Almost all theoretical oriented physicists including myself seem to feel almost certain that there is a mistake in the Opera paper (previously discussed by TRF; see also a video of the lecture) and the claimed violation of the relativistic speed limit will go away. See also why Nir Shaviv, Andy Cohen, and Shelly Glashow don't believe the superluminal claim.
If there's no mistake, and it is a big If, see Superluminal neutrinos from noncommutative geometry.
On the other hand, I think that many people who like technology etc. were impressed by the precision work that the Opera folks have demonstrated. It's a complex piece of work in which particle physicists became top metrologists – their work was endorsed by two teams of professional metrologists, too. In some sense, their measurement is also a pioneering work: as far as I know, the propagation of speed-of-light-in-the-vacuum signals between very distant places on Earth has never been tested against GPS metrology before so it shouldn't be shocking that one gets a 18-meter discrepancy when he tries it for the first time.
There's a lot of potential for errors. The measurement may be schematically represented as three steps: "measuring the distance", "bringing the proper universal time to CERN clocks", and "bringing the proper universal time to Gran Sasso clocks". So the mistakes may be divided into three basic groups:
So let me offer a more specific "functionalist" incomplete list of possible mistakes:
I have completely omitted the technicalities of their timing systems (their local, "lab" properties) because even if they're wrong about them, they're vastly more professional in dealing with them than all of us and we're unlikely to find a mistake here.
When we eliminate too big and too small potential errors, there are still many effects that are comparable to 18 meters. For example, if you happened to neglect that the GPS signals have a different speed and/or direction through the ionosphere because the ionosphere isn't the vacuum when it comes to the propagation of these signals, you will get a mistake as big as 10-100 meters. It's important to realize the positions of many things on Earth have been measured using GPS so if GPS consistently produces the same "precise" result which is however "inaccurate", all the GPS users may have adapted to the GPS mistake and no one has noticed.
Opera is hot in Czechia and Slovakia, too. Miss Patricia Janečková, then a 12-year-old German-born, ethnic Slovak opera singer living in Czechia, won the first Czech and Slovak Talentmania a few months ago. This opera-style version of "Con te partiro" (Time To Say Good Bye) was presented before it was known she would win. Thanks to Ann for the pick.
In plain English, "accuracy" and "precision" means the same thing. However, in scientific English, these two terms are deliberately distinguished. (In scientific Czech, we still don't have these two different words: a funny omission of our national revival guys 200 years ago.) "Accuracy" is given by the overall error, the difference between the right and measured value. "Precision" is the spread of the measured values, quantifying the repeatability of the measurements. You may be still getting the same result so it looks precise but all these results may still be away from the right answer, in the same direction. So "precision" refers to the "statistical error" while "accuracy" refers to the overall error including the systematic errors.
So just to be sure, the fact that GPS is serving very well and gives many subjects the information about location and time that is accurate up to decimeters or nanoseconds doesn't mean that this information is accurate. There may be a big error and all the users have adapted to these possible systematic errors produced by the GPS system. They may have sketched tables with distorted coordinates of their assets, deformed maps, and so on. The GPS system may have created its own "virtual reality" where the distances may be wrong but no one cares: everyone has adapted.
Relativistic effects
Metrologists are very likely to make mistakes in relativity whenever relativistic effects are needed. Is it plausible that the metrologists – and also the Opera folks who are particle physicists reeducated as metrologists – have neglected an important relativistic effect that you have to appreciate in order to measure the speed of the neutrinos?
Recall that the neutrinos need about 2.4 milliseconds for those 730 kilometers. What happens during 2.4 milliseconds? Well, for example, the GPS satellites are orbiting the Earth by speed equal to 3,900 m/s. So in 2.4 milliseconds, i.e. during the time when the neutrino gets from CERN to Gran Sasso, the satellites move by 10 meters or so (30 nanoseconds times \(c\)).
If you made an error in the distance measurement that is equal to the motion of the satellite during the neutrinos' trip, you would immediately erase more than a half of the Opera signal, most of 18 meters: that would reduce 6 sigma to 2-3 sigma. You could also make the error twice which could explain the whole signal. How could you make such an error?
