# Faster Than a Speeding Photon?

So all the buzz in the physics department yesterday was this announcement by organizers of an experiment called OPERA (Oscillation Project with Emulsion-tRacking Apparatus) that they’ve measured the speed of the neutrinos being produced at LHC particle accelerator in Europe– and that the speed is larger than the speed of light, Einstein’s famous speed limit for the universe. The one advocated by the bumper sticker above.

For some reason, the story really seems to have taken root outside the scientific community as well; it was featured prominently on a Washington Post, my family tells me it made the front page of the Denver Post, and to top it all off, an acquaintance I know only indirectly posted about it on my Facebook wall– a sign of total societal penetration if ever there was one. I don’t know quite why this bit of news has had such an impact, but I would guess it’s because the story lives in a happy place between being intriguingly futuristic and prohibitively complex. Lots of folks are aware of the “cosmic speed limit,” and the idea of someone breaking it (even someone subatomic!) is the kind of thing that would be right at home in an episode of Star Trek. Indeed, science fiction writers have made such prolific use of the concept of a “tachyon” (a blanket term for hypothetical particles that might travel faster than the speed of light) that there’s an entire wikipedia page devoted to their appearances in popular fiction.

But unfortunately, the apparent simplicity of the concept seems to have lulled the media into a false sense of security, with the result that many of the mainstream articles fail to give any of the interesting details, the context, or the implications, to the point that many of them could just be replaced with an extended headline reading “Scientists See Particles Moving Faster Than Light; Einstein Wrong? Carl Sagan Once Said Something About Extraordinary Claims.”

They aren’t all so bad. This piece from ScienceNow, reprinted in Wired, is the best I’ve seen in popular press, and not just because it quotes a professor I currently work for . And of course one can always turn to the actual publication of the result. But just in case your taste for detail falls somewhere between the two, I’d like to offer some clarifying information about the context of this little puzzle.

Maybe this is a bit longer than the casually curious have time for, and if that’s true for you feel free to skip ahead. But as far as I’m concerned, to really appreciate this experiment, and the reason the rest of the scientific community is treating it with such hesitation and caution, one has to go back to Einstein himself, and the Special Theory of Relativity.  In the very first few years of the 20th century, Einstein realized, initially though a series of clever thought experiments, that a great deal of new physical laws could be deduced if one assumes three relatively simply things to be true. The first is that the laws of physics look the same no matter where you are standing or what time of day you perform your experiment, which certainly seems to have been true throughout human existence, and indeed is sort of necessarily true if it is even going to make sense for us to talk about “the” laws of physics. The second assumption is that the laws look the same to anyone travelling at a constant velocity, no matter what that velocity is. This, too, is fairly uncontroversial; if you go from sitting still at home to driving down the highway at a steady 65, things don’t magically start to disobey gravity*. And the final assumption is that the speed of light is constant, even if the source of the light is itself moving. This one is a bit more counterintuitive. After all, the way “everyday” objects behave is to move faster if their source is already in motion– a fastball thrown from the hood of a speeding camero is faster than a fastball thrown by someone standing still. But Einstein was able to show that, unless you accept this as a property of the universe, then it is possible for a situation to be contrived in which an event can precede its own cause. Consequently, Einstein chose to believe in the constancy of the speed of light, by far the less disconcerting result, and which had actually also been recently demonstrated in a now-famous experiment.

Armed with these, Einstein set to work producing a variety of new laws, all of which logically and mathematically must be true in a universe which obeys the three principles above (interestingly, the bulk of this work contains nothing more advanced than high school algebra and trigonometry). Among the results is the now-iconic statement that $E = mc^2$, but far more relevant for our discussion today is its mathematical cousin:

$E = \frac{m c^2}{\sqrt{1-(\frac{v}{c})^2}}$

Even the math-phobic among you should give this at least a once-over to see if you can understand it’s significance, because I’ll bet you can follow: this formula gives the energy, $E$, that it would take to create a particle of mass $m$ and make it move at a velocity $v$. The symbol $c$ stands for the speed of light. Hence, we can see that if you try to move an object at a velocity of exactly $c$, it will require an infinite amount of energy. The term $\frac{v}{c}$ becomes 1, the denominator becomes zero, and the division by zero makes the whole thing blow up. Attempting a velocity greater than c is even worse– it gives you the square root of a negative number, and therefore requires an imaginary number for energy required. Indeed, the only situation in which we could reasonably allow $v = c$ is if we ALSO let the top of the fraction be zero. Glossing over a bit of calculus that’s needed to make this rigorously true, one can think that, although dividing by zero is usually forbidden (how can I divide 5 apples among zero people?), if there was ever a number I could divide by zero it should be zero itself (zero people can certainly have zero apples!)**

