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The effect of GPS clocks on neutrino speed excess at OPERA

October 17, 2011

Mohan, mdashf

Instead of this version you may like to read an updated version at: [Linked article]


I have added a few diagrams and explanations at the top of this article since it was first posted. I don’t think this will offset any chronological misunderstanding (that is the beauty of physics as long as it is correct) These only clarify the case much better since there is still friends arguing with me that Elburg’s correct (in what frame and what universe?)

Elburg’s reasoning on motion of satelite in GPS system. while a 4 km/s is correct it’s direction is always tangential to the orbit as is so in all circular motion we know from college physics. Plus allowing him a 4 km/s perpendicular to orbit speed still the baseline points are all moving at the same speed towards the satelite (S = source & D = detector, end points). All incorrect reasoning by Elburg is pointed out in red color and the correct motion is shown in magenta or brown. The brown arrows are all parallel although in actuality they have all to be almost 0, Not shown here: perpendicular motion of these baseline points that are of the order 4 km/s (within 3.5 to 4 because of earth’s spin of 0.5) but do not matter for our purpose because 1. that is what should have been Elburg’s focus 2. These perpendicular to baseline motion produces negligible effects.

Planetary or not planetary, circular motion are studied in convenient coordinate systems such as through Euler’s angles. But from basic intuition you gain, with college trigonometry and algebra (for vectors) you can see that, IN NO cases parts of a “RIGID line” move towards each other at a speed because some one else is moving wrt you. IN NO case. A crucial mistake of Elburg’s paper.

The rotation of earth and satelite together produce a very small speed (of 3.5 to 4.5 km /s  because of vector addition of velocities which at these speed simply add or subtract) Which means “any point on earth: has that speed wrt a satelite at that distance and speed.” The fact that earth rotates at 0.5 km/s just makes the 4 km/s satelite speed to 3.5 or 4.5 depending on “earth rotates along the satelite” or “opposite to it”. Dr Elburg missed this crucial; classical point, made a wishful “source Vs detector speed of 4 km/s” which means the detector or source are placed on a U-Haul truck as observed by the satelite, in the dreams of Relativity everyone forgot classical mechanics and look at the will with which the world now believes he is correct … Even with such an arrangement one can not apply Relativity because the speed is extremely small, Relativity will give results very close to Classical understanding.

Additional explanations: non-inertial ness of frames of motion in Newtonian and Galilean systems comes from rotation and acceleration. For a GPS clock orbiting earth this comes from two sources,

1. Centripetal and 2. centrifugal deflections unaccounted for by inertial considerations.

In one of my article I had shown (with siderial inertialness and earth’s spin of 0.5 km/s, will update that article with calculations that I did not show and link here) these cause a deflection of maximum 1.5 cm in one case and 0.5 cm in another.

For the non-inertialness of the GPS satelite motion we also have these effects if someone considers to calculate them for a reason. But speed being 4 km/s and centripetal motion of circular motion being mvv/R (this is force, acceleration being vv/R, mass of satelite is so small compared to earth one needs to see how much it reduces the effect) this will produce a few cm of deflection (below I will again give some explanations, without calculations it is giving an imprecise value of deflection, but it has a chance of going towards milimeters or below, so consider this an immediate upper limit because it rests on factors that are bigger but gives centi-meter values).

Altitude of satelite of 20,000 kms will only make this deflection large on teh surface of satelite orbit, not on earth. Again the trade off between the satelite mass and altitude may keep this to a really small value. You can calculate this.

BUT here is a hint: Why the non-inertialness of the GPS satelite does not matter, Newton’s 3rd law. Force on satelite by earth = force on earth by satelite. acceleration being vv/R for satelite from its circular orbit, force on satelite is mvv/R. This means this force is same on earth but earth’s mass is so huge the acceleration is tiny tiny bit compared to its own acceleration. That is because earth mass is billion billion time heavier than the satelites mass. What is it? ~10^24 Kg?? Satelite mass is the mass of a bus, what is it? 10,000 Kg? that means mass of earth is 10^20 times higher. 26,000 km of altitude of satelite will vanish like a coin in a ocean compared to that. That will give a tiny tiny acceleration to earth and we do not have to worry about such non-inertial ness from an angle of Coriolis or centripetal acceleration. They may produce milimeter deflections in the calculation, may be even less. I haven’t done this calculation. You are welcome to take as a home work.

