How IceCube Observes Neutrinos From The Cosmos

I’ve finished (more or less) a version of the promised article on IceCube — the giant neutrino experiment that may have made a major discovery, as announced last week, and that had an opportunity to make another a few weeks ago (though apparently nature didn’t provide).  The article is admittedly a bit rushed (darn computer trouble) and therefore a bit rough, and it also leaves out some more subtle points that may become important in the future — but I think it’s complete enough to help explain how IceCube made their most recent measurements.  As usual, please send comments and questions, and I’ll work on it further.

Here’s the link to the article.  You may also find it interesting to read more generally about how neutrinos are detected, and about the weird story of neutrino types, and how they can oscillate from one type to another as they travel.

14 thoughts on “How IceCube Observes Neutrinos From The Cosmos”

  1. Matt I read your excellent post on ‘Neutrino Types and Neutrino Oscillations’. First, though I have never said it before, I really appreciate ‘Of Particular Significance’ and all the work you obviously do. It is a great site, very informative and all your hard work really shows…

    I must admit I find the whole neutrino oscillation theory disturbing. I know it works, and there is a lot to be said for this, but there is something very disjointed about this theory relative to the ‘rules’ for other particles. I understand why position and momentum are mutually exclusive quantities in quantum theory. It makes sense. But why would flavor and mass be mutually exclusive? And why just neutrinos? I mean an electron never ‘oscillates’ into a muon or a tau right? Why not?

    According to present day physics a muon is just a heavy electron, yet a muon will never become an electron by emitting a photon (m -> e + y). Doesn’t this imply that a muon must be more than simply a heavy electron? And much to physics surprise when muons are used to measure the proton charge radius we get a different answer than when electrons are used. Something is amiss…

    I have a feeling that nature is hiding one of its greatest secrets with regard to this notion of three generations of fundamental fermions and were just all missing it…

    Also just wondering about the three mass states, is it possible that the lowest mass state m1 = 0?

    • The muon is not a heavy electron. It is a heavy cousin with similar properties, but it is not a heavy version of an electron. [In contrast, a Delta is a heavy, “excited” proton, and decays to a proton + a pion very rapidly.] But the three neutrinos, similarly, are just cousins too.

      Did you read my article on the muon/proton charge radius puzzle? What’s probably amiss is a theoretical calculation, and nothing odd about the proton or the muon at all. (The press on this has been quite misleading and really has led people to think something that’s very likely not true…) We’ll see eventually, with more experiments.

      How muons and electrons differ, other than through their masses, is unknown at this time. There is no need theoretically for there to be any other difference; there is no experimental indication of any difference (other than the muon/proton radius puzzle that I just warned you probably isn’t a puzzle.)

      As for what is special about neutrinos; what is special is that they are so light that we regularly observe them with energies vastly larger than their mass differences, by millions and more. This is not true for taus, muons and electrons. However, it is true for neutral bottom-quark mesons, charm-quark mesons and strange-quark mesons, which in some cases come in pairs with very small mass-differences compared to their energies. And there we also observe oscillations and the same kind of issue.

      In fact oscillations of this type occur throughout quantum mechanics.

      Flavor and mass are just two of many, many examples of quantities that can’t simultaneously be specified. Quarks have the same issue; what we call a “bottom quark” has two meanings, one being the object with a definite mass, the other being the object to which a top quark decays — and they’re not quite the same. In fact, *there are very few quantities that can be simultaneously specified * — generally, only those quantities which are conserved are immune from this kind of situations.

    • S. Dino: “I have a feeling that nature is hiding one of its greatest secrets with regard to this notion of three generations of fundamental fermions and were just all missing it… ”

      You are exactly right. As Matt said, “How muons and electrons differ, other than through their masses, is unknown at this time.” The current established (accepted by the mainstream) physics has no idea about the essence of “particle generations”.

      While I should not talk about speculative ideas in this site, one idea (G-string) was discussed at another physics blog ( ) might give you some hints about your very important question. As it was already discussed at other blog, I would like to beg the permission to explain it a bit more here.

      In addition to some important physics “principles” (such as conservation laws), there is a new rule (the music-chair game). When these music-chair rules were pushed to their limit, they are still confined by a pure dimensionless number, the Beta.

