The relativistic motion of clocks on board GPS satellites exactly accounts for the superluminal effect, says physicist.  Credit: axirv
The relativistic motion of clocks on board GPS satellites exactly accounts for the superluminal effect, says physicist. Credit: axirv


Special Relativity May Answer Faster-than-Light Neutrino Mystery

15 Oct , 2011 by


Oh, yeah. Moving faster than the speed of light has been the hot topic in the news and OPERA has been the key player. In case you didn’t know, the experiment unleashed some particles at CERN, close to Geneva. It wasn’t the production that caused the buzz, it was the revelation they arrived at the Gran Sasso Laboratory in Italy around 60 nanoseconds sooner than they should have. Sooner than the speed of light allows!

Since the announcement, the physics world has been on fire, producing more than 80 papers – each with their own opinion. While some tried to explain the effect, others discredited it. The overpowering concensus was the OPERA team simply must have forgotten one critical element. On October 14, 2011, Ronald van Elburg at the University of Groningen in the Netherlands put forth his own statement – one that provides a persuasive point that he may have found the error in the calculations.

To get a clearer picture, the distance the neutrinos traveled is straightforward. They began in CERN and were measured via global positioning systems. However, the Gran Sasso Laboratory is located beneath the Earth under a kilometre-high mountain. Regardless, the OPERA team took this into account and provided an accurate distance measurement of 730 km to within tolerances of 20 cm. The neutrino flight time is then measured by using clocks at the opposing ends, with the team knowing exactly when the particles left and when they landed.

But were the clocks perfectly synchronized?

Keeping time is again the domain of the GPS satellites which each broadcasting a highly accurate time signal from orbit some 20,000km overhead. But is it possible the team overlooked the amount of time it took for the satellite signals to return to Earth? In his statement, van Elburg says there is one effect that the OPERA team seems to have overlooked: the relativistic motion of the GPS clocks.

Sure, radio waves travel at the speed of light, so what difference does the satellite position make? The truth is, it doesn’t.. but the time of flight does. Here we have a scenario where one clock is on the ground while the other is orbiting. If they are moving relative to one another, this calculation needs to be included in the findings. The orbiting probes are positioned from West to East in a plane inclined at 55 degrees to the equator… almost directly in line with the neutrino flight path. This means the clock on the GPS is seeing the neutrino source and detector as changing.

“From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter,” says van Elburg.

According to the news source, he means shorter than the distance measured in the reference frame on the ground and the OPERA team overlooks this because it thinks of the clocks as on the ground not in orbit. Van Elburg calculates that it should cause the neutrinos to arrive 32 nanoseconds early. But this must be doubled because the same error occurs at each end of the experiment. So the total correction is 64 nanoseconds, almost exactly what the OPERA team observes.

Is this the final answer for traveling faster than the speed of light? No. It’s just another possible answer to explain a new riddle… and a confirmation of a new revelation.

Original Story Source: Technology Review News Release. For Further Reading: Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?.

, ,

Tammy was a professional astronomy author, President Emeritus of Warren Rupp Observatory and retired Astronomical League Executive Secretary. She’s received a vast number of astronomy achievement and observing awards, including the Great Lakes Astronomy Achievement Award, RG Wright Service Award and the first woman astronomer to achieve Comet Hunter's Gold Status. (Tammy passed away in early 2015... she will be missed)

30 Responses

  1. Al Marani says:

    Einstein is sitting up there somewhere chuckling away to himself at this :) Relativity 1, Modern Particle Physics 0

  2. Erica Morro says:

    “The physics world has been on fire, producing over 80 papers”— they have not repeated the experiment (to find the same result and help nail down the results) or got other labs to support these findings with their own experiments— but we have found that the speed of light is no barrier, at least according to CERN.

    Right now I just pay attention to Fermi/Hubble/Herschel/Chandra/Spitzer (there are more) spacecraft findings on new observations about particles, which are based on science and not hyperbole.

    • Anonymous says:

      Uh, that experiment took 3 years to run. They haven’t had time to duplicate it yet.