The general Lorentz transformation of time. (is there a mistake in the equation?)

I calculated using above eqn. that if GPS synchronization is not understood or practised the 2nd term of RHS gives ~900 nano-second because of large L’ and small v. L’ ~ 20,200 kms is clock altitude and v is average recession of the clock from the base-line… for each value of v along the baseline, which will be dependent on the detailed geometry but still close to this average value there will be a different phase-factor of time correction/synchronization which are to be corrected by the GPS system. This phase factor is within ~7 nanoseconds for OPERA instead of the crude ~900 nano-seconds because this is very well understood and accounted for, you can question that but Dr. Elburg has retracted his claims reg. GPS synch.. Once that is so the only other factor is less than 0.25 pico-seconds not a staggering 32 or 64 nano-seconds which comes from incorrect use of the equations and ideas of Relativity, eg. this eqn. above is all considered in earth frame, he mixed the frames and “created” a source-detector recession of 4 kms/s instead of a zero recession for distances on proper-frame.

Following scanned files are the calculations, you may read them before or after the discussion ..

(some discussion preceding the calculations)

These are really high and deep resolution *.jpg files, save or print them with lower resolution and read them .. and there are two mistakes, a slight mis-paging of the scanned papers but they are all in order, so not matter, 2nd mistake is on actual page-6, from equation in first line where you need to introduce “mod” sign on both sides as the minus sign has been misplaced on side, what matters is the modular value of time correction …

(main idea:

1. relativistic synchronization; I will describe the basics but the complicated case of GPS synchronization is described in these two publications, which Dr Elburg did not cite, although he cited a paper from 2001 which I haven’t read.

2. relativistic time dilation: Dr Elburg calculated this to be 64 nanoseconds, but the correct value as it should be because of small GPS speed is 0.25 picoseconds, now he does not have to look towards OPERA team to falsify his hypothesis, accidentally I have done it )

just an epithet: Once someone asked me “why everything is so delayed in India, what does Physics say about that? Chaos?” I said “NO, it’s Relativity, moving clocks run slower, India is moving really really fast wrt rest o’ the world, delay in relay”

At the outset of this article I would like to make a sincere apology for over-speaking on certain aspects of the paper by Dr. Elburg. Although I have shown above with detailed calculations why this paper has so much inconsistencies about it that it should not have been published without the correct reasoning and calculations and Dr Elburg has pointed with humility his own misunderstanding about his hypothesized  impractical judgement on the validity of the GPS synchronization, I feel profusely apologetic that I called it a hoax paper.

I realize that I have caused irrepairable damage to the innocence of a fellow scientist although this paper did not belong to the arXiv without good review of it’s calculation. I also silently witness how claims and counter claims are being incorporated into mass-media such as wikipedia where someone just remarks “without independent verification of the calculations this paper’s claims are suggesting a falsification of the OPERA experiment”.

While the spirit of this paper and such inclusion of it’s claims are fine it is rather shocking that in a world of 1000s of physicists everyone is making wishful statement (and I retract my erroneous claims and I am sorry) but no one is doing a simple calculation and showing it is right or wrong. It is this aspect which is making me somewhat impatient with the proceedings of this result which is indeed a remarkable one, or else it wouldn’t produce such colors of thinking and misthinking. In almost all my 11 or 12 articles so far I have taken clues from basic physics calculations. Only in 2 or 3 cases I had to modify a statement and only in one cae I had to modify my calculation although in this latter case the target equations have been wrongly used.

For sake of keeping an honest record of what I said so any over-response from my person is only  regretted and I own my faults of judgement entirely, I will produce some of the conversation I made elesewhere and try to make a note which of them are over the bound.

