Pique the Geek 20110925: Faster than Light

(9 pm. – promoted by ek hornbeck)

The recent results from CERN (the acronym for the original name for the outfit, Conseil Européen pour la Recherche Nucléaire) about neutrinos being propagated faster than light speed has caught a lot of attention.  I am still not convinced that the data are correct, but 15,000 individual measurements at the high certainty that is claimed certainly gets one’s attention.

I am not prepared to say whether or not these results are valid as of yet.  The folks at CERN are begging other laboratories with comparable apparatus and expertise to verify (or to refute) the findings.  That is how science is supposed to work!

However, 15,000 individual determinations are a LOT of data!  Let us for the moment take the data at face value and assume that this is not a fluke nor a mistake, but an actual “violation” of the Special Theory of Relativity that indicates that no massive particle can exceed the speed of light, henceforth called c.  Ready to do some thought experiments?  I am!  Let us go!

Before we get started with the really Geeky stuff tonight, how about a little diversion first?  The Moody Blues are one of my favorite bands, and on their seminal album In Search of the Lost Chord, they make quite a few references to photons and the speed of light.  This first selection is one of Grahame Edge’s poems, “The Word”.  Only the first 50 seconds are pertinant to this discussion, but the rest of the cut is Mike Pindar’s “Om” which is pretty fine, too.

The second is another of Pindar’s compositions, “The Best Way to Travel”.  Listen in at 18 seconds and there is a reference to faster than light velocities.  If there is enough interest, perhaps I should do a series on this band after I finish with The Who on my Popular Culture series.

First, a bit of background is in order.  In 1905 a rather obscure German physicist working his day job at the Swiss patent office published a paper that promulgated the Special Theory of Relativity.  One central point of the paper drove the concept that NOTHING could exceed the velocity of photons in a vacuum.  The author’s name was Albert Einstein, and his “cosmic speed limit” has come to be known as the speed of light, also know by the term c.  The best (or at least the accepted value) for c is woven into the SI system of measurements, and is defined as 299,792,458 meters per second, for photons in a perfect vacuum.  Note that this is accepted by the SI community as good to nine significant figures, but that this is not necessarily to BEST experimentally determined value.

Let us go back to 1905 for a few minutes.  The Wright Brothers had flown the first real aeroplane only two years before, and my grandmother was also born two years before.  Henry Ford was still trying to learn how to build cars, and there was NO fundamental understanding about protons, neutrons, and electrons at the time.  In a sense, it was the Dark Ages.  Around that time (actually published in 1906), the best value for the speed of light was 299,781,000 m/s, lower by 38000 parts per billion than the now accepted figure.  This might not sound very significant, but the point is that the speed of light was not known to a high degree of certainty in 1905.

It really does not matter what the actual value is insofar as Special Relativity is concerned, but it DOES matter what the actual value is when comparing the speed of light to the speed of photons to the speed of neutrinos.  It is also important to make the distinction that in the CERN experiments the neutrinos were passed through air, water, and earth between the source and the point of detection, and since photons strongly interact with matter, it is not possible for the speed of photons to be measured over that particular route.  Since neutrinos only weakly and rarely interact with matter, solid rock is not a problem for them.

This sort of begs the question as to how precisely the distance between the source and the detector is known.  Since it is not possible to verify the distance independently with photons, a very common way to measure distance, this becomes an important question.  The distance that the neutrinos travel is 730 km, to the best estimate, and at distance it should take photons, using the modern value for c, 2.43503786 x 10^-3 seconds for light to travel this distance.  This works out to 2435037.86 nanoseconds.  The neutrinos arrived in 2434977.86 nanoseconds.  Those of you with a scientific way of looking at things will immediately see that the distance between source and detector is good only to two significant figures, but the difference in times of arrival appear only beginning with the forth significant figure.  Therefore, the actual distance between the source and the detector needs to be known at least to five or six significant figures to have any validity.

I am sure that the scientists at CERN have taken this into account, but since it is not possible to do a side by side comparison using photons and neutrinos over the same route makes for a problem.  A logical question would be, “Why not conduct these experiments in the atmosphere where such a comparison could be made?”  Unfortunately, this is not possible because it is not possible to distinguish neutrino interactions with matter from interactions by cosmic rays.  This is why all neutrino detectors are deep underground, so that the earth can block the cosmic ray interference.  It bothers me that such direct comparisons can not be made, and I am dubious how one measures 730 km through mostly solid rock to six significant figures.