      • Erica Morro says:

        That’s right, CERN PR flacks way ahead of the science. Only thing in the universe travelling faster than neutrinos may be silly PR. And of course CERN is not the only organization guilty of this, its just that I thought CERN may have been above these kind of media shenanigans. I guess not.

    • Torbjörn Larsson says:

      Actually OPERA is a repeat on an earlier experiment that predicted the same effect, but not with enough resolution to be able to reach 5 sigma.

      That group is on it now though, and IIRC it would take them a mere 2 years. If OPERA continues to collect data (preferably with some changes to eliminate potential systematic errors), we will have two experiments with at least one independent in a few years.

      Hopefully it is a flaw, because it could take much less time to find out then. =D

      Also, OPERA is independent of CERN so they can’t be connected with this in no way or form (except being the neutrino source). At least the original press cover where very clear on this; maybe Tammy needs to add a disclaimer.

      And FWIW not even all in the OPERA team has signed on the original paper.

      Another point (ouch, am I a sunday grouch today!): In retrospect I don’t think this was hyperbole, except the unwarranted press conference. The rest of the work is cautious on the veracity of all this.

      FWIW I agree that this is very tenuous.

      The reason to go after systematic errors in time or distance measurements is because the discrepancy to relativity predictions were energy independent.

      But there are larger open holes to drive light speed trucks through. Above all they make the same observations on distributions instead of individual particles that drive all those analogous photon waveguide “ftl” claims.

  3. Anonymous says:

    So if I understand this correctly we are speaking of time dilation of the orbiting clock relative for the fixed clock because the orbiting clock moves at 28 km/h or so.

    But I don’t understand how did they set up the experiment. Did they not have 2 ground clocks that both gets synchronized by the same satellite? So they both should have the same time dilation error?

    Could the mass of the mountain not have given a problem in additional time dilation?

    • Roger Overcash says:

      A lot of details about this experiment seems to be cloaked. When someone sent in an idea concerning two clocks, OPERA almost rudely refused the idea saying we only used one clock and apologized for not having published better details. Yet someone else sent in an idea concerning one clock and OPERA said we used two clocks using the same apology…..??? I am like you if you are saying where is all the accurate details! I myself am not amused by the FTL claim ( I’m sure GR and SR will win out when and if resolved).
      I am more amazed by the claimed accuracy. Though many professionals were involved, a Mars Lander crashes while descending because of a technical glitch traced back to engineering. The Hubble Telescope went in orbit needing glasses. I make more than my share of mistakes. At least most of us are only human.

      About the mountain. Yes, the mountain will make a difference as will the detector being under ground. I know you heard it said that a clock on the second floor will tick slower than one on the first floor because relative to a radiant point at the center of the earth, the second floor covers more distance as the earth rotates, and thus travels faster than the one on the first floor. This is SR. Now however, GR also comes into play. The second floor experiences less gravity than the first floor so time goes by faster there than on the first floor. In this case, SR and GR will cancel out each other but not entirely! The difference between the two is the true time dilation. Frame dragging is another effect of GR that will affect satellites though by only a very tiny amount in respect with the mass and rotation of the earth.
      -Different latitudes on earth rotates at different speeds as well as different depths. (SR)
      -Different places even on the surface of the earth experiences different “strengths” of gravity, under ground is no exception. (GR)

      A GPS sending signals to a fixed place on the earth but moving in respect with the rotating earth will change continuously the distance the signals travel and thus the time it takes the signals to reach its destination. Also GR and SR changes this as well. This is, I think, usually corrected by continous algorithms. GPS does not however penetrate under ground. All of what is mentioned here isn’t even the tip of the iceberg. I wonder if OPERA over corrected (double corrected ), under corrected, or did not consider what should be. The time production of neutrinos is to me in question. I am sure there is plenty room for mistakes but I also do not know all the details about this experiment.

  4. responsive7 says:

    How fast is the speed of light in solid rock?

  5. Mike Walker says:

    Bad news for Andy Schlafly (the proprietor of that peddler of ignorance, Conservapedia) who has been waging an almost single-handed battle against the theory of relativity because it has supposedly led to the unleashing of the scourge of relativism upon this land (I kid you not!).