But the logic and final conclusions, after the minor corrections, are still on my side so I feel a little relaxed for not misleading anyone, but if you feel any calculations or claims are erroneous or bloated please feel free to correct. Be sure about the veracity of your own claims and I will only appreciate if you come with basic calculations rather than a diverting path of logic.

Following is all my discussion and I will note my erring remarks, all calculations in the scanned files at the top.

what rubbish is awaiting science? Any good physicist reviewing this paper would have drawn serious conclusions against this paper, but this is on the arXiV:
This paper, in addition to all the details I provided on my article yesterday, I saw this paper yesterday while I was still on commute and got some internet just for an hour, I read this paper through midnight did the calculations and you read my article what this paper is all about.
It has a serious thing that should have been clear right-away >> A photon moves at speed c. A neutrino even if it were not to move in excess of photon speed is still so close to it in speed. That is any time difference between these two are relativistic (not just elativistic) in nature which being 60 nanoseconds any time correction of that order must come from an object that is also moving at similar speed. That is the paper is saying, by implication, the GPS clocks is moving at around 3×10^8 m/s, a ridiculous aspect of the paper since the GPS clock is a satelite. That is a 1400 KG car would also move at the speed of light to produce a relativistic time effect of nano-second order. Since this is impossible this paper would have immediately raised an alarm to the reviewing physicist. Serious action should be taken aganist the scientist who has reviewed and allowed this paper. OR for ever science has gone to the wolves.
(I correct that while I am not happy with the review if any of the papaer and the hastiness with which it was published I apologize for such rash evaluations, howsoever correct I am on my logic)
needless to say now you may have understood that “if this correction had come from another particle” it was perhaps even worth reading. This paper which deals with the motion of a satelite making that kind of time correction (relativity allows only correct logic not incorrect ones) had something terribly wrong. It just can not move so fast to bring that kind of time correction.
Mike remarks: From the point of view of the clock, the detector is moving towards the source and therefore the distance traveled by the particles as observed from the clock is shorter. **By this the author means shorter than the distance measured in the reference frame on the ground** According to the author. the OPERA team overlooks this because it assumes the clocks are on the ground not in orbit***
The calculations, which are correct as far as I can tell show a difference of 32 nanoseconds. But this must be doubled because the same error occurs AT EACH END of the experiment. So the total correction is then 64 nanoseconds, almost exactly what the OPERA team observed….. so why are you so critical?
I remark: Mike, I already understand what the author is saying, but remember that the GPS clock’s speed is far far far less than speed of light, hence they only bring almost zero correction, a fact clearly stated by OPERA, that is square (gamma) = 1.
(I add: you have seen above in the scanned calculations, why this point has in-fact led to the flawed reasoning of the above paper by Dr Elburg)
That is the length shortening and time-lengthening measured by the clock are almost zero since it’s speed is really really small. In-fact any thing that can measure a 32 nanosecond time correction for the neutrino and photons is something that also moves at these speed, which is pssible only for elementary particles, not a massive satelite or a car.
Mike this is bullshit, this paper. This paper has made a mockery of basic physics, go read the paper. It adds a clock velocity to speed of light, it’s clock velocity is 4 km/s compared to light speed of 3,00,000 km/s that makes a correction in the 5th decimal place and amounts to a zero correction of time, not a nanosecond. I have already pointed out all these points in my article. I am sure you haven’t read my article…
(I correct myself here and apologize: the equations indeed give 32 nanoseconds, but the equations have been used wrongly, as you saw in the scanned calculations, if you already read them)
Mike remarks: It is possible since the satellite is farther from earth’s gravity well, thus the time difference… the speed and positioning of the satellite also has been taken into account here.. and I really disagree with you that it is a shit-paper…
The pitfall of this paper, HOWEVER is that these difference should already be accounted for automatically by the GPS positioning system
(I add: I agree with Mike that this indeed is a pitfall of this paper, now Dr Elburg realizes so, but I realized this after I did all the calculations independently)
Mike remarks: No I have not read your article yet… I just logged on for the first time since a few days… I got news of this paper in my arxiv email alerts and read it yesterday evening…
