## Saturday, September 24, 2011

### Potential mistakes in the Opera research

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:
• timing errors at CERN
• timing errors in Italy
• errors in the distance measurement
This is just a very rough, "geographic" separation of the possible mistakes. Various numbers in the calculations depend on each other and one should be more specific about the origin of the error, anyway.

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 $$10^{-19}$$)
This is just a partial list but I feel that most people who have tried to find a mistake will prefer and focus on one of the categories above. Recall that to find a mistake in the Opera paper, you need to find a discrepancy comparable to their signal of 18 meters (60 nanoseconds times $$c$$). Some of the proposed mistakes lead to much too big effects relatively to 18 meters and it's therefore clear that Opera hasn't made those errors; on the other hand, some errors and subtle effects are much smaller than 18 meters and may be ignored.

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:

1. Could the error be in the measurement of the speed of light?

2. Lubos:

It may not be necessary to look for gravitational effects to explain the approximately 66 nanosecond (20 meter) propagation time shortfall. For example, consider that (a) the earth is rotating about its polar axis, and (b) the center of the earth is rotating about the sun. As such, to analyze the time required for light (or any object) to propagate between two points fixed internal to the earth or on the surface of the earth, we must examine the problem relative to an inertial reference frame. This means that if the distance between two fixed objects is 732 km, we can't simply treat the propagation distance as being 732 km.

Let's assume the sun is a negligible-mass star at rest with respect to an inertial reference frame. Further, assume a second negligible-mass object-of-interest is rotating at a constant angular rotation rate of 2x(10-7) radians per second in a circle about the sun at a distance of 93,000,000 miles. These are, respectively, (a) the approximate angular rotation rate of the center of the earth about the sun and, (b) the approximate distance between the sun and the earth. We assume the circular motion is not the result of gravitational pull, but rather is produced by a "thruster" on the rotating object that always points towards the sun. In such a configuration, gravity can be ignored. But the fact that object-of-interest is traveling is a circular path relative to an inertial reference frame means that a reference frame in which the object is at rest is NOT an inertial reference frame. The postulates of special relativity apply only to inertial reference frames. As such, to compute inertial-space propagation times between objects fixed relative to a rotating reference frame, we must take into account all rotational motion effects.

To first order, an object traveling near the speed of light will take approximately 0.00244 seconds to propagate a distance of 732 km. Relative to our inertial reference frame, in 0.00244 seconds the object-of-interest rotating about the sun will move a distance of approximately 235 feet. Depending on the direction of neutrino propagation relative to the direction of object-of-interest motion, at the speed of light (approximately 1 foot per nanosecond), to first order this rotational motion can result in a neutrino propagation time "delta" relative to an inertial reference frame neutrino propagation time anywhere from -235 nanoseconds to +235 nanoseconds. Now I don't know whether this effect has been considered or ignored. However, if it has been ignored, it has the potential to provide the approximate 67 nanosecond error mentioned in this post.

If this is the source of the discrepancy, I believe there is a way to establish that fact. In particular, as the earth rotates about its polar axis the direction of neutrino propagation relative to the motion of the center of the earth about the sun changes with time. Over a 24-hour period, the orbital-plane component of the neutrino direction of propagation relative to the direction of object rotational motion about the sun passes through a maximum (positive value), passes through approximately zero, and passes through a minimum (negative value). By measuring the propagation time (a) when the direction of neutrino propagation is in the direction of earth-center rotational motion about the sun, (b) when the direction of neutrino propagation is opposite to the direction of earth-center rotational motion about the sun, and (c) when the direction of neutrino propagation is approximately perpendicular to the direction of earth-center rotational motion about the sun, the propagation time delta should change sign and pass through zero. If the propagation time doesn't so behave, this phenomenon (rotational coordinate system effects about the sun) cannot be the source of the discrepancy.

3. Lubos:

I add the following to my previous comment because I exceeded the 4096 character limit.

