Charles Francis,

If you are right in your explanation, then you must explain why in the experiment they using the centre of Earth as basic referential frame for relativistic calculations. In SR referential frames are equal, so time dilation should have been computing by the relative velocity of Observer and Source to each other. To evade ‘twin paradox’ of SR it is necessary to introduce a basic referential frame, but with that the experiment support LT. So it is misleading to claim that the H&K experiment (or GPS) prove SR and explain twin paradox, because they try to prove LT, where there is no ‘twin paradox’. 

Your problem in the discussion you don't reply to me by physics. ;)

Charles Francis,

You said: Azzam, I already explained they used a non-rotating reference frame, which is required in special relativity. The centre of the Earth is just a point, not a reference frame. 

Why you are not honest in the discussion? Do you think you can convince people by this dishonesty!!!

Dear all

I think we need to admit that special relativity does not recognize between stationary and moving frames it only recognizes the relative motion between these frames. If an event occurred in a stationary frame and is measured by a moving frame SR predicts the stationary frame will measure the least time, while experiments predict moving frame measures the least time for this event.

Charles Francis,

Instead of asking "If you don't know what rotating means" Ask yourself this question, because what is clear you do not know what is it mean in order to solve the Ehrenfest paradox in SRT. What is clear you go very far by your game in SRT, and the concept of fake space-time continuum. Try to reply to my last comment which I wrote it to you when you said  energy and momentum are both conserved in gtr as local laws in inertial reference frames, and then try to understand why you say like that, basis on what? and then we can understand what is rotating means when in case of considering relativistic case, that means time dilation, when t' not equal to t in Lorentz transformation, and then what is the difference when t'=t in Galilean transformation in the classical case. And then how you mixing between the two things by fake in order to appear SRT of Einstein is completely right by fake and magic.

Yes Danci

 I agree with you

OK, Valentin: yes, there are four frames, as you say. But of these four, only one is inertial. The Lorentz transformation only works between inertial frames. The way in which HK is explained consists in transforming the time happening between two very near instants on the airplane (during which the airplane is approximately in an inertial frame) to the inertial frame moving together with Earth's center.

But sa long as you are not willing to understand elementary issues, such as the Paris-London airplane, with 2 events only, HK will seem considerably more diffcult

Ok Charles so it is enough to Apply the Schwarzschild solution to the trajectory of the planes. The kinetics contribution  depends on the angular speed respect to the center of Earth which are quite different .

@Valentin: The Paris-London problem is by no means unrelated. In both cases, it is required to perform transformations between different inertial frames: two in the Paris-London problem, infinitely many here. So one should first learn the skill of performing a Lorentz transform from one system to the other, a skill which to hone the Paris-London problem is, indeed, due to its simplicity, ideally suited. So do attempt to understand the quite elementary remarks I have tried to make in that post to explain matters.

As far as inertial reference frames are concerned, of course, I do not contradict myself: the reference frame moving with the  plane, whether eastbound or westbound, or for that matter moving with the Earth, can at each moment be approximated by an inertial system, in the same way a curve can, at every point, be approximated by a straight line tangent to it.  This is not a contradiction, nor does it imply that a curved line is, in fact, straight, or viceversa. It merely requires some careful thinking.

I agree I may not have been as clear on that point in my last post as I might have been. Do accept my heartfelt apologies for this.

That the Earth system is not inertial was, of course, well known to Newton, when he discovered that the frequency of a pendulum varied with latitude due to centrifugal force. Correspondingly, it is an inescapable fact that Foucault 's pendulum turns in a reference frame that is fixed with respect to Earth. None of these findings are remotely affected by relativity, whether special or general (in the latter, the interpretation may change, but not the predictions). The airplane frames are in the same way non inertial.

As to the Paris-London problem, I have not seen anybody on that page who understood your remarks. You constantly make absolutely correct, altogether consistent Lorentz transformations, displaying the formulae in a wholly correct manner, and then, to derive the ``contradiction'' you suddenly resort to verbal incoherence, such as ``the time in London of the plane's arriving at Paris.'' I am essentially positive that you fully realise the inanity of your claims and only resort to permanent insult, as you have just again done, to hide this fact.

I do hope you will prove me wrong (but am not counting on it).