I remark: Mike disagree, but this paper is a hoax paper and you will eventually see that scientists will take note of this. How can any one in his right mind claim that a GPS clock moving at 4 km/s effects a relativistic correction??? Please, OK. Read the paper. It has incorrect invariant equations in the paper (I already pointed out) If you use their equations and put their values it does not give 32 nano-second, hence I say it is a hoax paper. Please do this calculation, you will see this fact.
(words of apology and correction: I did misjudge the intention of the paper to be a hoax and it’s my excess of response, I reiterate that the paper should not have made a relativistic effect at that minuscle velocity, in-fact very small deviations to classical mechanics start to accrue only when we reach eg 10% of speed of light that is 30,000 km/s not a meagre 4 km/s. 2ndly I was incorrect that if one puts 4 km/s one does not get 32 nanosecond, the reason why I was carried away. But one simply should not have used the wrong equation, I have shown in my calculations in the attached scanned files at the top that it is only 0.25 picoseconds and not a staggering 2×32 = 64 nano-seconds.)
ok … here is my article, read after the first 3 points,
when I first heard this claim I said wow, I downloaded the paper and it gradually set into me, what a joke this paper is making, (a pure joke, no physics here) SO I also expect you will take some time before seeing what is happening here, also you will notice (pointed out in my article) they claim a 12 hrs for a complete rotations of the satelite, serious papers do not do these kind of mistakes. I checked all the equations and most of them are wrong, relativistically …
(I correct myself here: I misunderstood the GPS time-period around earth and made a good search to find out about GPS system, but it does not matter since 2 or 4 km/s they both are judged equally from a relativistic view-point. My serious mistake also but I was prepared from a relativistic angle not from a non-relativistic angle)
Mike remarks: I’m reading your article now…. but I have to point out that the orbital time of a satellite can well be 12 hours… it depends on how far it is from earth etc… eg. semi-synchronous orbit can be 12 – 15 something hours… and the Molniya Orbit is a 12 hour orbit
Me remarks: OK see your point, will do some review , but does not matter, 2 km/s becomes 4 km/s it does not become 400km/s at which still it does not produce much significant relativistic effect compared to 3,00,000 km/s
Mike: Good 🙂 slow down slow down 🙂
Me: does not matter Mike, as I said relativistic effects show up quite close to light speed, say 1/10th speed of light gives you 30,000 km/s not 4km/s, but take your time
you do not have to understand GPS clocks to understand Relativity (** it could be the other way round), I made a mistake of assuming that the GPS clocks have a time period of 24 hrs, but since I did not deliberately use this reasoning in my conclusions about the paper that claims falsity of OPERA neutrino results, it does not matter what mistake I made. I understood my Relativity in undergraduation and use such to see that this paper itself is ***. Here is more about GPS clocks which move at ~4 km/s because of their sidereal time period of 12 hrs (compared to earth it would be 2 minutes less in 12 hrs, hence reaches 4 minutes off everyday)
GPS clocks are placed about 26000 km above earth’s center or ~20000 kms above earth surface which is about half of what a Geostationary satelite orbits above earth surface are placed in. But time is measured using GPS clocks which relies on speed of light hence the meagre speed of GPS clocks of 4km/s or height of the clocks does not matter in relativistic calculations, especially in the one which OPERA used for it’s neutrino speed measurement.
(correction: as  have pointed out in the discussion in the scanned calculations, the synchronization of clocks being valid the distance of the clock does not matter for additional relativistic effects)
slightly edited my article for saying GPS clocks time period to be 24 hrs, but the primary idea of the article stands corrected. The relativistic equations and ideas have been used wrongly … by the arXiv paper.
just one more epithet: “Confidence is a great measure of our existential survival. It takes all into account.”
After I did my complete calculations and was sure where the above paper by Dr Elburg has gone awry (I am confident now and one more time I am really sorry for all the emotional outbursts in the way, sometimes it is so frustrating finding faults when you know something is definitely wrong) I searched a little about the author and found this:
Dr Ronald van Elburg has apologized to the GPS community for suggesting corrections to GPS, I have done two calculations in addition to what I posted earlier which shows clearly why he is also wrong about OPERA experiment analysis, the only change I will make to my statements is with an apology myself for calling it a hoax paper as I have put 4kms/s into his equations and see that he indeed gets 32 nanoseconds which I erroneously myself called as hoax, but his equations are wrong which is why it still is not a good paper and should not have been published without good review.
I have shown  my detailed calculations at the top of this page.

