Theories about Superluminal Neutrinos

October 1, 2011 at 8:16 am 11 comments

Predictably, and happily, several theorists have posted calculations and speculations to the archives, spurred by the observation by the OPERA Collaboration that neutrinos appear to travel faster than the speed of light.

I say “happily” because a result like this one provokes new ideas in the heads of theorists and we all learn something in the process. Of course, experimenters have ideas, too, and I’ll bet that people in MINOS and T2K are hard at work, hoping to confirm or refute the OPERA result.

The theoretical ideas are wildly diverse and most of them are tentative. Although I am not a theorist and I am not capable of judging any of these ideas, I’ll try to convey the essence of the papers I liked the best. No offense to papers that I don’t cite here.

The first paper by Giacomo Cacciapaglia, Aldo Deandrea, Luca Panizzi (arXiv:1109.4980 23-Sep) describes a rather careful quantitative analysis of the available neutrino data – mainly SN1987a, MINOS and OPERA. As I explained
earlier this week, the authors find it difficult to reconcile the lack-of-spread of the MINOS data with a quadratic energy dependence and indicate that some kind of step function at Eν around 1 GeV is required.

The second paper by Jean Alexandre, John Ellis and Nick E. Mavromatos (arXiv:1109.6296 28-Sep) also look at the question of how strong the Eν dependence has to be in order to satisfy SN1987a and OPERA. They point out that conventional tachyons don’t fit because the effect should decrease with energy – i.e., the effect for SN1987a would be huge. Despite the difficulties with the data, the authors forge ahead to construct two example theories that allow for superluminal neutrinos. Their first speculation involves a Lifshitz-type Field Theory of gravity, leading to an interesting dispersion relation ω2 = m6 + M4p2 + 2M2p4 + p6, where m is a dynamical mass, M is a mass parameter characterizing Lorentz Violation and p is the momentum. Clearly this rises faster than p2, but it still does not fit the data all that well. Their second speculation is more interesting and is based on a Lorentz-violating gauge theory, involving a fermion coupling to a new U(1) gauge field. In this scenario, the light cone seen by fermions differs from the one seen by photons. An interesting point is that this theory generates fermion masses dynamically, and a Higgs mechanism is not needed. A Lorentz-violating term is included in the Lagrangian which alters the fermion propagator. In general, subluminal velocities result from this term, unless one adds a constant background gauge field Bμ. If the couplings are weak but the field is strong, superluminal velocities can occur. An important point is that neutrinos and anti-neutrinos would have different velocities. Also, the velocity would depend on the angle with respect to the background field, Bμ – so some experiments would see a positive TOF with respect to light, others a negative, and some no effect at all. This field Bμ could vary in strength on galactic distance scales, and have little effect on SN1987a while a major effect on earth-based neutrino sources. In any case, a like one of the closing statements by the authors: Superluminal neutrinos should not be discarded as a phenomenological impossibility, but rather be regarded as a scenario to be probed and constrained by experiment. Right on.

The third paper could not be farther in spirit form the second. Written by Andrew G. Cohen, Sheldon L. Glashow (arXiv:1109.6562 29-Sep), the abstract contains the sentence Thus we refute the superluminal interpretation of the OPERA results! The authors have noticed that superluminal particles can slow down by emitting radiation including pairs of fermions, and they completed the lowest-order calculation for neutrinos. The dominant mechanism is ν→ν+e+e. Although the prefactor is roughtly 10-6GF2, the rate of emission of the e+e pairs by the neutrino is proportional to E6 and the energy loss is proportional to E5. For the 730 km baseline of the OPERA experiment, the terminal energy is 12.5 GeV which is much lower than observed by OPERA – the neutrinos have radiated away the rest. According to Cohen and Glashow, the OPERA energy distribution directly contradicts the notion that the neutrinos are traveling faster than the speed of light. They go on to say that observations by the IceCube Collaboration of multi-TeV neutrinos passing through the earth is an extremely strong constraint on the order of δv/c < 1.7×10-11. This is a formidable result and its hard to think that the calculation is wrong.

Nonetheless, let me put aside the objection from Cohen and Glashow to point to two interesting papers.

The fourth paper is by A. Nicolaidis (arXiv:1109.6354 28-Sep) who sketches how [sterile] neutrinos could take a “short-cut” through the bulk in an extra-dimensional scenario. You’ll recall that these theories attempt to solve the hierarchy problem by extending Gauss’s Law to extra dimensions in which gravity can propagate but the gauge interactions of the standard model cannot. In essence, the neutrino can follow a geodesic in a many-dimensional space while light and other standard model particles are constrained to move along a curved surface. He writes down a toy model and concludes that one can match the OPERA result with the size of one extra dimension of about 2.7μm and a curvature parameter Ak on the order of 10-2. He does not discuss the facts from SN1987a or MINOS, however, and hopes that an experiment can be done with NESTOR which is 1676 km away from CERN.