In my opinion, time dialation is simply the gravitational or kinematic (Doppler) frequency shift of a massive particle. Cesium atom is an assembly of massive particles. These particles are in a bound state within the atom. When the aircraft moves eastward or westward, each massive particle within the cesium atom moves in the flight direction and they have an associated de Broglie wavelength in the flight direction. Now the direction of the Cesium beam within the atomic clock could be in the flight direction or opposite to the flight direction or could be perpendicular to the flight direction. This definitely makes a difference in time dialation and was not taken into account in the Hafele and Keating experiment. Therefore future time dialation experiments should take this into account for better precision. I can go one step further and say that the orbital period decay of a binary pulsar is simply due to the time dialation of group of massive particles of which the pulsar is made. Gravitational waves are not required to explain this phenomenon. More details in attached article.

Research Alternative explanation for orbital period decay of a pulsar

 Charles Francis,

If you said in SRT there is no Ehrenfest paradox, thus the solution of J.H. Field in his paper is right http://arxiv.org/abs/1405.5174

As he said space must be invariant. In fact you contradict yourself.  You do not understand if there is Ehrenfest paradox or not in SRT. And if there is Twin paradox or not. 

Robert J. Low,

sorry for the question but at first I did not consider that everything had to be referred to the center of Earth, due to the application of the Schw solution. The same as the Vessot and Levine experiment.

I already read your post in a similar question, it was enough to repropose your answer.

The kinetic energy per unit mass referred to the center of Earth of the plane, going in the opposite direction of the rotation of Earth, is very little, so the associated clock beats faster than the ground clock , while  the other  has a kinetic energy per unit mass greater than the gound clock, so it is more dilated.

Charles

Are not observations illustrate that the universe is flat and Eucledean? That means space is invariant as in the paper of J. H. Field. That refute all of your fake ideas about SRT and GR. I explained that for you. But your problem you believe something is illusion and not real. 

Charles,

The concept of "curvature of space" is fundamental to cosmology. A space without curvature is called a "flat space" or Euclidean space. Whether the universe is “flat″ could determine its ultimate fate; whether it will expand forever, or ultimately collapse back into itself. The geometry of spacetime has been measured by the Wilkinson Microwave Anisotropy Probe (WMAP) to be nearly flat. According to the WMAP 5-year results and analysis, “WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 1% margin of error). This is equivalent to a mass density of 9.9 × 10−30 g/cm3, which is equivalent to only 5.9 protons per cubic meter.The WMAP data are consistent with a flat geometry, with Ω = 1.02 +/- 0.02.

Charles!

What is clear you want to let everything in nature to move according to your stupidity of understanding physics.  You used to Falsify the facts according to your fake theories, and what about the Microwave Anisotropy as we discussed before. What about the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius. 

--------------------

Now that means if we consider time dilation which is resulted in SRT, then J. H. Field is right space must be invariant and we must look for new transformation considers space is invariant. 

Now light bending by gravity, precession, Shiparo delay, and the Pioneer anomaly can be interpreted by the uncertainty principle, and also the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius, and the dark matter and dark energy explained.

``Anyway, from a theoretical perspective J.H. Field showed that the theoretical paper is wrong too.'' By no means. Read the paper: Field shows how to do the relativistic calculation correctly, and shows that a certain way of doing the calculation, using relativistic velocity addition, quite different from that of Hafele and Keating, leads to a result different from both the experiment and  Hafele and Keating's theory. In the conclusions, he states ``In conclusion, the experimental results of the HK experiment falsify the conventional interpretation of the relativistic velocity transformation formulae (4) and (5),'' He says nothing about the theoretical paper of HK being wrong, and in fact, actually rederives the HK theory.

So do be a bit careful in your quotations.

Charles,

I like the word  "approximately flat"from you. Look at yourself how you are falsifying the facts. You forget that all the solutions that GR introduces are only approximations, and there is no exact solution. Now the flatness of the universe is approximation while GR is exact. The universe is wrong and the GR is right. 