Consequently this formula– a direct result of the simple assumptions above– says explicitly that only an object with zero mass can move at the speed of light, because it would take an infinite amount of energy to get a massive object to reach that speed. The incredibly fundamental nature of this result, coupled with the relative simplicity of its proof (and of course, the decades of scientific evidence in agreement) have made it one of the most incontrovertible results in all of physics: Nothing can move at or above the speed of light, except light itself because photons have no mass***.

And then along came OPERA, nearly 100 years later, boldly (if, perhaps, with a hint of self-consciousness) announcing to the world that they had measured the speed of the neutrino and found that it was larger than the speed of light. Granted, they did not find that it differed by a great deal. To be precise, they measured the quantity $(v-c)/c$ and found it to be $2.48 \cdot 10^{-5}$. In other words, their result is greater than the speed of light by just 25 parts per million. Nevertheless, Einstein’s formula is exact– not even small trips above the speed limit are allowed. And hence, it is a result that can’t just be swept away.

OPERA did not set out to challenge Einstein’s predictions. On the contrary, they wanted to use them, to settle a completely separate but longstanding question about neutrinos, the shyest and most elusive members of natures collection of subatomic particles. Of the three types of forces which can allow subatomic particles to interact significantly (gravitation between such small things is completely negligible), Neutrinos participate in only one, the “weak interaction,” which is also, as the name suggests, the wimpiest and least likely to occur. This kind of subatomic social anxiety disorder means that unlike every other particle we know, neutrinos can pass by trillions and trillions of other particles before they interact with even one. As a result, countless numbers of them are passing through you, your floor, and the earth itself even as you read this. They are nearly impossible to stop, because stopping something requires interacting with it, and, not unlike some physics students, neutrinos show almost no willingness to do this with anyone, ever.

This, of course, makes them very hard to study– how do you determine the properties of something that can travel right through all the scientific equipment you might use to probe it? It is like trying to dissect a ghost. And thus for many years the properties of neutrinos were only inferred mathematically from the best theories available, and not discovered by experiments. One of these early predictions was that the neutrino, like the photon, would be massless, and hence travel at the speed of light. Indeed, the “standard model” of particle physics continues to make that assumption to this day.

But in the last 15 years, experimental evidence has proven that this cannot be the case****. It is too far afield to discuss extensively in this post, but experiments have shown that the three types of neutrino- the tau, muon, and electron neutrinos, can change spontaneously into one another in between interactions–something called a “flavor oscillation,” which it turns out is possible only between particles with mass*****. Thus, the next natural question to ask is, just what IS the mass of the neutrino? Because of the particle’s reclusive nature, this is a tough question to answer. But the OPERA experiment sought to contribute to it answering it in a number of ways. Principally, they were looking for further, more complete evidence of flavor oscillations, but as an ancillary goal, they hoped to measure the speed of the neutrinos, and use this to deduce their mass (or at least an upper limit for it). They expected to find that the neutrinos had a speed of just slightly less than the speed of light, corresponding to their just slightly nonzero mass.

The idea behind the experiment is simple enough: A single neutrino has only the smallest of chances to interact with your equipment and is therefore unlikely to register in a particle detector. But a proton-smasher like the Large Hadron Collider (LHC) in Switzerland can produce an enormous quantity of neutrinos– so many that at least a few of them were likely to make an appearance. Thus, the scientists would start a highly-sophisticated version of a synchronized stopwatch when the neutrinos were created at the LHC, and run it until these neutrinos were detected at Gran Sasso National Laboratory, the home of the OPERA experiment in central Italy. The great distance between these two (nearly 500 miles) would actually serve to make the measurement more accurate– think, for example, of how a hundredth of a second can mean the difference between winning and losing in a 100-meter dash, but is completely insignificant in the time of a marathon runner who may beat his rivals by several minutes. Hence, the scientists could essentially just take the distance between the two laboratories, and divide it by the measured time to get a velocity. Then, in theory, the amount by which this velocity fell below the speed of light could be used to deduce just how far these neutrinos might be from being truly massless, and the OPERA folks would get some recognition within the scientific community for contributing substantially  to the question of the neutrino mass.

But of course, this isn’t what happened at all.

