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Mu Neutrinos as Tachyons?

by John G. Cramer

Alternate View Column AV-161
Keywords: muon, neutrinos, OPERA, Collaboration, CERN, superluminal, tachyon
Published in the March-2012 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 9/25/2011 and is copyrighted ©2011 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


Rumors have been circulating in the physics community for the last few days about a spectacular new result coming from the OPERA experiment at CERN.  This morning, CERN produced a press release about the result, and this afternoon hundreds of physicists crowded into the large seminar room at CERN's site at Meyrin , Switzerland , just West of Geneva, to hear a presentation by the OPERA Collaboration's physics coordinator, Dr. Dario Autiero of the Institute for Nuclear Physics in Lyon, France.  I was able to "attend" the seminar over the Internet from Westport , NY.

The OPERA group has just released a 24 page paper describing in detail a measurement detecting over 15,000 mu-neutrinos, showing with a statistical precision of about 6 standard deviations that, in traveling the 730 kilometers (454 miles) from the CERN site to a detector in the Grand Sasso underground laboratory buried in a mountain East of Rome, they travel at a velocity that exceeds the speed of light by 26 parts per million.

This result, if valid, shakes the world of theoretical physics to its very roots.  Einstein's special theory of relativity is based on a principle called "Lorentz invariance", an even-handedness in the treatment of inertial reference frames (coordinate systems at rest or moving with a constant speed) that would be destroyed if signals could be sent using particles travelling even slightly faster than the speed of light.  Such signals would break Einstein's frame even-handedness by selecting some reference frame as the "correct" one.  For this reason, the general view in the physics community is that there must be something wrong with the OPERA result.  Some subtle problem must be producing the illusion of superluminal neutrinos.

Before we get into the OPERA results, however, let me review what we think we understand about neutrinos. There are two classes of fundamental spin ½ particles, the six strongly-interacting quarks and the six weakly-interacting leptons. Three of the leptons (electron=e, mu=m, and tau=t) have significant masses and one electron-charge of electrical charge.  The other three leptons (ne, nm, and nt) have tiny masses, zero electrical charge and are called neutrinos. The simplest form of the Standard Model assumes that neutrinos, like photons and gluons, have zero rest-mass.  However, we have had to change that assumption, based on recent experimental evidence. Neutrinos have very small masses (perhaps a few hundredths of an electron-volt), they always travel close to the speed of light, and they rarely interact with anything.

Our Sun is a giant thermonuclear reactor that burns hydrogen into helium, making lots of neutrinos in the process.  Neutrinos from the Sun pass through your body and through the Earth as if neither was there. As you might imagine, this makes neutrinos very difficult to detect ... but not quite impossible. The first successful experiment to detect neutrinos from the Sun was mounted in 1968 in the Homestake gold mine in Lead, South Dakota by Ray Davis and his group from Brookhaven National Laboratory. This experiment, conducted 850 feet below ground level in a 100,000 gallon tank filled with perchloroethylene cleaning solvent, produced a famous result. They detected only about 1/3 of the expected number of solar neutrinos. This neutrino deficiency was later confirmed by the Kamiokande II detector in Japan , which, although it operated on a different principle, was sensitive to neutrinos in about the same energy range as the Homestake detector.

We now understand the missing solar e-neutrinos.  Neutrinos have a small mass, and this causes them to "oscillate", to change their flavor from e-neutrinos to m-neutrinos and back again, as they travel through space.  The solar neutrinos were not detected by Homestake and Kamiokande because 2/3 of them had oscillated to the m-neutrino flavor by the time they traveled from Sun to Earth, and these m-neutrinos could not produce the nuclear reactions used in detection.

The tiny rest mass of neutrinos is puzzling. Why do the three neutrinos species, unlike their charged lepton brothers and their quark cousins, have rest masses that are nearly (but not quite) zero? The standard model of particle physics is silent on this question. Unlike the photon, which must have a zero mass because it is the mediating particle of the infinite-range electromagnetic force, there is no fundamental reason why neutrinos should be massless.