I also did a back-of-the envelope calculation of earth rotational effects about its polar axis. Over a distance of 732 kilometers, the maximum delta to inertial system propagation time is approximately 3.7 nanoseconds--so I don't believe rotational motion about the earth's polar axis can be the source of the 67 nanosecond discrepancy.

4. Hey! Nice article. I did a similar calculation for gravitational effects like space-time curvature. Have the same result of a rediculus 3 micrometer longer distance between CERN and Gran Sasso :-D.

5. Hey! Nice article. I did a similar calculation for gravitational effects like space-time curvature. Have the same result of a rediculus 3 micrometer longer distance between CERN and Gran Sasso :-D.

6. Why did I decide to start reading this at the pub AFTER I had a pint on an empty stomach? (for those who care, a bottle of delerium tremens, which is good for a yellow beer, but I had to follow it with a proper schwarzbier.)

All in all though, it was a very good primer for a semi-sophisticated non physicist like myself.

7. But the Maxwell's equations, with its invariant speed c, could be just
an incomplete model for the behaviour of light. In principle, the
limit speed which appears in the Lorentz transformations could be
something slightly greater than the observable speed of light. Even if the Maxwell equations are
exactly correct, the observed photon speed is never exactly equal to
c, because there are always, among other things, the interactions of
the photons with the thermal background, or even virtual
electron-positrons pairs of the vacuum. Perhaps when these quantum
effects are taken into account the photon could be even slower than
the neutrino? Of course these effects are very small and will not
explain the anomalies recently observed in the OPERA experiment. But
in principle, the speed of the photon could be smaler than the limit
speed and perhaps some other particle could be faster than light.

8. One potential source of error is plate tectonics. No point on the earth's surface is fixed in space, and most are in very slow relative motion due to the movement of crustal plates. I would suspect that an electromagnetic signal would require a more round-about route - eart-satellite-earth - than a neutrino, which probably be a more or less straight line. That being the case, there is likely to be a drift between the speed an electronic signal requires and the time a neutrino takes. I would look for systematic shifts in the arrival times of both neutrinos and electromagnetic signals.

9. Dear Harlow, essentially No, there can't be this big an error (10^-5) in the measurement of the speed of light. Light is how we measure space and distances - that's really how we define distances and durations at a high accuracy.

Saying that something is wrong about these straightforward measurements means to say that we don't have any definition of distances and durations. You would first have to offer another operational definition of distances and durations - not using electromagnetic waves - and then we would could discuss. Now we can't. You can't just deny light and its relationship to accurate information about spacetime.

10. Dear Reed C, I don't understand your suggestion. It clearly has anything to do with the motion around the Sun. But within the relevant time, we may just use the inertial frame in which the Earth is moving freely - either along a circular orbit, or along a line. At most, this means to neglect the centripetal acceleration around the Sun which is R.omega^2 = 150e9 meters.(2.pi/3.15e7 sec)^2 which is just 0.005 m/s^2 and is thousands of times smaller than the Earth's gravity acceleration etc. that were shown to be irrelevant by themselves.

So the motion around the Sun can't possibly influence this experiment in a detectable way.

11. Dear Phelps, don't worry, there's no problem with causality because I have alerted the police already *before* you had the pint of the black beer - because you were just 12 years old and not allowed to drink black beer in the pub.

12. Dear skbrant, as I have repeatedly said, if the photons' speed isn't the maximum speed "c" controlling special relativity, then the photons' speed will inevitably depend on the velocity of the source, observer, and the energy of the photons - in all cases, you get a contradiction with the Morley-Michelson experiment, long-range character of electromagnetism, and/or other things.

13. Dear John, they *are* able to measure geological processes (crust) and indeed, they do see the changed distance after the 2009 L'Aquila earthquake (one for which the seismologists are hunted just like witches).

The distance between the two places jumped by a few centimeters. Look at the paper a little bit more carefully than so far, please.

14. Lubos,

Thank you for responding.

As a result of your 4096 character limit, it takes two entries to post my response. Thank you for your patience.

First part of response.