This is really the Straw  man....how you change the facts. And what about the dark matter and dark energy? What about the 'flat' appearance of the velocity curve out to a large radius???? These are all the consequence because the universe is flat, not curved as GR predicted. Because the calculations came against the GR predictions, now you try to find new interpretations to these anomalous calculations which came against GR predictions. Look at yourself how you are fixing data. You consider the universe is wrong and GR is right and the universe must move according to GR!!! All of that for what? You challenge who???? 

Robert J. Low,

Revelation 13:5-8

5 The beast was given a mouth to utter proud words and blasphemies and to exercise its authority for forty-two months. 6 It opened its mouth to blaspheme God, and to slander his name and his dwelling place and those who live in heaven. 7 It was given power to wage war against God’s holy people and to conquer them. And it was given authority over every tribe, people, language and nation. 8 All inhabitants of the earth will worship the beast—all whose names have not been written in the Lamb’s book of life, the Lamb who was slain from the creation of the world.

Charles Francis,

You said: Exact in science means exact to experimental accuracy. So yes, GR is observed to be exact, while flatness is observed to be incorrect even in the Solar system.

All of that to keep on objectivity and continuity same as in classical physics by only fake and then you hide the uncertainty principle in quantum in macro world, and why all of that??? I explained that too much.

Look at your self now how you are talking by the mouth of the beast of relativity of Einstein; 

Revelation 13:6

6 It opened its mouth to blaspheme God, and to slander his name and his dwelling place and those who live in heaven. 

God is honest and you are lier.

Now I'm busy to reply to you more!!!

Hafele and Keating explain the results by considering the rotating Earth by an inertial observer looking down to the North Pole at a large distance. Then, they apply a tricked Special Relativity. See the first link for an explanation of the trickery.

For the gravitational difference, they use the time-dependent height term which is explained in the second link.

http://www.conspiracyoflight.com/Hafele/HafeleKeating.html

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

It confuses me that it is freqently said in this thread-the space is Euclidean or not. Does it not the norm definition determine "Euclideanity"? This is then dependent on kind of measurement method of distances which is arbitrary. And if time is added as a dimension we have an abstract inhomogeneous mix that does not exist as a whole but only a mathematical object combinning quantities of two different kind for analysis

Azzam and Valentin,

what is the problem if I refer everything to the center of Earth?

It is the SCHW solution which has to be applied and is successful to a very good accuracy. It is not so accurate and appropriate to apply separately the gravitational contribution and the kinetic contribution to time dilation. The kinetic contribution has to be in any case referred to the center of Earth which is inertial  also for Newtonian Dynamics. It is always the energy per unit mass of each body which counts, referred to a sufficiently inertial reference frame (gravitational field of an orbiting body)

Anyway I agree that local and global adjectives are not appropriately usable or used.

Dear Stefano,

Anyway I agree that local and global adjectives are not appropriately usable or used.

That is because in between there is the uncertainty principle and proponents of relativity want to disappear this principle in macro world. Why quantum and gravity do not merge? Because proponents of relativity can't apply the quantum superposition in gravity in the right way. In this case quantum superposition working as the wave-function and the collapse of the wave-function and in between the uncertainty principle. Quantum superposition is hidden in Gravity because of the objectivity and continuity which is adopted in Lorentz transformation. The uncertainty principle is the connection point between what is local and what is global, and this connection point is hidden in Gravity. So we must distinguish between the motion of an object in constant speed v according to the wave-particle duality, and when I make a measurement for this object at a certain point in space, and the how in this case the wave-function collapse and the uncertainty principle is working.

As I explained before the equivalence principle of Einstein is only fake. The escape velocity of the freely falling object in gravity must be defined as relativistic which is depending on the gravitational potential at any point in space in the gravitational field. Globally I must define between the motion of the particle in the gravitational field where the wave-particle and the uncertainty principle play the rule in case of the motion in nonlinear dispersion according to quantum superposition, as in the light bending by gravity, precession, Shiparo delay and the Pioneer anomaly. And when I make a measurement at a certain point in space, and then the particle is localized at the same point in space in the gravitational field same as in the Pond-Rebka experiment.