      Beta = 64 ( 1 + first order mixing + sum of the higher order mixing)
      = 64 (1 + 1/Cos A(2) + .00065737 + …)
      = 137.0359 …

      A(2) is the Weinberg angle, A(2) = 28.743 degrees

      The sum of the higher order mixing = 2(1/48)[(1/64) + (1/2)(1/64)^2 + …+(1/n)(1/64)^n +…]
      = .00065737 + …

      In this Beta equation, there are only three numbers { Weinberg angle, 64, 48}. “64” is the maximum numbers of music-chairs allowed for the game. “48” is the maximum number of chairs reachable by the players. Yet, what the heck is the Weinberg angle in this game? If it has nothing to do with the number of chairs, then this Beta will be somewhat ad hoc. But, A(2) is a function of A(0) and A(1).

      A(0) = f (Pi, 64) = 1.4788425146211 degrees, f is a function.
      A(1) = g (Pi, A(0), 24 (48/2)) = 13.5211574853 degrees, g is a function. Similar to Cabibbo angle.
      A(2) = h (Pi, A(0), A(1), 24) = 28.75 degrees. h is a function. Similar to Weinberg angle.

      Now, A(2) is nothing but the result of those music-chairs (64 and 48). The details of these equations are available online, and I thus will not repeat them here.

      This is only a G-string-music-chair game, coincidentally able to explain your question.

  2. Ok fine; let’s assume the proton radius experiments utilizing muons are in error. Also by saying the muon is a heavy electron I did not mean to imply that it is an ‘excited state’ of an electron. I don’t think it is. Poor choice of words on my part. But if there is no need for any difference, except mass, between a muon and electron then why does a muon never decay to an electron and a photon? And if the electron and the muon are cousins just as the electron-neutrino and a muon-neutrino are cousins, then why no oscillations in the former case?

    • As to your first question, of muons decaying to an electron and photon, they presumably do. Only it happens so rarely we’ve never observed it. The way in which this happens in the Standard Model is that the muon briefly becomes a virtual state of a W- boson and a muon neutrino. The neutrino then oscillates into an electron neutrino, the W- radiates a photon, and then the virtual W- and neutrino recombine into an electron. I believe the dominant suppression in this process is the probability of the neutrino oscillaion. Also, I’m not sure how theory deals with the oscillation of virtual particles.

      As for your second question, it really has to do with the mass difference between the particles which are oscillating. The neutrinos have very small mass differences of tenths or hundredths of an eV, as do the B mesons which Matt mentioned earlier (and their mass difference is thousandths of an eV). However, the electron has a mass of ~ 500 keV (1 thousand eV per keV), and the muon has a mass of ~ 100 MeV (1 million eV per MeV). This mass splitting is a major parameter in controlling the frequency of oscillation, the smaller the faster.

      It’s also likely that electrons and muons would oscillate into each other given enough time, but that time scale is vastly larger than the time it takes for a muon to decay, putting it out of any contemporary attempt to observe the phenomenon. Mixing is a general feature of quantum systems. We see it in strange mesons (K mesons), charmed mesons, and bottom mesons. Top quarks decay too quickly so we can’t see it there. And I’m not really sure why we don’t see it for up and down quark systems. Maybe something to do with a protective chiral symmetry.

    • I wanted to further point out that the mu to e gamma is a channel of active research (mu2e experiment at Fermilab). Observing it would cool enough, but since it is such a rare process in the SM the rate can be significantly affected by “new physics”, e.g. supersymmetry. If you’re interested in this specifically, you can probably find a bunch of material at the experiment’s website.

      • “Only it happens so rarely we’ve never observed it.” Processes so rare they have never been observed.

        I see…like Proton decay. You will forgive my skepticism. I guess we all have our prejudices, and in light of the fact that there is no experimental evidence either way, you will kindly allow me mine. I favor holding on to the conservation laws (call me old-fashioned) that physics has recently (from an historical perspective) thrown under the bus. Until experimental evidence indicates otherwise, I do not believe in any violation of the Law of Conservation of Baryon Number. I know why physics dumped it – you can’t get the universe going with it. You need those antiprotons or their massive antimatter equivalents to decay at a slightly greater rate than those protons or their massive matter equivalents – though you have experimental evidence for neither. And no one seems to ever ask, let alone answer, why nature would favor a slower decay rate for matter over antimatter.