The added "delta" time is not related to acceleration--rather it is related to applying the laws of special relativity only in an inertial reference frame. Consider a flat disk of radius "R" rotating at a constant angular rotation rate "w" about a point that is at rest with respect to inertial space. Now consider two points (A and B) on the circumference of that disk separated by a distance "d". In our case the approximate values of the quantities are R=93,000,000 miles, w=2x10^-7 radians per second, and d=732 kilometers. Because light travels at the speed c in an inertial reference frame independent of the motion of the source of the light, as viewed from the inertial reference frame in which the center of the disk is at rest, light would leave one of the points and travel at a speed c towards the other point. During the time interval the light is traveling from point A to point B, point B will be moving. For the case of two points separated a small distance on the circumference of a large disk, most of that motion is either towards object A (if the rotation direction is such that point B will soon occupy the location that point A ocupied at the time of light emission) or away from point A (if the rotation direction is such that point A will soon occupy the location that point B occupied at the time of light emission). To first order (i.e., ignoring the motion of object B), the light will have to travel 732 kilometers to reach object B. This will take approximately 0.00244 seconds. During this time interval, object B's position will have changed. For our case, the speed of object B in the inertial reference frame is 98,208 feet per second. In 0.00244 seconds, relative to our inertial reference frame object B will have moved approximately 240 feet. Thus, in our inertial reference frame, the light that propagates from object A to object B will have traveled a distance of either 732 km plus 240 feet or 732 km minus 240 feet. It will take light approximately 240 nanoseconds to travel the "distance" of 240 feet. Thus, in our inertial reference frame and depending on the relationship of points A and B relative to the direction of angular rotation, when propagating from object A to object B, the light will either take 240 nanoseconds more or 240 nanoseconds less to travel from A to B than it would have if the rotation rate had been zero. In some circles, this is often referred to as the Sagnac effect.

15. Lubos,

Thank you for responding.

As a result of your 4096 character limit, it takes two entries to post my response. Thank you for your patience.

Second part of response.

However, this phenomenon raises a second question. Specifically, points A and B on the disk circumference are moving (and accelerating). How do we account for these effects? As you pointed out, the acceleration is negligible, so I agree with you that it won't affect either propagation time or the rate at which a clock fixed to the surface of the circumference of the disk runs. To account for the speed of points A and B, at a speed of 98,208 feet per second, the value of "speed/c" is approximately 9.82x10^-5, which when squared is approximately 10^-8. Thus, in an inertial reference frame moving at the speed of objects A and B, the time dilation factor is on the order of 0.5x10^-8. When applied to the approximate 0.00244 second propagation time, the time dilation effect is approximately 0.012 nanoseconds. Thus in an inertial reference frame moving at the speed of objects A and B relative to the inertial reference frame at rest with respect to the center of the rotating disk, the correction to the 240 nanosecond delta is very small. This implies that if all gravitational effects are ignored, even for a "pseudo" inertial reference frame rigidly attached to the circumference of the disk, a correction of approximately 240 nanoseconds relative to "732 km divided by c" must be made to the light propagation time from object A to object B.

Note that the above analysis assumed both points were on the circumference of the rotating disk. If one point is on the circumference but the other point is on the same radius but 732 km closer to the disk center, then relative to the inertial reference frame for which the center of the rotating disk is at rest, the light travels almost exactly 732 km plus or minus a negligible fraction of a foot. This is why for a fixed separation of 732 km, the delta correction to propagation time can be anywhere from -240 nanoseconds to +240 nanoseconds. In the case of the earth, earth's rotation about its polar axis means that over a 24-hour period cycles the direction of light propagation relative to rotation about the sun through 360 degrees. Now I have no idea of the propagation geometry of the CERN experiment. But unless the propagation direction is perpendicular to the plane of the earth's rotation about the sun, it will have a component in that plane. As such, as the earth rotates about its polar axis the component in the plane of rotation (the plane of the disk) will cycle through 360 degrees relative to the direction of rotation about the sun.

Finally, as mentioned at the start of this comment, I believe because the earth is traveling in a circle about the sun, you cannot apply the laws of special relativity (even ignoring gravity) to a reference frame at rest with respect to the center of the earth.