Note:  after writing the previous two paragraphs I rooted around on CERN’s website and found the statement that the uncertainty in the 730 km is 20 cm.  Expressed another way, the 730 km equates to 73,000,000 cm, so the distance is good to six or seven significant figures.  So that potential defect in the methodology is out the window.  In addition, the press release indicates that the time measurements are good to 10 nanoseconds, and the 60 ns time difference is thus well outside of experimental error.  A bit more rooting around on the OPERA site indicates that the actual distance, to three significant figures, is 732 km.

Let us for a moment do and Einstein-like thought experiment.  Let us say that the 730 km between source and detector were composed of perfectly transparent glass.  Then such a comparison could be made, but even that is not without complication.  A typical crown glass has an index of refraction of 1.52, meaning that light travels that factor more slowly in the glass than in a vacuum.  With that in mind, it would take light 3701257.55 nanoseconds to make the trip.  Now the neutrinos are traveling over 50% faster than the photons!  This is not really a fair comparison, though, because photons move more slowly in most media than in a vacuum because of the electromagnetic force, causing the photons to interact with the medium and thereby slowing them down.  Neutrinos are not affected by this force, but only by the weak nuclear force and gravity.  As a matter of fact, neutrinos were first postulated as a carrier of the weak nuclear force to explain beta decay in radioactive materials because of the necessity to keep conservation of momentum, conservation of angular momentum, and conservation of energy in the equations governing this decay.

Now that we have looked at some of the potential flaws in the methodology, let us next think about the ramifications and possible explanations if what has been reported actually holds up after other investigators reproduce the findings, if they do.  Does that mean that everything we know is wrong as far as the Standard Model of particle physics goes?  Maybe, maybe not.  Remember, the Standard Model is based in large part on Special Relativity, the central tenant of which is that all massless particles (specifically the gauge bosons, mediators of the four “fundamental” forces) must travel at the speed of light, represented as c, in a vacuum.  Never any faster, and never any slower.  These include the photon, carrier of the electromagnetic force, the gluon, carrier of the strong nuclear force, the Z and W particles, carriers of the weak force, and the graviton, carrier of the gravitational force.  In addition, the Standard Model assumes that neutrinos are massless and thus must also travel at c.  A corollary is that any particle with mass MUST travel more slowly than light.

Note:  Albanius has corrected me about the W and Z bosons.  They are among the most massive particles known.  I appreciate the correction.

However, it is now pretty much established that neutrinos actually have mass, although not much.  There are three “flavors” of neutrinos, the electron neutrino, the muon neutrino, and the tau neutrino (and their antiparticles, unless they are their own antiparticles, a question that is still open to debate).  Theory suggests that if neutrinos were actually without mass, they would stay their original flavor forever until they finally interact with matter.  However, it is known that neutrinos can change flavor as they travel, so it seems that neutrinos MUST have mass.  This makes things even more strange, because one would expect any particle with mass tends toward infinite mass as its velocity approaches c.  The OPERA experiment, where these faster than light velocities were discovered, was originally designed to measure the oscillations between muon and tau neutrinos, so this discovery was really quite an accident.  That is often the case in science.

Now, if might be that there is a mechanism for massless particles to oscillate flavors that has not yet been discovered.  For the moment, let us assume that neutrinos are actually massless.  If that be the case, then Einstein may just have chosen the wrong particle to set the “cosmic speed limit”!  When Special Relativity was proposed in 1905, photons were the fastest thing known, but their velocity was not known with a high degree of accuracy, as mentioned earlier.  Neutrinos were not even postulated until 1930 when Wolfgang Pauli used the concept to account for some properties in beta decay that I mentioned above, and not positively identified until 1956 by Cowan and Reines.  Thus, Einstein had no way of knowing that there might be a faster particle than a photon.  But why might neutrinos be faster than photons?  I have a postulate.