One way of measuring the e-neutrino rest mass does so indirectly by examining the energy spectrum of electrons produced in low-energy nuclear beta decays. The "end-point" or energy region where the most energetic electrons are found is most sensitive to the mass of the e-neutrino (or e-anti-neutrino, which should have identical mass). If the e-neutrino has zero mass, the energy region near the end-point smoothly merges into the baseline. But if the e-neutrino has a small mass, the distribution at the end-point is chopped off early, producing a "nose" with an abrupt edge at the end of the electron energy distribution.

It is not widely appreciated, but this end-point technique does not actually measure the mass of the neutrino. Because of the way that the neutrino mass affects the electron energy spectrum, the measured quantity is the square of the neutrino mass.  Curiously, essentially all of the experimental determinations of neutrino mass have shown some significant probability of negative values for the measured mass-squared.  However, the negative mass-squared region is not taken seriously by the physics community because the error bars are too large, and the implications of a negative mass-squared are too bizarre.  A negative mass-squared would occur only if the e-neutrino had an imaginary rest mass.

Can a particle actually have an imaginary rest mass? In 1967, Gerald Feinberg of Columbia University suggested the existence of hypothetical imaginary-mass particles, which he christened "tachyons". Feinberg's tachyons are particles that always travel at velocities greater than the speed of light. Instead of speeding up when they are given more kinetic energy, they slow down so that their speed moves closer to the velocity of light from the high side as they become more energetic. Feinberg argued that since there are no physical laws forbidding the existence of tachyons, they could exist and should be looked for. This prompted a number of experimental searches for tachyons.  However, until OPERA, there has been no convincing evidence of their existence.

What did OPERA measure?  The motivation for the experiment was to use the proton beam of the CERN SPS to produce a beam of m-neutrinos and observe their oscillation into t-neutrinos as they traveled from the CERN site near Geneva to the underground Grand Sasso Laboratory in a highway tunnel through the mountains East of Rome.  The detector consists of two "brick walls" of passive emulsion detector bricks backed by magnetic muon trackers that point to the bricks that should be examined.  The trackers can identify energetic m leptons produced in m-neutrino interactions with matter and back-track them to the emulsion bricks or rocks in which they were produced.  So far, in three years of operation, OPERA has unambiguously identified one t lepton with their system (as compared to an expected number of 1.6), which presumably was produced by a t-neutrino that oscillated from their beam of m-neutrinos.

A byproduct of the OPERA experiment is that they detect thousands of m-neutrinos, and they can in principle determine the m-neutrino velocities by dividing the flight distance by the flight time.  This, however, is not as easy as it sounds.  The source and detectors are located 454 miles apart, and one must know the flight time and the separation distance to parts per million to make a significant speed measurement.

The measurement of the source to detector distance, to an accuracy of 20 cm, was accomplished using GPS techniques to precisely locate reference points at CERN and at the two ends of the 10 km long Grand Sasso tunnel.  The experimenters then transported these references into the laboratory inside the tunnel (blocking off one lane of automobile traffic in the Grand Sasso tunnel in the process).  They thus measured the benchmark neutrino flight path to be 730534.61 m to an accuracy of 0.20 m.  The precision of these distance measurements also permitted them to observe the effect of continental drift, changing the measured distances by about 1 cm per year, and they also saw a 10 cm shift from an earthquake in 2009 in the L'Aquina region of Italy .  The tidal forces produced by the Moon and the Sun on the Earth are also a potential source of distance change, but fortunately the flight path from CERN to Grand Sasso is primarily North-South, and the tidal flexing of the Earth is primarily East-West, so that effect proved to be negligible.

The other issue is the precise determination of the neutrino flight time. The synchronization of clocks between CERN and Grand Sasso proved challenging, but was accomplished to a precision of a few nanoseconds through an elaborate scheme using GPS synchronizing of cesium clocks.  The more serious problem was that the neutrinos were produced during the CERN SPS synchrotron acceleration cycle in two successive "beam spills", each of which had a duration of about one microsecond.  The uncertainty of which proton during the spill actually produced the detected neutrino made nanosecond time-of-flight timing difficult.