Well, it's easy. You could assume that for every individual measured neutrino, the GPS satellites have a particular fixed position. However, the distance between the two places is measured without any neutrinos; it doesn't depend on the neutrinos' trip. So it's a little bit hard to imagine how this error could be incorporated to the measurement of the distance; or to the synchronization of the clocks at the two places.
Let me offer you something fancier: relativity. Imagine that you watch the things from the viewpoint of a satellite. You're a GPS satellite and you see the Earth's surface moving by speed 3,900 m/s. You also see a neutrino that is moving from Switzerland to Italy. What is the speed by which the neutrino is moving relatively to you?
Well, normal basic school pupils would say it's moving by the speed c + 3,900 m/s. However, that's wrong according to relativity. The speed is still just c. Obviously, if you accumulate this error in the velocity over 2.4 milliseconds, you get the same error of 10 meters I mentioned previously. It's huge, isn't it? Does it mean that you really can't afford to use Newtonian intuition from the satellites' viewpoint?
Well, you actually can make a "nearly self-consistent" Newtonian picture from the GPS satellites' reference frame but you must define the simultaneity of events according to the Earth's frame, not according to the reference frame of the moving satellites. What is the problem with the simultaneity of events?
Well, imagine that something clicks in Gran Sasso at the same moment when the neutrino is created at CERN. "At the same moment" is evaluated from a quasi-inertial frame of the Earth. Do these events occur at the same time from the satellite viewpoint? The satellite is moving by the speed 3,900 m/s which is \(1.3 \times 10^{-5} c\). The Lorentz transformation gives us the answer:
\[ t' = \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}} \] The denominator is 1 within the accuracy we can measure because it only contains corrections that are quadratic in \((v/c)\). However, the numerator contains a term that is linear in \(v/c\). Indeed, for the separation \(x=\)730 kilometers, the second term in the numerator is 30 nanoseconds i.e. 10 meters over c. It's the same mistake as before. More than one-half of their famous effect.
You could get a kind of a valid set of numbers if you used Newtonian mechanics and used the Earth's frame only. The worst thing you can do is to use relativistic effects but only somewhere. For example, if you correctly acknowledge that the relative satellite-neutrino speed is still just \(c\), you must also acknowledge that the neutrino birth at CERN and the click in Italy don't occur at the same moment. If you only incorporate one of these two effects, an error of 10 meters (30 nanoseconds times \(c\)) is born: it's the distance by which the satellite moves during the time when the neutrinos fly from CERN to Gran Sasso. This is simple high-school relativity but it's surely unusual in metrology. Think about the probability that a gang of experimenters makes a mistake in such a thing. It may be much lower than 100% but there are many possible errors of this kind and the overall probability of a mistake is rather high.
General relativity, curved spacetime
General relativity is needed inside the GPS satellites, otherwise their announced positions would drift by kilometers a day. It's a huge effect but most of it is obviously taken care of. In particular, the atomic clocks carried by the satellites correctly appreciate that time is ticking faster if you're further away from the Earth; and the speed of ticking depends on the velocity, too.
The warping of time – the fact that time is ticking slower in the depths of a gravitational field where the gravitational potential is large negative – is arguably the most important effect of a curved spacetime. It may be correctly appreciated but it's not the only one and even some subleading effects may possibly be important, although most of them are not.
For example, the Earth is spinning around its axis so it's not an inertial frame. When you sloppily assume that the rotating Earth's frame is inertial, could it induce an error? If you make a simple calculation, you will see that the error isn't enough. The worst thing that could happen would be to make a mistake in the speed of light that is incorrectly modified by the speed of motion of the Earth's surface. But the latter is just 460 m/s or so at the equator and only 300-400 m/s or so in the moderate zone so this is a 10 times smaller speed than the speed of the GPS satellites and correspondingly induces 10 times smaller linear effects only: the spinning of the Earth could at most give you a one-meter error and most likely, you will avoid these linear errors and relativity will only produce higher-order effects (higher powers in the speed of the surface divided by the speed of light) which are utterly negligible.
