What's Wrong With Those Neutrinos?
    By Johannes Koelman | September 24th 2011 03:51 AM | 36 comments | Print | E-mail | Track Comments
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    Do you believe neutrinos can exceed the universal speed limit of 299792.458 km/s? Be careful before you respond with "yes". Rumor has it that the set of all people who believe superluminal speeds have indeed been observed in the OPERA experiment is disjoint from the set of all people who have a deep understanding of relativity. (Which doesn't imply that any person unconvinced by the OPERA results necessarily understands relativity.)

    Has the universal speed limit been violated?
    The OPERA results appear to indicate that the much discussed (see here for the blogpost breaking the news last Monday) rogue neutrinos traveling the 730 km from CERN to Gran Sasso, did so at speeds of around 299800 km/s (give or take 2 km/s). What to make of this?

    To me this sounds like a second Pioneer anomaly in the making. It might take years before the dust settles, but that leaves little doubt in my mind that Lorentz invariance (the cornerstone of Einstein's relativity theory) will come out unscathed and validated by yet another experiment.

    Sounds narrow minded?

    Let's see if I can render you equally convinced.

    Lorentz transformations are rotations in spacetime. As we are dealing here with spacetime, and not just space, these rotations go beyond changes in orientation in space, and also include changes in speed (= orientation in a spacetime plane). Just like rotations in spatial planes can range from 0° to 360°, rotations in spacetime planes range from 0 m/s to 299792458 m/s. There is nothing magical about these specific numbers. Just like the number 360 appears due to the selected measurement unit for angles (degrees), similarly the number 299792458 appears due to the selected measurement unit for speeds (m/s).

    We fully understand the trigonometry of spatial rotation angles. And we have the same level of understanding of the trigonometry of spacetime rotations. This spacetime trigonometry is referred to as 'special relativity'. It is key in the formulation of local interaction laws such as the electromagnetic interaction. Without spacetime trigonometry, there would be no Maxwell's laws.

    Will the ultimate trading package be available soon? If the neutrinos traveled at superluminal speeds, they must have arrived younger than when they were send away. Encoding current foreign exchange rates in superluminal neutrino packets would allow you to get access to future exchange rates. The ultimate trader's dream come tru?

    Now suppose a high-energy physics collaboration reports on experiments with neutrinos in which they bring back neutrinos to their original orientations by turning them over an angle of 360.01 degrees. Would you believe this claim? Of course you don't. These folks must have made some systematic error in their measurements. You understand trigonometry all too well to believe anything else. And you certainly are not going to throw the whole machinery of trigonometry out of the window because of one single anomalous rotation measurement.

    Exactly the same holds true with the OPERA experiments. These folks must have made some systematic error in their measurements. We know spacetime trigonometry all too well to believe anything else. And we certainly are not going to throw the whole machinery of spacetime trigonometry out of the window because of one single anomalous speed measurement. The OPERA paper (submitted two days ago) itself is very open and explicit on this point, and mentions that more work is required "in order to investigate possible still unknown systematic effects that could explain the observed anomaly".

    All-in-all, amongst all the neutrino media hype of the last two days, the following cartoon from XKCD stands out as the most sensible reaction:

    Get more insight into relativity:
    - What's Wrong With 'Relativity'?
    - What's Wrong With E=MC2?


    Well, of course I would balk at the claim that neutrinos could be returned to their original state after a 360.01° rotation -- that's much too low, it should be 720 degrees! :P

    But regardless, it's of course everyone's expectation that this result will be due to some subtle systematic error -- all other explanations are just that much less likely. If neutrinos actually exceeded c, as in the special relativistic speed limit, they ought to be tachyonic, so that less energetic neutrinos should travel even faster -- which is in direct violation of the data from the 1987 supernova. If they only exceeded the speed of light, and that speed was slower than c, then it ought to be the case that the photon has mass -- which would for instance imply that differently energetic photons travelled at different speeds, on which there are bounds that I believe are far too strict to be consistent with an effect of the needed magnitude. If something even more exotic is happening, like the neutrinos taking a shortcut through the bulk in some braneworld scenario, then again, why didn't the neutrinos from the 1987 supernova find a similar shortcut?

    So the result is in disagreement with numerous very well established experimental results, and I can't see any wiggle room anywhere to fit this in as a physical effect -- and this is apart from very strong and general theoretical considerations like you mention in the post (which are certainly enough on their own to warrant severe scepticism).

    Reminds me of the superliminal speed reported before when there was a mix-up of particle speed, group velocity, and phase velocity.

