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 …
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 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
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.
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]
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 nano-seconds 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.
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 above 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 3-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 above 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.
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