This problem was addressed by carefully recording the beam profile of each spill and correlating these with each neutrino detection. Fortunately, the two spills each had a distinctive "fingerprint" of intensity fluctuations, as well as distinctive leading and trailing edges, and these could be matched by maximum likelihood analysis to the time profiles of the 16,000 detected m-neutrinos.

The result was that the time of flight of the m-neutrinos could be determined to a statistical precision of about 6.9 nanoseconds (ns) and a systematic uncertainty of 7.4 ns, and has a value of 60.7 ns.  This corresponds to a m-neutrino velocity that is 24.8 parts per million faster than the speed of light.  This is a 6 standard deviation (6s) effect, where 3s is generally considered to be the threshold of believability.

The OPERA group also performed one interesting refinement of their analysis.  The average m-neutrino energy of their entire data set was 28.1 GeV and gave a transit time of 60.7 ns with a statistical uncertainty of 13 ns. They divided their data into two subsets of about equal statistics, one with an average m-neutrino energy of 13.9 GeV and the other 42.9 GeV and computed the transit time of each subset.  The 13.9 GeV data set gave a transit time of 53.1 ns and the 42.9 GeV data set gave 67.1 ns, both with statistical uncertainties of about 18 ns.  The difference in transit times shows no convincing energy dependence of the kind that would be expected for tachyonic particles, but at the 1 s level the lower energy neutrinos do show an indication of being slightly faster.

Are the m-neutrinos really travelling faster than the speed of light?  The odds are against it.  The usual outcome of such a spectacular physics result is that a flaw is found somewhere in the analysis, and the result is withdrawn.  The OPERA result needs to be confirmed or contradicted.  Fortunately, the MINOS experiment at FermiLab did a very similar measurement.  They also found a slight indication of FTL m-neutrinos, but their experimental precision was an order of magnitude poorer, and the superluminal result was taken as a statistical fluke.  However, the MINOS precision can be improved by careful metrology to determine the distance from the FermiLab source site to the Soudan Mine detector location, and this is now being done.  (We note that the Tevatron collider at FermiLab, the injector of which was used to make neutrinos for MINOS, is having its final run on September 30, 2011, just a few days after the OPERA announcement.)  The Japanese also have a neutrino oscillation experiment using the Super-K detector that may be able to shed light on the OPERA result.

This is a science fiction magazine, and so I want to close by taking the OPERA result seriously and exploring its implications.  Are m-neutrinos tachyons?  Are all neutrinos tachyons?  Superluminal m-neutrinos constitute a serious discrepancy in our supposed understanding of the way the universe works, and raises many questions.  A new revolution of physics would be needed, throwing out many cherished ideas.  It's encouraging to SF readers that something seems to be able to travel faster than light.

One can take the OPERA numbers at face value and calculate the imaginary rest mass that a tachyon should have, if its total energy was 28.1 GeV and its velocity was 1.0000248×c.  A tachyon with these characteristics would have an imaginary rest mass of i×198 MeV.  This is not a low- mass particle, and its numerical value is suspiciously close to the mass of the mu lepton (105.7 MeV).  It would be interesting to know if the evidence for neutrino oscillations from SNO and Kamiokande could be reconciled with tachyonic neutrinos with imaginary masses so large. (I doubt it.)

Finally, let me mount my hobby horse and go for a short ride.  My AV column in the October-1993 Analog, at a time when the mass-squared of electron neutrinos was measuring negative, described a space drive using tachyons.  The basic idea is that tachyonic particles can be made to have an infinite exhaust velocity and carry significant momentum but to have zero total energy (i.e., no energy cost).  They represent a "free" fuel that could be created in unlimited quantities and used for space propulsion without violating any physical laws.  If the OPERA results hold up, it may be worth having a closer look at the idea of a tachyonic space drive.  

Folloup note (11/22/2014):  A few months after the initial Opera announcement, they produced a folow up that identified two possible sources of error in the time-of-arrival of the neutrinos.
The conclusion was that the apparent superluminal transit times were the result of hardware malfunction rather than a real physical effect.


John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


"Measurement of the neutrino velocity with the OPERA detector in the CNGS beam", The OPERA Collaboration, preprint arXiv.1109.4897 [hep-ex].

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