Also, you could suggest that the experimenters incorrectly assumed that the neutrinos are moving along a "straight path" between Switzerland and Italy. However, you could correctly say, the neutrino is actually moving along a null geodesic in spacetime which means that it's bent much like starlight measured by Eddington in 1919. Using a Newtonian approximation which is wrong by a factor of 2, the neutrinos are actually moving along a "free fall" parabola on the surface. Could this explain this error?
Well, it couldn't. The bending of the neutrino's path because of the Earth's gravitational field is totally negligible. During 2.4 microseconds, the Earth only makes the neutrino fall by \(gt^2/2\) which is about 26 microns. Moreover, the distance that the neutrino travels wouldn't even be by 26 microns different: you would have to square 13 microns or so, compute the Pythagorean hypotenuse with the other side being 730 km, and this result would only get longer by some truly pathetic tiny distance.
Analogously, Dave Miller asked about the Coriolis force in the fast comments. The magnitude of the Coriolis acceleration is \(2v\Omega\) where \(\Omega=2\pi/86400 {\rm s}^{-1}\) and \(v=c\). You numerically get a large acceleration \(a=44000 {\rm m/s}^2\) but \(at^2/2\) for \(t\) being two milliseconds is still just a decimeter or so: the real modification of the curved path is much shorter than that once again.
So this can't be an issue. A related question is whether the non-Euclidean, curved character of the spatial geometry in the Earth's gravitational field may matter. Recall that the spatial terms of the Schwarzschild metric are
\[ ds^2 = R^2 (d\theta^2+\sin^2\theta d\phi^2) + \left( 1 - \frac{2GM}{Rc^2} \right) dR^2 \] So the angular distances are measured by the angles multiplied by the coordinate that is called intuitively just \(R\). However, the radial distances have an extra factor. How big the factor is for the Earth? Well, the whole factor in front of \(dR^2\) differs from 1 just by \(10^{-9}\) or so, and it can therefore be neglected. Recall that we need relative errors in the measured speed of light (i.e. in the measured time and/or distance) that are as big as \(10^{-5}\). Moreover, it's likely that this factor wouldn't influence the measured velocity "directly": only some powers or differences of the warp factor (well, it's actually not called warp factor but I will get some extra tweets because of this buzzword) would affect the measured velocity so their effect would be even smaller than one part per billion.
One may also discuss frame dragging and other fancy general relativistic effects. I haven't done a specific rough calculation of this thing; my guess is that once the satellites-induced locations are adjusted not to "drift", there is no significant effect of the frame dragging that could influence the measurement of the distances between the two labs. But maybe I am wrong. Maybe the frame-dragging has been partially taken care of by the GPS system so that things don't drift; but they still produce wrong distances between CERN and Gran Sasso by 18 meters.
Summary
I want to summarize the situation by saying that lots of very delicate issues had to be thought about when the paper was being written and most of them were surely done carefully. There's still a nonzero potential for mistakes and omitted subtleties; but it's also true that most of the potential errors that some of us suggest can be quickly "shot down" because the Opera team (or more general users of the GPS system etc.) couldn't have possibly done these errors (e.g. because these errors would produce much higher deviations).
Old-fashioned physics as well as technology has to be rechecked, much like some special relativity. And of course, one must appreciate that there could have been a simple miscommunication in between some of the Italians and others:
If there's no mistake, and it is a big If, see Superluminal neutrinos from noncommutative geometry.
On the other hand, I think that many people who like technology etc. were impressed by the precision work that the Opera folks have demonstrated. It's a complex piece of work in which particle physicists became top metrologists – their work was endorsed by two teams of professional metrologists, too. In some sense, their measurement is also a pioneering work: as far as I know, the propagation of speed-of-light-in-the-vacuum signals between very distant places on Earth has never been tested against GPS metrology before so it shouldn't be shocking that one gets a 18-meter discrepancy when he tries it for the first time.