    Johannes Koelman
    A first article thats zooms in on this issue has appeared today.
    Hmm, or maybe the speed of light in a vacuum isn't c not because of a photon mass, but because of vacuum polarization effects as in the Scharnhorst effect -- this might allow for neutrinos to propagate faster than light, i.e. closer to c, without running afoul of the constraints I mentioned, and without needing to scrap nice things like Lorenz invariance etc.

    Johannes Koelman
    Jochen -- the hypothesis that light travels at speeds lower than the causal propagation speed (and therefore the true c > 299792458 m/s) due to either a tiny mass or a refractive index from the vacuum, would both run into problems with earlier constraints. The observed effect on the neutrinos might seem small, but is quite large from a metrology perspective.
    I'm aware of the bounds on photon mass (I've mentioned those are too strict in my first post), but what constraints are there on a vacuum refractive index? I'm not sure we should even be able to draw any, keeping in mind the 'Lorentzian' view on special relativity (see Bell's 'How To Teach Special Relativity', for instance) which implies that viewed 'from the inside', we have no way to tell with conventional probes whether or not the photon propagation speed differs from unity...

    Take as an analogy the view of an 'inside observer' in a condensed matter system. Let's say there's a maximum speed of lattice excitation in this system, and let's furthermore say that this speed is anisotropic. Could our inside man detect this anisotropy? I don't think he could, because all the probes he has available to him are also lattice excitations -- which are bounded by the same speed and subject to the same anisotropy. So from the inside, this system would appear relativistic, even if from the outside, there's clearly a preferred rest frame (that of the lattice).

    We could be in the place of this inside observer, and be similarly unable to detect variations in the propagation speed of 'lattice excitations'...

    Johannes Koelman
    "I'm aware of the bounds on photon mass (I've mentioned those are too strict in my first post), but what constraints are there on a vacuum refractive index?"

    I was hinting at the constraints resulting from the lack of significant timing differences between neutrinos and photons arriving from distant supernovas. The difference in speed between neutrinos and light reported by the OPERA collaboration would translate into neutrinos arriving years ahead of the photons. Instead, both particles arrive at the same time (within experimental error). Now I know these are lower energy neutrinos that are of a different type as well, but clearly you woud need an incredible dispersion behavior to reconcile the OPERA anomaly with the supernova measurements.

    On you inside/outside analogy: why would the OPERA neutrinos provide us with an 'outside observation'?
    Bonny Bonobo alias Brat
    Wouldn't the Mikheyev–Smirnov–Wolfenstein effect be responsible for the different neutrino speeds being observed between the the man made ones being beamed through 'matter' or rock and the other extraterrestrial neutrinos?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at
    "On you inside/outside analogy: why would the OPERA neutrinos provide us with an 'outside observation'?"

    Not outside in the sense of 'outside the system', but outside of the electromagnetic interaction -- if you live on a crystal lattice, and there's a maximum speed cmax at which lattice excitations may propagate, and all you have access to are excitations propagating at a very slightly lower speed ceff -- the analogue of the case of photons being slowed down due to vacuum polarization effects --, you'll see special relativistic behaviour with invariant speed ceff; but if you then gain access to excitations not subject to the slowdown, i.e. neutrinos, you may potentially observe speeds in excess of ceff.

    But you're right wrt the supernova results -- it seems impossible to cook up anything that gives a steep enough energy dependence to fit both those and OPERA's results into a consistent framework. However, maybe the MSW effect, also being mentioned here, might be of some help...

    Or, well, it's just an experimental error, which still seems by far the most likely explanation to me.

    The Stand-Up Physicist
    The neutrinos were not travelling in a vacuum, nor an inertial frame. The Earth has stuff in it, has a gravitational field, and is rotating. While usually easy to ignore, it is possible they matter at one part in ten to the five. I have confidence that the OPERA team looked into each of these. It would be great if they made those calculations accessible in some way more than just a formal paper. 