The last paper I’ll mention today (-again- sorry that I do not try to discuss all of the papers that have appeared) was written by Marco Matone (arXiv:1109.6631 29-Sep). This curious paper begins with Hamilton-Jacobi theory in quantum mechanics. I don’t understand the calculations at all but the upshot seems to be that some extra constants of integration appear when one addresses the time evolution of the particle. In a particular rather generic case, the usual result for the velocity of a quantum particle is modified by a function of these extra constants, and this function can have a value greater than one, thereby leading to superluminal solutions. While Matone’s calculation is relativistic, it ignores field theory so it probably cannot be taken at face value. That said, I think it is great that the OPERA result can spur thoughts about fundamental quantum mechanics!

So here’s what we have – ad hoc parametrization of the dispersion relation, two or more parametrizations pulled out of Lorentz-violating field theory, extra dimensions and unconventional quantum mechanics – plus an observation based on “simple” physics that the OPERA results are simply impossible. You might look upon this as theoretical bedlam, but I am happy to see so many creative ideas emerging, which can help shape the experiments we need to do in order to verify or refute the OPERA results.




Entry filed under: Particle Physics.

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11 Comments Add your own

  • 1. Daniel L. Burnstein  |  October 1, 2011 at 2:16 pm

    I predicted those exact results (superluminal neutrinos) a little more than a year ago, in the early drafts of my treatise on quantum-geometry dynamic ( see ).

    At the time, considering the outrageous predictions the theory made, more than a few of the researchers I have been in contact with thought that QGD was some kind of crackpot theory, but in the last few months a number of its predictions have gained some support from experimental data.

    QGD predicted the exclusion of the Higgs boson, refuted supersymmetry and the idea of extra dimensions, put in question the theory of relativity’s explanation of the constancy of the speed of light and, specifically predicted that neutrinos and only neutrinos shared structural properties with photons, which would allow them to move at superluminal relative speeds.

    No one will argue that the ultimate test of any theory is the observation of its predictions. If this is true, than QGD is certainly in a very good position.

    Getting back to the topic of the OPERA results, QGD not only predicted but also provided an interpretation of the results which goes as follows: Since, according to QGD, neutrinos can only move at the absolute speed of light (the absolute speed being the speed measured against the quantum-geometrical space itself), then the difference in between the relative superluminal speed of the neutrinos of the OPERA experiment and speed of light must be due absolute speed of the Earth along the axis of motion of the neutrinos. What the OPERA experiment unexpectedly allowed to measure would actually be the speed of the Earth relative to quantum-geometrical space.

    If as I believe the OPERA results are duplicated, then QGD predicts that other experiments will show neutrinos’ speed will vary slightly depending on the orientation of the axis between the source and target of neutrinos. The relative speed of the neutrinos will be exactly the speed of light when the axis is perpendicular to the absolute direction of the Earth (relative to the quantum-geometrical space background). It’s important here to insist that I’m not talking about the speed of the Earth relative to the Sun, the centre of the galaxy or relative to any other object.

    The relative speed will be at its minimum but less than c when the axis between the source and target is parallel to the axis of direction of the Earth but move in the same direction. And the maximum relative speed, which will be higher than c, when the axis between source and target is parallel with the absolute direction of the direction of the Earth and move in the opposite direction.

    These are very exciting times for physics. Especially exciting for me is that in these last few months a number of QGD predictions have been confirmed or are near the point of confirmation. The exclusions of the Higgs boson, the indirect exclusion of extra-dimensions, the relative superluminal speed of neutrinos (QGD also predicts superluminal photons). I know these observations do not prove that QGD is correct, but they certainly support it.

    I think the biggest prediction of QGD (which I know LQG also ST makes) is that space is both discrete and emergent from the interactions between one of two types of fundamental particles the theory admits. If space is discrete as QGD predicts, than it is not matter that determines the structures of space, but the structure of space that determines the structure of matter and how it propagates and interacts.
    Discreteness of space also precludes the existence of time. This implies that time being a purely relational concept; it should not be unified with space. Discreteness of space is alone sufficient to explain the constancy of the absolute speed light (time dilation being the unavoidable consequence of the continuity of space is unnecessary if space is quantum-geometrical).

    None of the dominant theories have predicted the recent LHC results, much less explain them. QGD does both. I’m looking forward to opportunities to defend it.

    Also, for those who are interested in cosmology, QGD predicts that the Universe didn’t evolve from a singularity, but from an isotropic state which gave birth to the CMBR.

    Daniel L. B.

    • 2. Peter  |  April 26, 2012 at 5:31 am

      Sadly, as we now know, OPERA’s measurement apparatus were faulty and the neurtinos were not superluminal, as Cohen and Glashow so powerfully argued.