There's a lot of potential for errors. The measurement may be schematically represented as three steps: "measuring the distance", "bringing the proper universal time to CERN clocks", and "bringing the proper universal time to Gran Sasso clocks". So the mistakes may be divided into three basic groups:
- timing errors at CERN
- timing errors in Italy
- errors in the distance measurement
So let me offer a more specific "functionalist" incomplete list of possible mistakes:
- inconsistencies in the whole GPS methodology of measuring space and time coordinates
- inconsistencies of units (meters, second) used at various places: the errors would have to be huge, indeed, so this is unlikely
- subtle old-fashioned physics issues neglected by GPS measurements: the index of refraction of the troposphere and (even more importantly) ionosphere that slows down and distorts the path of GPS signals; confusing spherical Earth and geoid; neglecting gravitational effects of the Alps; neglecting magnetic fields at CERN that distort things; and so on
- forgetting that 2 milliseconds isn't zero and things change (e.g. satellites move) during this short period, too
- subtle special relativistic effects neglected in the GPS calculations
- subtle general relativistic effects neglected in the GPS calculations
- wrong model of where and when the neutrinos are actually created on the Swiss side
- more radical: wrong model of the wave equation for the neutrinos (regardless of oscillations etc., neutrinos should never move information faster than light in the vacuum, but maybe we're doing some mistake about the group vs phase velocity and entanglement of the two places: recall that the difference between the phase and group velocity for these neutrinos should be negligible, around \(10^{-19}\))
I have completely omitted the technicalities of their timing systems (their local, "lab" properties) because even if they're wrong about them, they're vastly more professional in dealing with them than all of us and we're unlikely to find a mistake here.
When we eliminate too big and too small potential errors, there are still many effects that are comparable to 18 meters. For example, if you happened to neglect that the GPS signals have a different speed and/or direction through the ionosphere because the ionosphere isn't the vacuum when it comes to the propagation of these signals, you will get a mistake as big as 10-100 meters. It's important to realize the positions of many things on Earth have been measured using GPS so if GPS consistently produces the same "precise" result which is however "inaccurate", all the GPS users may have adapted to the GPS mistake and no one has noticed.
Opera is hot in Czechia and Slovakia, too. Miss Patricia Janečková, then a 12-year-old German-born, ethnic Slovak opera singer living in Czechia, won the first Czech and Slovak Talentmania a few months ago. This opera-style version of "Con te partiro" (Time To Say Good Bye) was presented before it was known she would win. Thanks to Ann for the pick.
In plain English, "accuracy" and "precision" means the same thing. However, in scientific English, these two terms are deliberately distinguished. (In scientific Czech, we still don't have these two different words: a funny omission of our national revival guys 200 years ago.) "Accuracy" is given by the overall error, the difference between the right and measured value. "Precision" is the spread of the measured values, quantifying the repeatability of the measurements. You may be still getting the same result so it looks precise but all these results may still be away from the right answer, in the same direction. So "precision" refers to the "statistical error" while "accuracy" refers to the overall error including the systematic errors.
So just to be sure, the fact that GPS is serving very well and gives many subjects the information about location and time that is accurate up to decimeters or nanoseconds doesn't mean that this information is accurate. There may be a big error and all the users have adapted to these possible systematic errors produced by the GPS system. They may have sketched tables with distorted coordinates of their assets, deformed maps, and so on. The GPS system may have created its own "virtual reality" where the distances may be wrong but no one cares: everyone has adapted.
Relativistic effects
Metrologists are very likely to make mistakes in relativity whenever relativistic effects are needed. Is it plausible that the metrologists – and also the Opera folks who are particle physicists reeducated as metrologists – have neglected an important relativistic effect that you have to appreciate in order to measure the speed of the neutrinos?