The path of neutrinos travelling between the LHC and the OPERA detector. Since neutrinos almost never interact with anything, they actually travel directly through the earth, never deviating from a perfect straight line. Image created with Google Earth.

Instead, they found themselves thrust into the middle of an extraordinary scientific debate, by announcing a violation of the speed of light. I can only imagine the furrowed brows and sweat-drenched collars at their meeting to determine if they should announce their result. To declare a challenge to Einstein, patron saint of physicists, one has to be absolutely sure he or she hasn’t overlooked a much simpler explanation. What if the ‘stopwatches’ (which were actually atomic clocks, of course) weren’t properly synchronized? What if they were wrong about the distance between our laboratories? What if they detected some other neutrinos that weren’t the ones manufactured at the LHC?

Their publication and subsequent press conferences make it clear they spent months trying to think up and take into account alternative explanations. Ultra-high-frequency lasers were used to measure the positions of source and detector. Multiple GPS systems were compared against each other to confirm the measurement, and a private, independent contractor with no knowledge of the measurement process was brought in to confirm the confirmation through a third technique. Fiberoptic cables were laid across half the continent so the timing system could be used to measure the speed of photons. The result was in exact agreement with the speed of light, suggesting that all the timing equipment was working fine.

At the Saturday press conference, the scientists in attendance peppered the collaboration with questions: Had they accounted for the minuscule effects of continental drift? Yes– their equipment had been precise enough to measure it all along, and they’d even detected and accounted for a 7 cm change in the distance that resulted from a minor earthquake. Could neutrinos from elsewhere be interfering with the detector? No, only those with a trajectory that coud be traced exactly back to the expected source were measured.

Countless other possibilities are examined and quantified in the paper, which, rather unusually, is dedicated almost entirely to an explanation of possible sources of uncertainty (most papers contain just a small section for this at the end). Scientists have developed a large and extensive toolkit to catalogue and quantify such uncertainty and the best of these tools were put to work. True, the neutrinos were above the speed of light by only 2.48 thousandths of one per cent– small enough that one might expect it to be an accident. But after quantifying every source of uncertainty they could think of in the experiment, they concluded that their result could be off by no more than 0.28 thousandths of a percent from statistical fluctuations, and not more than 0.30 thousandths more from constant offsets (for example, a timer that fired one nanosecond late every time) which had gone overlooked. In other words, the smallest this number could actually be was 1.9 thousandths of a percent above the speed of light– still unquestionably faster.

In fact, by scientific standards the amount by which the result outstrips the possible error is HUGE, and represents one of the most brazen parts of the scientists claim. There is always a chance that, due to a random coincidence of errors, a measurement will be off by more than the calculated amount of uncertainty, even if every source of uncertainty is taken into account. Scientists quantify the odds of this possibility with something called a “sigma value,” and it’s become common practice in particle physics not to accept any discovery unless it meets the so-called “5 sigma” threshold– which means it had only a 0.2 percent chance of occurring by random accident. This particular result clocks in at well over 6 sigma: less than a 0.0003 percent chance of being an accident, assuming the collaboration had identified all significant error sources.

Of course, the key phrase is “identified all significant error sources.” In the coming months, scientists the world over will be sifting through the experimental detailes with the finest of fine-toothed combs to look for anything that’s been overlooked. Other groups that work with neutrino sources and detectors, such as MINOS at Fermilab or Japan’s T2K (whose co-chair works here at Stony Brook!), will create similar but completely independent experiments and try to reproduce the result. If they can’t, it’s a good bet that something simply went wrong in the Italian experiment, and we may never know exactly just what. On the other hand, if they show the same effect, a great deal more physicists will start telling their grad students “go home and read everything you can about superluminal extensions of the theory of relativity! And bring me five ideas for how we can write a grant proposal about that by tomorrow morning!”

Scientists would also have to explain why this effect hasn’t been seen in the past. Few people have looked directly at neutrino speeds before, but the team at Gran Sasso had the brilliant idea to examine the data from a 1987 supernova explosion, which should have produced an enormous burst of both photons and neutrinos. Because the supernova was so far away, even a tiny, 2.48 thousandths of a percent difference in speed would have meant the neutrinos arrived at earth nearly four years ahead of the accompanying photons. And yet, no neutrino detector that was in place at the time registered any anomalous hits until the same day the supernova was seen, and its photons detected. Of course, the detectors of that era were substantially less sensitive than the ones we have now. Could it be that some, but not all the neutrinos from the supernova travelled faster than the speed of light, but avoided detection? And then there is the matter of a measurement made at MINOS in 2007, in which the speed of neutrinos was also seen to exceed the speed of light, but just barely, and only with a statistical significance of 1.7 sigma. This corresponds to about a 10% chance that it was simply a statistical fluctuation, well below the level of certainty insisted upon by science, and thus at the time it was assumed to be an accident and an outlier. But perhaps it was instead the first ray of light in the dawn of a new era of physics?