Also read this paper J D Franson 2014 New J. Phys. 16 065008

doi:10.1088/1367-2630/16/6/065008

Dear Dr. Quattrini, I presented a problem about the H-K experiment. I do not think this experiment is credible. Please see: 

Is the Hafele-keating experiment credible? 

https://www.researchgate.net/post/Is_the_Hafele-keating_experiment_credible

Dear Yin,

I was a bit confused when I asked this question, because I thought that the HK did just involve one round of the world trip. I did not know that its aim was also to show something related to the twin paradox, but the twin paradox is solved also in SR itself.

Even under the Hypothesys of considering he experiment of HK not well performed, the GPS system works mostly  thanks to the application of GRT nowadays. What is strange though is to notice that the centripetal potential (centrifugal potential) is used and before the 1980's it was a big  mistake not to include it in the calculations.

Basically the HK experiment says that the SR is not applicable whenever gravitation is involved.

 Stefano Quattrini,

The defenders of relativistic theories claim that the experiment performed in 1971 by Joseph C. Hafele and Richard E. Keating on commercial airplanes proves Einstein’s Special and General Relativity theories. The shortcomings of the experiment however undermine the authenticity of its results.

H&K experiment (and GPS computing) support Lorentz’s transformation (LT) instead of Special Relativity (SR).because of using the centre of Earth as basic referential frame for relativistic calculations. In SR referential frames are equal, so time dilation should have been computing by the relative velocity of Observer and Source to each other. To evade ‘twin paradox’ of SR it is necessary to introduce a basic referential frame, but with that the experiment support LT. So it is misleading to claim that the H&K experiment (or GPS) prove SR and explain twin paradox, because they try to prove LT, where there is no ‘twin paradox’.

Strange Consequence: Geocentric Universe?

Nor GPS application, neither the H&K experiment involved the orbiting speed of Earth around Sun when computing relativistic time dilation. This is possible only if there is a stationary electromagnetic field around the Earth, or Ptolemy was right and we live in a geocentric Universe.

The shortcomings of H&K experiment

Atomic clocks are sensitive instruments, influenced by temperature, vibration, humidity, magnetic field etc. Because the drifting rate (measuring deviation) of the atomic clocks were higher then the detected time dilations, the experiment failed to reach the level of authenticity.

"Most people (myself included) would be reluctant to agree that the time gained by any one of these clocks is indicative of anything" J.C. Hafele about the atomic clocks used in his experiment - 1971

Missing calculation of GPS

The H&K experiment triggered more then a dozen similar experiments measuring even the time dilation of cyclists traveling with 30km/h speed. What is needed however is not a speed of a snail against atomic clocks. The Global positioning system consists of 24 satellites which travel round the Earth and send signals from which the Observers can calculate their own positions. The satellites are orbiting with 3874 m/s velocity in about 20 170 km high (R= 26 541 km).

As the satellite orbits, its distance to a point on the Earth changes continually causing frequency change and time deviation for Observer, which can be calculated by the factor of Real Doppler Effect. If there is any relativistic time dilation, it must be over this time deviation (not counting the error factors):

Relativistic Time dilation = Total time deviation – Time deviation of Real Doppler Effect

Doppler Time deviation decreases when the satellite is nearing (the angle of move nears 90 degree) and increases when it moves away. Its accumulation is limited by time delay determined by distance (L/c). Relativistic time dilation accumulates by time so it can be separated from time deviation caused by Doppler Effect. Satellites and space stations could measure accumulated time dilations or the relative velocity of light by measuring its speed while traveling toward Sun, such experiments however weren’t published.

GPS disproves Special Relativity

GPS use Sagnac effect to calibrate the time delay of the arriving signals to the relative move of Observers. This proves that the relative speed of light changes depending on the speed of Observer, which contradicts Special Relativity.

Sagnac effect with the relativistic or other corrections and filters may compensate the missing Doppler factor, but over some level cannot replace it.