Recall that the neutrinos need about 2.4 milliseconds for those 730 kilometers. What happens during 2.4 milliseconds? Well, for example, the GPS satellites are orbiting the Earth by speed equal to 3,900 m/s. So in 2.4 milliseconds, i.e. during the time when the neutrino gets from CERN to Gran Sasso, the satellites move by 10 meters or so (30 nanoseconds times \(c\)).
If you made an error in the distance measurement that is equal to the motion of the satellite during the neutrinos' trip, you would immediately erase more than a half of the Opera signal, most of 18 meters: that would reduce 6 sigma to 2-3 sigma. You could also make the error twice which could explain the whole signal. How could you make such an error?
Well, it's easy. You could assume that for every individual measured neutrino, the GPS satellites have a particular fixed position. However, the distance between the two places is measured without any neutrinos; it doesn't depend on the neutrinos' trip. So it's a little bit hard to imagine how this error could be incorporated to the measurement of the distance; or to the synchronization of the clocks at the two places.
Let me offer you something fancier: relativity. Imagine that you watch the things from the viewpoint of a satellite. You're a GPS satellite and you see the Earth's surface moving by speed 3,900 m/s. You also see a neutrino that is moving from Switzerland to Italy. What is the speed by which the neutrino is moving relatively to you?
Well, normal basic school pupils would say it's moving by the speed c + 3,900 m/s. However, that's wrong according to relativity. The speed is still just c. Obviously, if you accumulate this error in the velocity over 2.4 milliseconds, you get the same error of 10 meters I mentioned previously. It's huge, isn't it? Does it mean that you really can't afford to use Newtonian intuition from the satellites' viewpoint?
Well, you actually can make a "nearly self-consistent" Newtonian picture from the GPS satellites' reference frame but you must define the simultaneity of events according to the Earth's frame, not according to the reference frame of the moving satellites. What is the problem with the simultaneity of events?
Well, imagine that something clicks in Gran Sasso at the same moment when the neutrino is created at CERN. "At the same moment" is evaluated from a quasi-inertial frame of the Earth. Do these events occur at the same time from the satellite viewpoint? The satellite is moving by the speed 3,900 m/s which is \(1.3 \times 10^{-5} c\). The Lorentz transformation gives us the answer:
\[ t' = \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}} \] The denominator is 1 within the accuracy we can measure because it only contains corrections that are quadratic in \((v/c)\). However, the numerator contains a term that is linear in \(v/c\). Indeed, for the separation \(x=\)730 kilometers, the second term in the numerator is 30 nanoseconds i.e. 10 meters over c. It's the same mistake as before. More than one-half of their famous effect.
You could get a kind of a valid set of numbers if you used Newtonian mechanics and used the Earth's frame only. The worst thing you can do is to use relativistic effects but only somewhere. For example, if you correctly acknowledge that the relative satellite-neutrino speed is still just \(c\), you must also acknowledge that the neutrino birth at CERN and the click in Italy don't occur at the same moment. If you only incorporate one of these two effects, an error of 10 meters (30 nanoseconds times \(c\)) is born: it's the distance by which the satellite moves during the time when the neutrinos fly from CERN to Gran Sasso. This is simple high-school relativity but it's surely unusual in metrology. Think about the probability that a gang of experimenters makes a mistake in such a thing. It may be much lower than 100% but there are many possible errors of this kind and the overall probability of a mistake is rather high.
General relativity, curved spacetime
General relativity is needed inside the GPS satellites, otherwise their announced positions would drift by kilometers a day. It's a huge effect but most of it is obviously taken care of. In particular, the atomic clocks carried by the satellites correctly appreciate that time is ticking faster if you're further away from the Earth; and the speed of ticking depends on the velocity, too.
The warping of time – the fact that time is ticking slower in the depths of a gravitational field where the gravitational potential is large negative – is arguably the most important effect of a curved spacetime. It may be correctly appreciated but it's not the only one and even some subleading effects may possibly be important, although most of them are not.