    According to him, the discovery of FTL neutrinos was somehow the death knell for the theory of relativity (but don’t expect him to explain how), so it would be deliciously ironic if the observed discrepancy in the timing can be explained entirely by the effects of special relativity.

    • squidgeny says:

      The same guy believes one of Jesus’s miracles happened faster than the speed of light according to the bible, therefore relativity must be wrong. The mind boggles.

  6. Anonymous says:

    I like this explanation much better than the “time travel” one. Everyone knows that the Vulcan Science Directorate clearly states time travel is impossible . . .

  7. Anonymous says:

    I’m skeptical that this paper offers a simple refutation of the apparently superluminal observations by CERN/OPERA. The relativistic factors associated with the GPS system have been well-known and understood since the system was designed. In fact, the system would not work if Special Relativity hadn’t been taken into account when the system was designed. That’s right–relativistic effects would produce gross navigational errors if the GPS system didn’t compensate for them. Though I agree that the OPERA paper did not explain the timing system very well, I’ll reserve judgment until I see what they have to say.

    • Baksa Péter says:

      The team is European and GPS is USA, maybe some of the algorithm is top secret :)

    • email 000019 says:

      i agree with you; the people in charge of this experiment must of already though of this and a thousand other things. i do not think they would willingly put themselves under the gun and embarrass themselves by overlooking something that another physicist comes up with within a couple days of announcing their discovery.

      it’s kind of insulting that this scientist would be so trivial as to suggest they had not taken into account the relativistic clocks.

  8. Antonio e Ana says:

    No matter, measurement of light speed will have the same error.

    • Ummon Karpe says:

      If you’re implying they sent light beams through the earth, then you’re wrong. They didn’t do that. No doubt, if light was able to travel underground and wasn’t slowed down by the material in the ground, it would reach at the same time as the neutrinos.

  9. Torbjörn Larsson says:

    Too many of these ideas out there now. (I put one out too. But at least I was early! [/ducks]

    But yeah, turn every stone and/or repeat the experiment.

  10. zetetic elench says:

    Are not GPS satellites geosynchronous? Tip of the iceberg indeed. (nose of the herring?)
    Interesting point made about how the deeper in the gravity ‘well’ the slower the time passes.
    Or is it the slower the clocks run?
    Clocks in Space sure get the chatter going. (Does it matter that they are all also going in circles?)

    • Roger Overcash says:

      I would think true geosynchronous orbits do not exist. Though stationary to a point on the earth, it (GPS) also rotates with the earth passing alignment with the sun and moon. These tidal forces would certainly change the height of the orbit on a regular basis thus changing earth/satellite (GPS) distance.

      In a gravity “well”, time would pass slower, clocks will tick slower and electrons will “orbit” the nucleus slower by the same rate but only relative to an inertia frame not as deep into the well.

      You brought up some good points.
      I added two quotes here that you might enjoy;

      Not all that can be counted counts and not all that counts can be counted. Albert Einstein

      Insanity: doing the same thing over and over again and expecting different results. Albert Einstein

      • Mike B. says:

        Hahahaha you can act like you understand cosmology and the speed of light but you acting as if you know god and all life’s answers is a contradictory idea to your very history and existance mr overcash christian “theoretical cosmologist”.

    • Torbjörn Larsson says:

      GPS satellites are medium orbit satellites.

      You are thinking of television satellites, some of those can be geostationary.

      • Roger Overcash says:

        I got off on left field on geosynchronous orbits. I though It was an interesting point to ponder, it was fun. However, you answered the question that was presented. I stand humbled.