    Do they have a means for an internal consistency check? One place I had read they also were able to detect protons from the same event. If so, then that might add constraints to the data. Will have to let others figure out this mystery.
    After 2 frustrating yrs at LHC, devoid of SUSY, mini-BlackHoles, an eerily small window left for SM Higgsy, & every expt. just reconfirming the SM, I would think we would all be Cheering for the extraordinary results by the OPERA crew to be validated by MINOS or KEK ASAP. If any particle is sufficiently weird enough to go FTL, then the neutrino fits the bill.
    Invented by Pauli in the 30s to preserve energy conservation in beta decay, it was discovered in the 50s, & soon shown to violate conservation of parity, like Lorentz invariance, a Sacrosanct law of fundamental physics. In the 80s, the first hints that it might be massive, contrary to the SM's assumption, were published, & indisputable expt. proof of such, via neutrino oscillations, followed in the late 90s.
    Now, 20 yrs later, it appears that the `little neutral one' continues to confound. What if its non-zero mass is in fact `imaginary' ? Such particles termed `Tachyons' by Gerald Feinberg in the 60s, are permitted by special relativity, but are a pariah of modern physics, `forbidden', & can only propagate FTL, outside the light cone. Nonetheless, Alan Kostelecký has extended the SM to show that tachyonic neutrinos may exist.

    From what Ive seen the group of people who claim this result automatically violates special relativity is disjoint from the people familiar with the content of this wikipedia page

    ....particularly with some arguments that have been around since 1967.

    Johannes Koelman
    Jimbo, Cliff,

    In this context tachyons are nothing more than nice fantasies. Quantum field theory tells us that at a fundamental level there is not just a maximum speed, in fact there is only one speed: the speed at which causations propagate. In simple terms: massless particles propagate at this speed, and so do massive particles. However, these massive particles obtain their mass by zig-zagging in spacetime, an effect that causes them to move with speeds less than the causation propagation speed over larger intervals. This leaves no room for tachyons.

    In other words: forget about all the mathematical complexites of relativity theory, at a fundamental level the causal structure of spacetime (the light cones) is the only thing that matters.
    Do have some articles or papers on this 'just one speed' thing.

    Johannes Koelman
    Promise you I will dedicate some future blog posts to this subject. In fact, this subject is on my list since I started this blog, but it will require a series of posts, and I need to find the time to work on it. So be patient, particularly so as there are a few other things on my list that I want to discuss before.
    Thanks for providing the link to the Pioneer anomaly, and how it was solved by using a 3D technique to more closely examine the effects of heat on deceleration of the spacecraft...

    Could the gravity field of Earth and the general relativity be behind the missing 20 or so cm? Geneva is at 375 m (take away another 50 to get to the muon source) and OPERA facility must be at ~900 m or more - Assergi at the west end entry to the tunnel claims 895m.

    Sort of brachistochronic way out of the bind (g).



    Johannes Koelman
    General relativistic effects on GPS signals are well known. It would be very surprising if the meteorologists involved would have overlooked the effects of earth's gravity on the local spacetime metric.
    "General relativistic effects on GPS signals are well known." It was just a thought - a knee-jerk reaction. It could just as well be some higher-order element that's normally dropped.

    "It would be very surprising if the meteorologists involved would have overlooked" - yes, but during two 70+ slides of ... and we checked this and we re-measured that ... (chapeau!) general relativity was not mentioned at all.

    On the balance of probabilities "If it's too stupid too be true, it's too stupid to be true". Applies to other ideas here as well (g).

    Johannes Koelman
    Metrologists will probably work in post-Newtonian approximations, and your remark about higher order terms being unjustifiably ignored could be a real possibility. (I hope not, as that would be very embarrassing following the headlines suggesting Einstein has been overthrown...)

    "Too stupid to be true"... yes, but maybe it is time to modify a well known saying into: "Never attribute to new physics what can be explained by stupidity".
    Johannes Koelman
    Wow, hopping in and out of bulk hyperspace...!

    ... what have you been smoking Sascha?

    Of course there is a lot of fringe physics that can be called in whenever an anomalous result is reported. Better to keep your head cool though, and wait for the inevitable report on a systematic error that was overlooked.
    In modern physics (is that what you call fringe?), we know that any one description may be dual (read completely equivalent) to other, seemingly very different ones. This and the fact that I explicitly talked about the membrane/bulk only as one intuitive example, I would have guessed somebody into entropic gravity (= emergent gravity) would not stay on the "I can't see 4D so it doesn't exist" kind of level.

    I have clearly stated that the data are likely due to systematic errors, however, calling this outcome "inevitable" disqualifies you from the scientific discourse.
    John Starrett
    Or maybe something much more interesting and confounding. You never know.
    John Starrett
    The author of this article is so presumptuous and arrogant that it makes it impossible to take his arguments seriously.

    Let me make a simple analogy:

    "Now suppose a geology collaboration reports on experiments with exotic dating methodologies in which they confirm that the Earth is definitely older than 6,000 years. Would you believe this claim? Of course you don't. These folks must have made some systematic error in their measurements. You understand the Bible all too well to believe anything else. And you certainly are not going to throw your whole faith in Biblical literalism out of the window because of one single anomalous measurement of the age of the Earth."