So far, you can count me firmly in the skeptic camp, along with just about every real physicist out there (including, I’m sure, many at Gran Sasso). The things we’d seemingly have to give up just seem too fundamental: A faster-than-light particle could create temporal paradoxes, events happening before the event that caused them, even, perhaps, a tachyon anti-telephone, a device with which you could call up and speak to any of the telephones previous owners. Or perhaps instead we can explain this as a result of neutrinos moving through some hidden, fifth dimension, as at least one theorist at Fermilab has already suggested. This would allow us to keep the precious laws of special relativity, which have worked so well in the past, and stipulate that they simply don’t apply in this fifth dimensional shortcut. But why would one type of particle have exclusive access to this fifth-dimension club? Why don’t we see Proton beams also moving faster than expected? Whatever explanation was proposed, the number of new questions it posed would exponentially outstrip the number of questions it answered.

And so now, we play a waiting game: waiting for MINOS, waiting for T2K, and waiting for theorists to give us their best guess about how these neutrinos might have cheated Einstein, so new experiments can be designed to test these theories. And all the while Einstein will be looking over our shoulders: the man was, after all, famously reluctant to accept radical realignments of science (other than his own, of course!) As far as I’m concerned, the man has earned the right to a little skepticism. And if I had to place a bet, I’d certainly put a large sum of money on the side that says it’s all just a mistake.

Nevertheless, as a graduate student looking for an exciting new project to write my thesis on, I can’t help but hope that it’s a bet I might lose.

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*But note here, the fact that I said “constant velocity” here is important. Suppose you were a scientist who was born and lived his whole live in a car which did NOT have a constant velocity, but rather was always picking up speed, as though gunning it up an incredibly long highway entrance ramp. You might easily conclude that one of the laws of physics was “things tend to get pushed backwards into their seat cushions,” which of course someone in a car at constant velocity wouldn’t agree with.

**This does NOT mean that all photons have zero energy, or take zero energy to create. That quantity 0/0 is an indeterminate form which does not tell you exactly what it is equal to, and so we have to use different equations to study the energy of photons.

Also, you may be wondering, doesn’t this same argument allow for massless particles moving FASTER than the speed of light? And there’s something to that. Other equations and experimental results discourage it from being true, but it’s arguably not expressly forbidden. In fact, this is precisely the kind of thing that physicists consider when the contemplate the possibility of a tachyon.

***Other particles in the photon “force carrier family” which also have no mass move at the speed of light as well, but these are not seen outside atomic nuclei.

****One of the best gifts I ever received was a T-shirt which says “Protons have mass? I didn’t even know they were Catholic.” My one regret about this shirt is that it doesn’t say “Neutrinos have mass?” instead.

*****The reasons for this are quite technical, but accessible to anyone with a background in rudimentary quantum physics. The neutrino’s mass eigenstates are different from it’s weak flavor eigenstates, so it naturally reverts to a superposition of weak states in between interactions, and then will randomly choose one of those states to return to the next time it interacts. A massless particle, of course, does not have quantized mass states and thus there is no gravitational interaction to force the neutrino out of the weak state it was initially observed in. This kind of oscillation is the same as the strong-flavor mixing observed among quarks, as described by the CKM matrix. The neutrino mixing-matrix is more clumsily called the PMNS matrix.

Colin West is a graduate student in quantum information theory, working at the Yang Institute for Theoretical Physics at Stony Brook University. Originally from Colorado (where he attended college), his interests outside of physics include politics, paper-folding, puzzles, playing-cards, and apparently, plosives.

### 3 Responses to Faster Than a Speeding Photon?

1. Moominmamma says:

Fascinating! This is a terrific explanation of the significance of this result. Your graphics are a welcome addition to the test-love the Einstein pix! Thanks for going to all the work of explaining this for us, because now I’m excited about it, too!

2. Spandextor says:

Quick, build Einstein a FTL phone so we can rub it in!

http://xkcd.com/955/

3. Derek says:

just to clarify? neutrinos only interact with van der waals forces?