      • 3. Daniel L. B.  |  May 3, 2012 at 7:01 am

        There is a distinction to be made between data and the theoretical interpretation of data. Icarus refutes the Opera measurements, but more revealing than the measured speed are the variations between them. In that way, Icarus and Opera agree and though for different reasons, the original conclusion of the Opera group still holds.

  • 4. Ricky  |  October 2, 2011 at 4:31 pm

    So how does your “prediction” deal with the objections of Cohen and Glashow?

  • 5. Daniel L. Burnstein  |  October 3, 2011 at 12:04 am

    The Cohen and Glashow argument is tautological. They use the extension of the theory the OPERA results would refute if confirmed to refute them. It is intricate way of saying that the results are false because they don’t fit the theory.

    The prediction of a theory should not be tested against the predictions of other theories (I know it’s done a lot but it shouldn’t), but against experimental results.

    If the results of the OPERA group are confirmed, then special relativity falls and so does the Cohen and Glashow argument, and QGD’s prediction is confirmed. If the results don’t hold, then QGD’s prediction is refuted.

  • […] Blog: Theories about Superluminal Neutrinos […]

  • 7. xyz  |  October 6, 2011 at 10:22 am

    Imagine the c limit space time is a gloomy slow jello only for certain fields like electromagnetic, electrons etc. Matter
    from c space time cannot exceed the speed of light but the
    “supermatter” can but cannot c1 and so even more supermatter
    the c2. What if c is quantized for various type of matter. The
    supermatter can slow down to below c and accelerated above
    c but the ci matter cannot exceed ci+1 velocity. Nothing really
    happens to neither special or general theory of relativity: The spaceship build with type j matter is simply not detectable
    with j-1 matter and measures proper type according to metrix
    c1 so it sees the electromagnetic field always c below c
    but later suddenly stops and can be detected only with compatible
    kind of massless field from below c spacetime. It simply
    disappears for c kind matter detector. The most striking consequence
    would be the the rest energy of supermatter c1 would be m c1^2 where
    c1 may be even 10 time larger then the speed of light !!!
    This fast predict the supernuclear exothermic reaction where
    the exoti kind of matter releases the energy according to different
    critical velocity and later even more super matter.
    Is the neutrino experiment the prove of c1 ? It is very diffcult
    to say because of low budget but it may be !!!
    The Einstein relativity theory is the radio theory most of all
    and Einstein himself never heard about neutrinos neither of superluminal clocks from them living in c1 spacetime.

  • 8. Juan Ramón González (@juanrga)  |  October 11, 2011 at 12:22 pm

    It seems evident that OPERA guys did something wrong. Myself contributed to a joke about their supposed measurement (hashtag #mundaneneutrinoexplanations) that spread in twitter.

  • 9. check this  |  October 14, 2011 at 8:02 am

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  • 10. David Brown  |  November 12, 2011 at 2:15 pm

    Has the OPERA neutrino anomaly confirmed MOND in the form of the Rañada-Milgrom effect? Did Einstein make a mistake in assuming that the dark-matter-compensation-constant = 0? What is the explanation for dark matter (DM)?
    “I think few people appreciate that the main difficulty for DM is that the host of regularities pointed out by MOND, if taken as just a summary of how DM behaves and interacts with normal matter, suggests that these two matter components are coupled and correlated very strongly in many ways. … if MOND does turn out to have some truth to it, the fact that it has encountered so much opposition will just show how nontrivial a thought it was.” — Mordehai Milgrom, interview entitled “Dark-matter heretic”, American Scientist, Jan.-Feb. 2003, Vol. 91, #1, p. 1
    Consider the following argument:
    Premise 1. There is overwhelming empirical evidence in favor of Milgrom’s non-relativistic MOND, according to the work of Milgrom, McGaugh, and Kroupa.
    Premise 2. For low gravitational accelerations, non-relativistic MOND is approximately equivalent to the Rañada-Milgrom effect, because the approximate equivalence is easily shown by a scaling argument.
    Premise 3. The approximate value of the dark-matter-compensation-constant is given by the Pioneer anomaly, and this value is approximately confirmed by the OPERA neutrino anomaly.
    Conclusion. The Rañada-Milgrom effect is approximately valid, at least for low gravitational accelerations and non-relativistic velocities.

  • 11. Mart Vabar  |  November 24, 2011 at 12:13 pm

    On the neutrinos track, there might be some particles (or coherent collections of these?) which might absorb a neutrino at one side, while on the other side, in the same time emitting a similar neutrino. Thus we get an illusion of a faster-than-light movement of a neutrino which seemingly “jumped over” another particle with no time…
    If so, could the neutrinos run even faster in heavier materials (?like Earth’s core)?
    I wrote about this in Physics Forum, too, trying to make it a little bit funny (link added).


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