    Be not so dogmatic.

    Well, no, a more accurately analogy would be if they said their experiment found evidence the Earth was only 6,000 years old.  That is counterintuitive to everything we know so it would be a bold claim - then people would ask if GPS is really the most accurate way to determine that, etc.
    It depends on who you ask. The Christian fundamentalist will tell you that the Earth *not* being 6,000 years old is counterintuitive to everything he knows and that would be the bold claim; not his worldview. I'm merely saying the author of this article is taking such a strong view of special relativity that it's quite alarming. I expect someone with a strong science background to be a bit more open to new possibilities. But he's as closed minded as the Christian fundamentalist when he talks about this. I'm not saying that neutrinos do travel at superluminal speeds at all but the results are certainly interesting enough that the thing I would dismiss is our current understanding of how the universe works rather than think that somehow we have it all figured out.

    Phuc, so you would be open minded to a report that claims neutrinos getting back to their original orientation following a rotation over 360.01 degrees?

    It is better to keep your mind not too open to avoid the risk of your brains blowing out.

    Over 360.01 degrees? Sure. 720 degrees comes to mind. As does 1080. But I jest.

    However, don't let my extreme analogy take attention from my point here (and for the record, I do not agree with the Christian fundamentalist/literalist). Unlike Euclidean geometry (although the term Euclidean geometry is somewhat redundant) that deals with something very concrete that every human can verify with nothing more than his/her hands and everyone have had some kind of personal experience with, rotation in spacetime isn't something that is concrete and it's not something *anyone* has had a personal experience with. The *concept* of the fabric of spacetime is awesome no doubt. And it's used to accurately explain a great, great many things (until it doesn't of course). But that happened with Newtonian physics as well. Spacetime is simply a concept Einstein postulated to better explain things... a great concept but a concept nonetheless with absolutely no analog in the real world that we all live in.

    Let me be clear. I do not question the mathematical & predictive correctness of general & special relativity at all. But I do have a problem when someone has such a hard on for a conceptual construct that they'll immediately dismiss anything that might be contrary to it. That's why I had equate his argument with that of the Christian fundamentalist.

    By the way, the name's "Phuoc"... with the O. Without it's a whole nother name completely.

    FIrst, thanks for an interesting blog - perfect for someone like me with some undergrad physics from many, many years ago.
    In reading about the OPERA results, I ran across mention of this 1984 paper by Alan Chodos et al: The Neutrino as a Tachyon and I'm curious if it is relevant.

    Johannes Koelman
    Yes, it is relevant, but see my response to Cliff and Jimbo.

    Bottom-line is: there is a good reason why tachyons have never been observed. This reason is simple: there is only one speed: the speed at which causations propagate. nothing can go faster, and nothing can go slower.

    So how come massive paticles seem capable of moving at much smaller speeds? That is because the fast motion takes the particle N steps forward, and then N-1 steps back. This 'Zitterbewegung' (trembling mtion) is a microscopic effect that gets averaged out when observing the coarse grained motion of the particle.

    In a future blog I will go much deeper into this matter.
    Assuming the data from OPERA about neutrino velocity is rigth, and considering 1987a supernova neutrinos, how sooner (than ligth) the supernova neutrinos would arrived to earth ?

    Could be scientists ignore this possibility in 1987a data ?

    Johannes Koelman
    "Assuming the data from OPERA about neutrino velocity is rigth, and considering 1987a supernova neutrinos, how sooner (than ligth) the supernova neutrinos would arrived to earth ?

    That would have been several days earlier.
    I am not a physicist so forgive my supidity. But do neutrino's photon-tunnel? If so (and I do know that neutrinos only interact very weakly with matter), could they be tunneling through some obstruction in the earth that the bulk pass through more slowly?

    It is entirely possible that this was already factored in, however if it wasnt than it could possibly explain the results measured.

    Basically as I understand it the neutrinos travel through matter with little to no effect so if you release a neutrino at zero velocity the Earth rotating and moving through space would make the neutrino appear to be traveling relative to us and move from one location to another. So the measured speed of the neutrino is the sum of the neutrino traveling from Cern to Gran Sasso and the Gran Sasso lab traveling towards the neutrino. If that vector and speed was aligned right it could add up to the result measured but regardless it would create systematic and consistent error if omitted.

    John Starrett
    No matter the outcome, we should not forget that physical theories are only approximations and not God given. We are constantly being surprised and will be surprised again and again.

    John Starrett