Admittedly the first version of the paper was written in a rush. My latest version, which due to the workings of the archive is only available here, is more careful in pointing at the potential pitfalls of the GPS and puts more stress on the fact that my proposal is just a hypothesis. Fu…
I remark: last night I figured out what errors he had in his analysis before reading his apology itself. I didn’t even know he had a second version of paper, I had based my conclusion on the version 1, but it does not matter … (I have also read quickly his version 2 where he has changed some of his notations, but my analysis stands unchanged as he used the same calculations)
NOW here is my commentary after which I will post/append my calculations (perhaps when I wake up, I am sure nobody here at home will steal my calculations to cause trouble to me)
finished reading the ~20 page OPERA paper on neutrino AGAIN, no trace of uncomfortable facts … they have a maximum GPS (UTC) time error of ~7 nano-seconds **well they combine GPS, Atomic clock average and fiber-optics calibration** All atomic clock timing in the world today, the most precise timing known to human-beings are being calibrated by the GPS, not just by this experiment but by thousands of experiments, military, aviation industry and so on, hence no-one should have questioned the role of GPS.
GPS standard gives ~200 ns capability but this experiment used most advanced time-synchronization **which also measures distance to orders of millimeter which in effect gives a 20 cm uncertainity for a 730 kms** NOW that GPS synchronization effect is out of purview the only other effect that relativistically bothered a few experts, semi-experts, quasi-experts, wanna-be experts, enthusiastos, scientio-absurdos, lay-men, awake-men, walk-in-sleep men and non-experts and excited consumers of scientific info. was the motion of the satelite at 4 km/s at an altitude of 20,200 kms from earth.
The 20,200 kms of altitude with 4 km/s velocity of a clock introduces complicacies into relativistic-synchronization of time, but this was head-ache of GPS and is taken care evidently (GPS clocks and their relativistic understanding came decades earlier than this result of last month). The Lorentz time dilation of the satelite clock introduces only 0.25 pico-seconds of inaccuracy according to my relativistic calculations, which Dr Elburg mixed (his mistake was he mixed the relativistic synchronization and the relativistic dilation) to predict an arbitrary and inconsistent time-correction from relativistic effects to falsify the OPERA result.
As such, as of now, therefore, the OPERA still stands correct. Let us give the experiment some more tests of falsification. But let us also remember this has got nothing to do with main aim of OPERA experiment and this is clearly mentioned on the preliminary pages of this brilliant paper. Also if you do not see what I am saying consider this, You go to a Regal theater: your main aim is to watch the movies, but you do not adhere to a NO popocorn policy do you? If you do it’s your personal choice, not an illogical choice for entertainment, in addition you can do plenty of other things which are as important as the main aim of watching the movie.


painful eyes from all the study

Heartfelt apologies for any over reaction if anybody has felt so


Post a comment
  1. October 19, 2011

    Hey you should contact Elburg to see how he views what you have pointed out.
    Moreover I still think Elburgs calculations are correct; but, the result is still bad as he just assumes some sort of non-sync. I don’t know all the details of GPS synchronization are not evident but they do follow a standard (which I wrote about on facebook and which I also have studied at uni) so it shoud not be so hard to find out the fact regarding the variables of the satellite frame …. Probably all aspects of time dilation are accounted for and hence it becomes o non-factor in the calculation…. if they are not accounted for it would mean that we are getting real time info from satellites and that kinda defeats the point of satellite communication….. however I might be wrong

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