For example, the Earth is spinning around its axis so it's not an inertial frame. When you sloppily assume that the rotating Earth's frame is inertial, could it induce an error? If you make a simple calculation, you will see that the error isn't enough. The worst thing that could happen would be to make a mistake in the speed of light that is incorrectly modified by the speed of motion of the Earth's surface. But the latter is just 460 m/s or so at the equator and only 300-400 m/s or so in the moderate zone so this is a 10 times smaller speed than the speed of the GPS satellites and correspondingly induces 10 times smaller linear effects only: the spinning of the Earth could at most give you a one-meter error and most likely, you will avoid these linear errors and relativity will only produce higher-order effects (higher powers in the speed of the surface divided by the speed of light) which are utterly negligible.
Also, you could suggest that the experimenters incorrectly assumed that the neutrinos are moving along a "straight path" between Switzerland and Italy. However, you could correctly say, the neutrino is actually moving along a null geodesic in spacetime which means that it's bent much like starlight measured by Eddington in 1919. Using a Newtonian approximation which is wrong by a factor of 2, the neutrinos are actually moving along a "free fall" parabola on the surface. Could this explain this error?
Well, it couldn't. The bending of the neutrino's path because of the Earth's gravitational field is totally negligible. During 2.4 microseconds, the Earth only makes the neutrino fall by \(gt^2/2\) which is about 26 microns. Moreover, the distance that the neutrino travels wouldn't even be by 26 microns different: you would have to square 13 microns or so, compute the Pythagorean hypotenuse with the other side being 730 km, and this result would only get longer by some truly pathetic tiny distance.
Analogously, Dave Miller asked about the Coriolis force in the fast comments. The magnitude of the Coriolis acceleration is \(2v\Omega\) where \(\Omega=2\pi/86400 {\rm s}^{-1}\) and \(v=c\). You numerically get a large acceleration \(a=44000 {\rm m/s}^2\) but \(at^2/2\) for \(t\) being two milliseconds is still just a decimeter or so: the real modification of the curved path is much shorter than that once again.
So this can't be an issue. A related question is whether the non-Euclidean, curved character of the spatial geometry in the Earth's gravitational field may matter. Recall that the spatial terms of the Schwarzschild metric are
\[ ds^2 = R^2 (d\theta^2+\sin^2\theta d\phi^2) + \left( 1 - \frac{2GM}{Rc^2} \right) dR^2 \] So the angular distances are measured by the angles multiplied by the coordinate that is called intuitively just \(R\). However, the radial distances have an extra factor. How big the factor is for the Earth? Well, the whole factor in front of \(dR^2\) differs from 1 just by \(10^{-9}\) or so, and it can therefore be neglected. Recall that we need relative errors in the measured speed of light (i.e. in the measured time and/or distance) that are as big as \(10^{-5}\). Moreover, it's likely that this factor wouldn't influence the measured velocity "directly": only some powers or differences of the warp factor (well, it's actually not called warp factor but I will get some extra tweets because of this buzzword) would affect the measured velocity so their effect would be even smaller than one part per billion.
One may also discuss frame dragging and other fancy general relativistic effects. I haven't done a specific rough calculation of this thing; my guess is that once the satellites-induced locations are adjusted not to "drift", there is no significant effect of the frame dragging that could influence the measurement of the distances between the two labs. But maybe I am wrong. Maybe the frame-dragging has been partially taken care of by the GPS system so that things don't drift; but they still produce wrong distances between CERN and Gran Sasso by 18 meters.
Summary
I want to summarize the situation by saying that lots of very delicate issues had to be thought about when the paper was being written and most of them were surely done carefully. There's still a nonzero potential for mistakes and omitted subtleties; but it's also true that most of the potential errors that some of us suggest can be quickly "shot down" because the Opera team (or more general users of the GPS system etc.) couldn't have possibly done these errors (e.g. because these errors would produce much higher deviations).
Old-fashioned physics as well as technology has to be rechecked, much like some special relativity. And of course, one must appreciate that there could have been a simple miscommunication in between some of the Italians and others:
Potential mistakes in the Opera research
Reviewed by MCH
on
September 24, 2011
Rating:
Reviewed by MCH
on
September 24, 2011
Rating:
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