The effect of GPS clocks on neutrino speed excess at OPERA

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 satelite’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 brown. The brown arrows are all parallel although in actuality they have all to be almost zero.

Not shown here: perpendicular motion of these baseline points that are of the order 4 km/s (in actuality within 3.5 to 4 km/s because of earth’s spin of 0.5 km/s) but it does 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, a point of Relativity.

Planetary or non-planetary, circular motion are studied in convenient coordinate systems such as through Euler’s angles. But from basic intuition one gaina, with college trigonometry and vector algebra one 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 the rigid line. 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. These are non-relativistic speeds. This 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 effected as 3.5 or 4.5 km/s depending on “earth rotates along the satelite: prograde motion” or “opposite to it: retrograde motion”. 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, a point of Relativity.

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 [Ref?] 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 the 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.

One 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 large, the acceleration is tiny-tiny bit compared to its own acceleration. That is because earth mass is billion-billion times 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? One always needs to b careful with Relativity. Because it is confusing in the least, there is reciprocation in inertial frames which I had described in detail in some article, Ref? and in one paper: Binomial Analysis )

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.

GPS User

The Science of Time-Keeping

2. Relativistic time dilation: Dr Elburg calculated this to be 64 nano-seconds, 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”.

Did I say the above in a humorous spirit? YES. Why should I feel any apologetic towards careless ramblings in papers where ArXiv publishes bullshit but refuses to publish my papers? ArXiv has really become a piece …

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 statements (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 case I had to modify my calculation although in this latter case of Elburg’s paper 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, at-least if political correctness is a much sought-after virtue in the lonely corridors of science.

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 suggest corrections. 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: http://arxiv.org/abs/1110.2685

The relativistic contribution of GPS satelite to OPERA neutrino

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, linked just above, 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

NOW LET US MOVE TO THE IDEAS I SEARCHED ABOUT THE GPS SYSTEM

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, considered from earth it would be 2 minutes less in 12 hrs, hence reaches 4 minutes off everyday. GPS Orbits . [Read linked article]

GPS clocks are placed about 26000 kms 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 I 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.”