16. Lubos,

I want to correct something I said in my previous comment. In particular, I said: "Thus in an inertial reference frame moving at the speed of objects A and B relative to the inertial reference frame at rest with respect to the center of the rotating disk, the correction to the 240 nanosecond delta is very small." This statement is incorrect.

Create two inertial reference frames: an Unprimed Reference Frame (URF) and a Primed Reference Frame (PRF). Let the URF be moving at the speed of point A along a straight line tangent to the rotating circular disk at point A when light leaves point A for point B. Let the PRF be at rest with respect to the center of the rotating disk. Assume in the URF point B is also on the rotating disk circumference a distance d=732 km from point A. For a disk radius of 93,000,000 miles, to a very good approximation, point B is "co-moving" with point A and at rest with respect to the URF. Hence in the URF the time required for light to propagate from the stationary point A to the stationary point B is 732 km/c or approximately 0.00244 seconds. Since the PRF is moving relative to the URF at a speed of 98,208 feet per second in either (a) the URF direction of light propagation or (b) opposite to the URF direction of light propagation, the PRF time interval required for light to propagate from point A to point B is

(d/c)*[1{+/-}V/c]/sqrt[1-(V/c)^2].

{If you're interested, send me your e-mail address and I'll email you a microsoft word document that derives the preceding result.}

The "+" sign applies when in the PRF the vector from point A to point B is in the direction of point A's motion. The "-" sign applies when in the PRF the vector from point A to point B is opposite to the direction of point A's motion. For a V of 98,208 feet per second, the effect of the V/C term is much larger that the effect of the (V/C)^2 term. In particular, in the PRF the V/c term correction to the URF propagation time is approximately {+/-}240 nanoseconds.

Thus, (a) to the degree the earth can be treated as being at rest with respect to an inertial reference frame, and (b) all distances/times are measured in that inertial reference frame, I agree with you--the rotation of the center of the earth about the sun will have negligible effect on the propagation time. However, if for some reason unknown to me, distances/times are measured in an inertial reference frame at rest with respect to the sun, then I'm not so sure. I have insufficient knowledge of GPS to know which (if either) is correct--although I'd bet on an "earth-based" inertial reference frame rather than a "sun-based" inertial reference frame.

In any event, thank you for your time.

17. Another possibility is this

http://blog.zorinaq.com/?e=58

18. Hi, I have this back-of-the-envelope calculation. I haven't checked for details because lack of data, time, etc...

I suggest the problem is with the calculation of distance among points A and B, which is about 700 kms. We simplify to 1 GPS satellite for position measurement. The height (h) of such satellite is of about 20.000 kms. Imagine that they do the synchro using a non-inertial system of reference, and so they ignore the rotational translation of Earth. Now they miss system of reference for an inertial one (which sees the Earth moving). Let's see all the data:
According to the height h referenced, the time of flight to travel from GPS satellite to point A is roughly 0.07 seconds ( h / c, where we simplify to vacuum for a great percentage of the travel). The tangential speed of Earth due to rotation around its axis is of about 0.5 kms / s. Then the point A translates, in an aproximate straight line, 0.07 * 0.5 = 0.035 km = 35 meters from the previous point in this inertial system. If the translation is deviated a given angle theta respect to the direction connecting A and B, we could have an effect which may be consistent with 18 meters, which is the adventage of neutrino respect to an hypothetical competing photon. I ignore how this gross error could have been made, if the signs and theta angles would be the appropriate, and if this hypothesis could be consistent with different measurements along different seasons of the year. Extremely unlikely, anyway, but wanted to share it. Thanks.

Best regards,

Cesar Sirvent

19. About the Czech terms for precision and accuracy: terms "přesnost" and "správnost" are used in analytical chemistry(at least at the university).

