross-check their experiment to rule out other possible sources of error. But also I would like them to run OPERA-2 again, for about two or three months, and detect about a hundred neutrinos rather than twenty. And then I’d want to see a plot, for all of the neutrinos they observe, of the neutrino’s energy on one axis and the early-arrival time on the other axis. In fact I’d already like to see it for the data they’ve got from OPERA-2, though there may well be too few events to show the effect I’m going to describe now.
In Figure 5 I’ve shown three hypothetical versions of the plot I’d like to see, with three possible ways the data might appear. Let me explain the details of the three plots, and what makes them different.
A very important constraint on the speed of neutrinos is that we know, from measurements of neutrinos and of light from the 1987 supernova, that neutrinos with energies about 1000 times smaller than those in OPERA’s neutrino beam travel very close to the speed of light. (Even though the neutrinos are of a different type in OPERA’s beam than in supernovas [and in fact are mainly anti-neutrinos], evidence from neutrino oscillations indicates that they must all travel at the same speed for a given energy.) Click here for my description of the supernova neutrinos and how we can use them to learn about neutrino speed.
In other words, it would seem, from the supernova measurements, that if we took a beam of neutrinos with energies of 0.01-0.04 GeV, instead of 10-40 GeV as in CERN’s beam, and aimed it at OPERA, those neutrinos would arrive at the expected time to within better than 1 nanosecond. I’ve plotted those supernova-like neutrinos as a purple dot on the three plots, indicating that neutrinos with energy well below 1 GeV would not, according to what we know from the supernova, arrive significantly early.
Meanwhile, I’ve sketched how OPERA-2’s neutrinos, shown in red dots, might look on such a graph. In the first plot at upper left, I show you what would happen if Einstein’s equations were exactly right and if there were no mistakes in the OPERA measurement. In that case, the neutrinos would on average have an early-arrival time of zero — some being measured to arrive a bit early and others a bit late just due to imperfect measurements. This is what we might have expected, but this isn’t what happened in OPERA-2.
Instead, OPERA-2 might be showing us one of the two possibilities shown in the other plots. If OPERA-2 has made a mistake in the distance measurement, or a mistake in calculating times, or if there’s some subtlety with relativity that their calculations missed, these errors will probably be independent of the neutrino’s energies. All the neutrinos, regardless of their energy, will be early by the same amount (though as always the observed times will vary a bit, due to experimental imperfections.) In that case we’d see something like the plot at lower right in Figure 6. But if in fact OPERA’s neutrinos travel about 2 parts in 100,000 faster than light, then since supernova neutrinos have speeds that differ from light by less than a few parts in 1,000,000,000, neutrino speed must vary by a part in 100,000 between about 0.02 GeV and about 20 GeV. And if it varies that much, we should expect (though it is not guaranteed) that it will still be varying between 10 and 30 GeV, and between 30 and 60, etc. Therefore, if in fact Einstein’s theory of relativity needs modification, we would expect the data to give something like the plot at lower left in Figure 5, with OPERA’s lower energy neutrinos traveling slower and arriving later than its higher energy neutrinos. If we saw a plot that looked like that, with a clearly varying arrival time as a function of energy, that would make us all sit up very straight in our chairs. Very few mistakes that OPERA might have made could make the plot look like that.
Again, I don’t know why OPERA didn’t publish this graph already with their existing data; maybe they felt the result was too ambiguous. But I hope either (a) it isn’t too ambiguous, and they’ll make it public very soon, or (b) if it is too ambiguous, then they’ll run another round of OPERA-2 next year, and get a couple of additional months of data that they can combine with their current results to make the plot of energy versus arrival time.
So… The OPERA seems far from over. Whether OPERA’s measurements are right or wrong, OPERA-2 is a real step forward, both allowing us to narrow the list of possible problems with the experiment and offering hope for more insights down the road.