        That is one of the reasons I almost always mention (here I go again) doing experiments to determine the gravitational acceleration of antimatter even though I know the vast majority of physicists regard such experiments as a waste of time and money owing to their faith in General Relativity. But GR notwithstanding, I am not terribly impressed with physicists professed ‘love’ of symmetry. It’s like the ‘love’ a husband professes for his wife from his mistresses hotel room.

        As to Conservation of Lepton Family Number I’m not even sure if physicists themselves have come to a consensus on its current status. Is it considered to hold now only for charged leptons? Or is it as Paul maintains, its violation is expected but so rare it has never been observed?

        I still can’t help but wonder if there is a theory out there that would account for neutrino observations without sacrificing yet another conservation law.

  3. Great article as usual!

    A few weeks ago I stated that (admittedly naively) my first guess would be:

    Fermion Bosons
    gimp gravitational
    neutrino gravitational, weak
    electron gravitational, weak, electromagnetic
    quark gravitational, weak, electromagnetic, strong

    but that I thought it is then difficult to give the “gimp” its mass through the Higgs mechanism. I recently found out that actually such a “gimp” (gravitationally interacting massive particle) naturally arises, in the form of a sterile neutrino, if one adds mass to neutrinos to account for neutrino oscillations. In this case the mass can indeed not be generated directly by the symmetry breaking but can be (or has to be) included in the Higgs mechanism (Yukawa coupling) and its mass is a free parameter. So at the moment this is the most natural candidate for gravitationally interacting dark matter. I also learned that many sterile neutrinos experiments are coming up and is at the top of the list for Sheldon Glashow.
    So my question to you Matt: are you planning (if you haven’t done so already) to write something about sterile neutrinos on your blog?
    Of course many thanks in advance!

    • I have been wondering about this matter myself Matt. I have found myself on the same side of an online discussion/argument as Dr. Weinstein on a couple of occasions over the past several years. I remember that I appreciated his input/agreement. However, until a few days ago I had no idea he had been working on his physics for over two decades!

      Anyway Duncan, I just read that he will give his Oxford Lecture again tomorrow. If true, I suspect it will have better attendance than last week!

  4. In cognitive science, in artificial intelligence, mathematics seems useful because, it consider self (consciousness?) as, “sedimentary informations (or genetical codes)”.
    Sometimes mathematics seeming above consciousness. Example is “Geometry of Pythagorean theorem”. Human’s geophysical understanding was basically “Axion (Logos)” – not on physical reality (Axion is a belief, not to have a mathematical proof).
    Geometry is the perception of encapsulated quantum of action, in a photon, we call it mass (E = hv) – which was made as Dirac constant “h-bar” = h/2π.
    There is no comprehension of physical information without consciousness – it is not possible to replace it with mathematics.
    Consciousness is non local, like physical information of a field(amplitude?).
    The “quanta” is a localized consciousness through mathematics by E = hv.
    The matter wave or de Broglie waves reflects this connection. Out of this mathematical connection, non local de Broglie-Bohm theory was constructed?

    This is the consequence of Pythagorean theorem.

    Like perpetual (penrose) stairs, Mathematics connects the wavefunction (quanta) with π. Consciousness could perceive this quantum of action or mathematical quanta.

    This is possible only with photons, because of 3D space ?

  5. Thanks a lot for this video (conversation with Nima Arkani-Hamed) Mr Tienzen (Jeh-Tween) Gong ,
    It took two hours to watch it. I felt, he carry a light inside him. Concrete spacetime will emerge ?

    PYTHAGOREANISM: When the apeiron is inhaled by the peiron it causes separation, which also apparently means that it “separates and distinguishes the successive terms in a series.” Instead of an undifferentiated whole we have a living whole of inter-connected parts separated by “void” between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using maths, but truly mathematical since it shows numbers and reality to be upheld by the same principle. Both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos — both are a play of emptiness and form, apeiron and peiron.

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