20. Reed C is correct about always using the same inertial frame for position determination of the start and end points. He points to a "sun-based" measurement, whereby the pair of points both lie on the geodesic of the earth's orbit around the sun. I agree that Earth's rotation cannot account for the discrepancy, since it's too small. But if we really mean "inertial frame", then we have to include the galactic rotation also; and what about the proper galactic motion relative to the local cluster? This isn't so much about absolute reference frames (which are meaningless in SR) as it is about measuring distance in the same inertial frame.

Ironic that this blog is called "Reference Frame" :)

21. Two quick notes on previous remarks:

a) The Coriolis correction needed to calculate the exact distance travelled by the neutrino in an inertial reference frame is just 2.2 nanoseconds or 66.1 cm. The calculation can very easily be done exactly in Cartesian Earth-centred Earth-fixed (ECEF) coordinates: http://arxiv.org/abs/1110.0392

b) GPS/GNSS receivers certainly do all their pseudo-range calculations in an inertial coordinate system (in practice the same used for calculating the orbits), before converting the resulting position-velocity-time solution into a rotating ECEF coordinate system for the user, such as the European ETRF2000 one used by the OPERA experimenters.

22. While all these comments are very interesting, I am going to assume the experimenters have taken them into account. My thought is that it is most likely an accuracy in the creation event that is the problem. While CERN has precise control of the creation, they do not necessarily know the exact time of the beam interaction. This is not really necessary for their purposes. Precision is all they need not absolute accuracy in the exact Universal atomic time.

23. Note that extending the distance to a "sun-based" spacelike measure exacerbates rather than ameliorates the discrepancy.

24. It seems to be important to know if the speed difference changes with time. If there is a cyclical variation it indicates a reference frame problem.

The same issue arose when the first atomic clocks were flown around the world in both directions. The 'stationary clock' on the surface didn't give the 'right' answer so a reference point high above the North Pole and a spinning Earth was used.

If the time of arrival varies with a Siderial day (I suspect it does) an absolute reference frame (CBMR?) should be used.

It looks a bit convenient to have several reference frames to choose from, trying a foot in each until something fits.

Leave it turned on and see if there is a variation in the arrival discrepancy that is consistent, or varies daily, Siderial daily, annually, or 'other'.

25. We are going forward in Technology but it is time to replace the actual flawed Paradigm in Physics-Cosmology, especially SR and GR, for the New One, Autodynamics, which explain more experimental results and astronomical observations than the actual one plus Newton. Start with

Why is Pauli Wrong for Layman
http://autodynamicslborg.blogspot.com/2011/10/why-is-pauli-wrong-for-layman.html

Never any Detector Detected any Neutrino
http://autodynamicslborg.blogspot.com/2011/06/never-any-detector-detected-any.html

And
Quantum Universal Gravitation
http://autodynamicslborg.blogspot.com/2011/05/quantun-universal-gravitation_06.html

Lucy Haye Ph. D.
SAA’s representative.
lucyhaye22@gmail.com

26. The Classic Fantasia of the 20 century.
All related to Neutrino is a pure fantasy,
Why is Pauli Wrong? For Layman
http://autodynamicslborg.blogspot.com/2011/10/why-is-pauli-wrong-for-layman.html

Calorimetric Experiment (No Neutrino).
http://autodynamicslborg.blogspot.com/2011/07/calorimeter-experiment-no-neutrino.html
Lucy Haye Ph. D.
SAA’s representative
lucyhaye22@gmail.com

27. Hi Lumo,

here seems some clean up needed ;-)
I know this particular cannonical spammer from Matt Strassler's site ... :-/

28. The Classic Fantasia of the 20 century.
All related to Neutrino is a pure fantasy,
Why is Pauli Wrong? For Layman
http://autodynamicslborg.blogspot.com/2011/10/why-is-pauli-wrong-for-layman.html

Calorimetric Experiment (No Neutrino).
http://autodynamicslborg.blogspot.com/2011/07/calorimeter-experiment-no-neutrino.html
Lucy Haye Ph. D.
SAA’s representative
lucyhaye22@gmail.com

29. This is Excellent blog article. so Impressed your blog article. said for this sharing site.
Thanks.
satellite