Remember, photons are the gauge boson of the electromagnetic interaction, and thus respond to all electromagnetic fields, including those made by other photons.  Since this force obeys a inverse r-squared relation, photons do not have to touch to influence each other.  Now, the entire known universe is immersed in the microwave background radiation, perhaps this universal field puts just a bit of a “drag” on the ultimate speed of photons.  Neutrinos, not subject to this interaction, would not experience any drag and so would be able to attain the full value of c, just a bit faster than photons.  If this be the case, there is not a fundamental flaw in the Standard Model, but rather just some minor modifications are required.  The weak interaction is an extremely short range one, and at about 10^-18 meters is comparable in strength to the electromagnetic one, but at even 3 x 10^-17 meters is only about 1/10000 as strong as the electromagnetic interaction.

If neutrinos actually do have mass, and it looks like they do, then that causes much more difficulty for the Standard Model.  According to Special Relativity, the relativistic mass of any particle with any mass at all follows the following equation:

m_rel = m₀/(1-v²/c²)^1/2

where m₀ is the rest mass of the particle, v is the velocity of the particle, and c is the velocity of light in a vacuum.  Note that as v approaches c, the denominator of the fraction approaches zero, and thus the relativistic mass of the particle approaches infinity.

This is a real problem.  Accordingly, if neutrinos actually have mass, they should not even be able to attain c, let alone surpass it!  Either my first hypothesis is correct, or something like correct, or there has to be some “exception” to Special Relativity for neutrinos.  No one likes exceptions to principles that have been verified for over 100 years, so there is something fundamentally wrong with the Standard Model if neutrinos DO have mass AND meet or exceed the speed of light.

But it gets even worse!  On the assumption that the speed of photons in a vacuum is really c, AND if neutrinos exceed this value, then the denominator takes on an imaginary value.  Mathematically, the square root term involves the square root of -1 (aka i), and things get very weird indeed.  It is not difficult to do the maths, but trying to tie an imaginary mathematical value of a mass to physical reality is difficult.  Now, imaginary numbers are used all of the time in physics, so it is not impossible.  Electrical behavior often is often expressed using imaginary numbers, so on its face there is not a problem.  However, what is an imaginary (or to be more precise, a complex) mass?

Until Thursday last, faster than light velocities were a theoretical curiosity and the stuff of science fiction.  Now the entire tenor of the discussion has changed.  Until this issue is resolved, most particle physicists are having either their worst nightmare or their best wet dream!  Speaking of particle physicists, any reading please chime in in the comments (you need not specify what kind of dream that you are having).  Obviously, I am not a particle physicist, but I certainly am a scientist and realize the ramifications of these observations if shown to be correct.  This would be the first confirmation, possibly, of tachyons, particles that can not travel at light speed or slower.  This idea is not original with me:  Chodos, Hauser, and Kostelecký first floated that idea in 1985 in Physics Letters B, here.

These are exciting times.  Never has anything been found incorrect with Special Relativity, but there are often first times for things.  Newton’s laws of motion were sacrosanct from 1687 when Principia Mathematica was published to 1905 when Special Relativity was, to we are due for some refinements.  I rather like the idea that we do not know everything, yet!

To finish, my gut feeling is still that there is something wrong with the data from CERN.  As I said before, the folks there are still shaking their heads, wondering what they might have done wrong to get these results.  That is why they are asking for other groups to try to affirm or refute their results.  Personally, I would be more comfortable if the differences in velocities were larger that their data are clean, but you go with what you observe.  The next few weeks will be pretty interesting.

Well, you have done it again!  You have wasted many more einsteins of photons reading this fast piece!  And even though Mike Huckabee realizes that it makes him look petty and hateful to open his shows with cheap and childish shots by a hack actor at the President when he reads me say it, I always learn much more than I could ever hope to teach by writing this series.  Please keep comments, questions, corrections, and other feedback coming!  I shall stay here as long as comments warrant, and shall return tomorrow after Keith’s show for Review Time.  By the way, if Keith had had me on as the science guy rather than the one that he had Friday, “neutrinos” would not have been called “neutrons”.  Call me, Keith!

Just as a final note.  I have been signing off using the phrase

You have wasted many more einsteins of photons reading this …

To this day, no one has ever asked what “an einstein of photons” actually is.  Is anyone curious?  Just drop a comment!

Warmest regards,

Doc, aka Dr. David W. Smith

Crossposted at The Stars Hollow Gazette,

Daily Kos, and

firefly-dreaming