Monday, September 26, 2011

More Thoughts on the Possibility of Superluminosity

My last post on the possibility of neutrino superluminosity rather surprised me with the amount of feedback it got, considering I put it together on the spur of the moment and hadn't really had time to think about it too much. But it's a good kind of surprise, because it shows people are interested in physics, and that makes me happy. Because really, how can you not be interested in physics? It's so fascinating! But I digress...

Anyway, this post is just intended as a bit of an expansion on my previous post, with some things I've thought of or had introduced to me in discussion over the weekend. It's important to keep in mind the way the experiment was conducted: basically, the Large Hadron Collider at CERN produces bursts of neutrinos which are detected at the OPERA detector about 730 kilometers away. These neutrinos are produced in bursts when protons slammed at high speeds into a target create pions and muons that then in turn decay after a random time into neutrinos. It's these bursts that OPERA actually detects. The time between the emission of a burst and its detection is then divided into the distance between the LHC and the detector, and the answer comes out to be about 60 nanoseconds (that's 60 billionths of a second) shy of the time it would take light in a vacuum to travel the same distance. Let's analyze this setup a little closer...

1. Distance measurement. The distance between the points of emission and detection is not the kind of distance you go out and measure with a meter stick. As stated before, it's about 730 kilometers from one to the other, and that's as the crow flies. In reality, the straight distance between them is through the Earth's crust, so you have to take that into account, along with the fact that the Earth is not spherical, nor even smoothly deformed, but a complicated shape called a geoid. Finally, both the LHC and OPERA are quite a ways under the ground, so that needs to be kept track of, and the standard way to measure large distances -- using GPS -- doesn't work that far underground, so you have to measure from a point on the surface, and work your way down. Now, in 60 nanoseconds light travels almost exactly 18 meters, so the two would need to be about 18 meters closer than currently thought for this explanation to account for the discrepancy (at least, it would need to be that much is this is the only explanation; in reality it may be a combination of factors). On the one hand, when you're measuring a distance of 700 kilometers, it would be easy to miss 18 meters; on the other hand, the scientist appear to have done a lot of work measuring using some precise equipment, and claim to know their relative location much better than 18 meters. This is definitely something that could stand to be reviewed. Finally, as I mentioned before, the neutrinos are produced at random lengths along a tunnel at the LHC; while the scientists claim that it makes very little difference at what point in the tunnel the neutrinos are produced, I think a careful review of the math may be in order.

2. Time measurement. This is where it gets a bit hairy, in my opinion. Time is a notoriously tricky concept in relativity, especially coordinating time between two observers. Two events may be seen to happen simultaneously or sequentially, all depending on the relative motion between the observer and the events. Remember, the time difference we're talking about is tiny, only 60 nanoseconds. The scientists at OPERA claim to be have resolution down to 10 nanoseconds (plus or minus a few), but that's an awfully tiny number. There's another twist I've seen pointed out: GPS satellites use general relativity in order to be as accurate as possible, but if these neutrinos truly are moving faster than light, it indicates that there is something wrong with relativity as we know it, so how much can we actually trust the satellites?

The first two points were some of the ways I could see the measurements being off. These next points are various tests I thought of that would go a long way to determining what exactly is going on.

3. Measuring with light. One of the best tests I can think of would be send a light beam along the same path as the neutrinos and measure how long it takes. If your light beam ends up faster than it should be, it rules out that the neutrinos are traveling superluminally. It would indicate one of two things: either the measurements of either time or space are off, or there is some sort of strange spacial-temporal disturbance going on in the Earth's crust between CERN and OPERA (which I'll perhaps expand on in a later post, as this one is long enough already). Unfortunately, this test is out of the question because the path of the neutrinos is through solid rock, not vacuum.

4. Measuring the energy of a neutrino. This is one I'd really like to see, because instead of taking the estimated time of flight for the neutrino and dividing it into the distance to get the presumed speed, you could take the energy of a neutrino and from there directly calculate its speed. If that turns out to be a hair under the speed of light, as it most likely would, then you know for a fact that a) the neutrinos were not moving superluminally and b) that either your time or distance measurement is off. Sadly, I don't know if OPERA is capable of detecting the energy of a single neutrino -- in fact, I'm not sure it's currently possible at all. This test would certainly do a lot to eliminate the possibility of superluminosity, though.