  11. Anonymous says:

    From my viewpoint, … irrelevant.
    ” Light ” is movement of particulate matter of specific structure, … not all particulate matter travels at the speed-of-light, … nor in Quantum Physics find any absolutes that light particles travel faster than all the others we are just beginning to isolate and classify.
    Apples and oranges, …
    Just my opinion, … Lol, … ” I ” am welcome to keep it, … thankee’, … ” I ” will

  12. Anonymous says:

    A physicist I just wrote a paper with gave a “wait a minute” message on this. The Elberg paper is special relativistic, but the problem is more generally in curved spacetime. The delay is not just caused by the velocity of satellites, but the curvature of spacetime as well. The metric on the equatorial plane of an orbit is

    ds^2 = Adt^2 – A^{-1}dr^2 – r^2d?^2

    for A = 1 – 2GM/rc^2, r = radius of orbit. The dr = 0 for circular orbit and the d? gives a velocity

    V_? = sqrt{-g_{??}/g_{tt}}d?/dt = r/sqrt{1 – 2GM/rc^2}d?/dt ~= r(1 + GM/rc^2)d?/dt.

    The angular motion in general relativity obeys Kepler’s law so that for d?/dt = ?, ?^2r^3 = GM, or (r?)^2 = GM/r and so V_? ~= sqrt{GM/r} + O(1/c^2). The motion of a particle in an orbit of constant radius is then

    ds^2 = (1 – 2GM/rc^2)c^2dt^2 – (V_?/c)^2dt^2 = (1 – 2GM/rc^2 – (V_?/c)^2)c^2dt^2

    = (1 – 3GM/rc^2)dt^2


    ? = 1/sqrt(1 – 2GM/rc^2 – (V_?/c)^2) = 1/sqrt{1 – 3GM/rc^2}

    is the general “gamma factor.” The ground based observer has a essentially zero velocity and the relevant metric coefficient is g_{00} = 1 – 2GM/Rc^2 for R = radius of Earth. This has a gamma factor ?‘ = 1/sqrt(1 – 2GM/Rc^2).

    For a signal send from Earth to the satellite there is a Doppler factor

    ? = ds/ds’ = ?/?‘ = sqrt{(1 – 2GM/Rc^2)/(1 – 3GM/rc^2)} ~= 1 – (GM/c^2)(1/R – 3/2r)

    which gives the relative slowing of a clock on Earth as seen by an observer on the spacecraft..

    The relative magnitudes may now be considered. The contribution from the gravitational portion of the space craft motion is from a 1/r, for r = 18500 km half geosynch orbit. R = radius of Earth which is 6400 km. So the gravitational part of the shift is (1/R – 1/r) ~ 1×10^{-4}km^{-1}, where as the part due to motion is 5×10^{-5}km^{-1}. So the gravitational part contributes about twice the amount.

    So if the data error resulted from a failure to account for both of these then there might be an even large effect expects — I might think. So the question may be a bit persistent. It is important to do this anaylysis, for it is likely that some glitch exists in the computations.

    Cheers LC

    • Anonymous says:

      “The ground based observer has a essentially zero velocity”

      Are you sure? The one thing that leaps out at me is that nobody is thinking of the Sagnac Effect. Both CERN and Gran Sasso are moving in circles around the Earth’s axis but at different speeds due to their different latitudes (and altitudes). The neutrinos must take an almost straight path between the emission and detection points so even if the times are translated to UTC, surely the locations still need to be translated into an earth-centred non-rotating frame so that the motion of the sites during the flight can be taken into consideration. Elburg talks of a “baseline reference frame” but is that the CERN or Gran Sasso frame? They are not the same, and neither is inertial.

      • Anonymous says:

        I invoked the argument that the ground had zero velocity for the sake of the argument I was making. It is actually a very small effect, far smaller than the contribution from the orbital velocities of satellites and teh differences in gravitational potential. In a real algorithm which runs GPS the rotation of the Earth is of course factored in.


  13. Anonymous says:

    The bartender says, “Sorry, we don’t serve particles that travel faster than the speed of light.”

    A neutrino walks into a bar and orders a drink.

  14. Alessio De Benedetto says:

    I don’t know exactly how they calculated time, but…
    If at the CERN the clock is 32 nanoseconds earlier than that of the satellite, and the Gran Sasso clock is 32 nanoseconds earlier that that of the satellite…
    They show the same identical time! So this won’t affect any calculation at all!

Comments are closed.