5. Two-way measurements. This would also help a lot. One-way measurements of speed are difficult because of the relativistic effects I mentioned earlier. It's a lot more reliable to measure the speed of something going away and back, and simply dividing twice the distance by the time. Yet again, this test is impossible due to the way neutrinos interact with matter. To put it mildly, they don't. Hardly at all. In fact, billions of neutrinos from the Sun's core are passing effortlessly and unobtrusively through your body as you read this sentence, regardless of the time of day or night. You'd need a bar of lead over a light-year in length before you'd have a 50% chance of any one neutrino interacting with it. The only reason OPERA is able to detect the emitted neutrinos is because there are so many of them -- and it still probably misses more than 99%. For this reason, you can't fire a beam of neutrinos at a mirror and have them bounce back, like you can with light, making this yet another test that can't be performed. In its absence, simply firing a beam of neutrinos back along the same path would have to do, but even that can't be done, as there are only a few places on Earth capable of creating neutrino bursts, and they tend not to coincide with the locations of the detectors capable of detecting said bursts.

Any of the three tests proposed above would do quite a bit towards resolving what's really happening here, whether that be simple mis-measurement or a whole new era of physics. Of course, none of them are likely to be done anytime soon, although personally I think that measuring the energy of a neutrino would probably be the most likely and easiest. There is, however, one test that has, in a sense, already been done. When supernova SN1987a went off in the Large Magellanic Cloud in 1987, we detected a burst of neutrinos coming from it a few hours before the light became visible. While this might at first glance seems to support the superluminal neutrino theory, it is actually easily explained by our current theories of supernovae (when the core of a supernova collapses and initiates its destruction it releases a burst of neutrinos that have no trouble getting out through the outer layers of the star, while the energy and light from the explosion take a few hours to work their way to the surface). The neutrinos in the experiment, if they were traveling faster than the speed of light, were only going about 1 part in 40,000 faster. The LMC is about 160,000 light-years away, so if the neutrinos from that event exhibited the same behavior, they should have arrived 4 years before we saw the light from the supernova. This doesn't entirely disprove the superluminal velocity theory (there were only a few [two?] neutrino detectors working at the time, and it might not have been noticed), but it does seem to go against it. It would be amazingly useful to have another supernova go off somewhere visible within the Local Group so we could see if there were any detectable neutrino bursts from it that would fit with this, but this is, yet again, depressingly unlikely to happen in the near future (although it can't be ruled out! There's always hope...).

Of course, I don't want to end this post on such a depressing note. While none of these tests can be done at the moment, I wouldn't put it past some brilliant mind out there to think up some test that could be done, and which will help resolve the question (put a neutrino detector and mirror array out in space, then simultaneously fire a laster and a neutrino burst, maybe). Really, whatever happens will be interesting; either Einstein is proven correct yet again and relativity stands vindicated, or we enter the brave new world of post-Einsteinian physics, which I can only imagine would be just as exciting as the introduction of relativity and quantum mechanics. Speaking of QM, I haven't mentioned it at all in this post, but not because I haven't been thinking about it in relation to this experiment. But you'll have to wait for another post for that, I need to get some sleep now. A hui hou!

1 comment:

  1. My thoughts on this whole issue are that these findings probably won't pan out. This would not be the first time an experiment has found evidence that seems to contradict the cosmic speed limit. The catch, in this case, is that the confidence is very low, only 1.76-sigma, from what I remember. That might be good enough for medicine, but it's not good enough for physics. GPS satellites are indeed very accurate time-keepers. If it weren't for the relativistic correction factor, their locating ability would drift off by several feet per hour. Anyway, a few things should be pointed out here. For one, relativity does not say that nothing can go faster than the speed of light. It just says that nothing can go faster than the speed of light if it was originally going slower than the speed of light. In fact, tachyons, in contrast to the hilariously-named tardyons, require more and more energy to go SLOWER, mirroring their tardy friends' behavior about the c asymptote. For two, nothing can exceed the speed of light if it carries information and/or mass. Rigorously speaking, c is the upper limit on information travel through spacetime. As you may have guessed, this means that tachyons are antisymmetric with respect to causality, so a real tachyon would be created at the moment it appeared to be detected and destroyed at the moment appeared to be emitted.


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