-----

The data of the Hafele -Keating experiment:

Starting point: USNO (U.S. Naval Observatory) in Washington DC, latitude: N 38.9

East trip: 65.4 h; Traveled time:41,2 h; avr ground speed 243m/s; avr altitude 8,9km; avg latitude N 34;

(USNO, Dulles, London , Frankfurt, Istanbul, Beirut, Tehran, New Delhi, Bangkok, Hong Kong, Tokyo,, Honolulu, Los Angeles, Dallas, Dulles, USNO)

Time gain: -40ns

West trip 80.33 h; Traveled time:48,6 h; avr ground speed 218m/s; avr altitude 9.36 km; avg latitude N 31;

(USNO, Dulles, Los Angeles, Honolulu, Guam, Okinawa, Taipei, Hong Kong, Bangkok, Bombay, Tel Aviv, Athens, Rome, Paris, Shannon, Boston, Dulles, USNO)

Time gain +275ns

Let’s calculate time dilation ‘dt’ caused by gravity

dt=tgh/c^2 (there are more equation in General Relativity. In non relativistic interpretation this formula gives the velocity change of light(dc) caused by gravity when h

Valentin,

one thing is to predict time dilation according to certain relations and the SCHW solution seems to work.. the other thing is to explain what physically provokes the slow down of the clocks.

@Azzam: in your long post above you state, quite at the beginning:

``In SR referential frames are equal,''

No: only inertial frames are equivalent (which I assume is what you mean by equal). This is precisely what makes the interpretation of the HK experiment a bit difficult: none of the three immediately available reference frames are inertial, so none can be transformed into each other using Lorentz transformations. That is why the measurements in all reference frames are interpreted via an inertial frame, for which unfortunately no time measurements are available.

It might be useful for you to get some kind of reliable information on special relativity.

Valentin> The global result is not the result of only General Relativity calculation!

It is, but HK do not do a complete GR calculation in the Schwarzschild geometry,  as Stefano points out can be done. Instead, since the effects are small, they separate the effect into (i) a special-relativistic time dilatation due to motion relative to the center-of-earth, ignoring the curvature of space-time (i.e. gravity), and (ii) a gravitational time-dilation as predicted by Einstein before GR was completed, ignoring any motion relative to the center-of-earth.

By calculating space-time path lengths directly in the Schwarzschild geometry one would find the sum of these two contribution to lowest non-trivial order, plus (utterly negligible for the HK experiment) higher order corrections as well.

Robert> ... at this point I will take the advice of Proverbs 26:4 ...

I have great sympathy with that, but it does give some association with taking the fifth amendment (and a string of Mafia bosses who once did that in front of congress...).

Anyone out there who can help me understand how Valentin can draw the conclusions he does from what I wrote? Where, and how can I express the matter clearer?

Kare,

Just one thing. What calculated by Einstein in 1911 by using his personal interpretation of the Equivalence principle, regarding the effects of the gravitational force compared with the effects of acceleration, is something very disputable. WIth the same personal interpretation he predicted the Red shift as a consquence of gravitational potential of photons, not instead as a consequence of the different gravitational potential of the masses of emission and absorption.

He managed to predict two effects extrapolating something, the Eotvos equivalence principle, unproperly, but the actual relations  came out approximately right.

Valentin,

if you consider the Schwarzschild solution which links two different regions of space, you get together a relation which includes both effects gravitational effect and kinematical effect. Actually the kinematical effect is transformed in a "centripetal potential" (equivalent to a Newtonian centrifugal potential) and is summed up to the pure gravitational potential of the position calculated from the center of the planet. It is a good way to account for the effects of the angular momentum which are present and undisputable and otherwise would be lost using only the linear contribution of special relativity and the direct consequence of a static contribution of the time dilation between two radial distant points.

Valentin> gravitational "red shift" effects, which are supposed to be calculated in a Schwarzschild geometry already

ignoring any motion relative to the center-of-earth. 

Valentin> those effects would be less than the total result calculated in a Schwarzschild geometry (based on the path lengths)

I did not say their sum would be less. I said that there will be a completely negligible correction to their result (slightly positive or negative). The exact Schwarzschild geometry expressions, for objects in motion relative to its center, are given by messy integrals (which would provide difficult-to-decode information to the readers of Nature). It makes much more sense to publish the simpler expressions, which are of sufficient accuracy.

Valentin> Did anybody actually do and write such a Schwarzschild solution calculation for that H-K experiment?

I am sure it has been given as a simple exercise in zillions of GR classes throughout the universe (and I seem to remember sometimes by me). I will post a pdf with the calculation here later. 

Dear Stefano,

Now you see my theory explains exactly the H&K experiment. And in law velocities it agrees with relativity of Einstein. The interpretation of my theory to H&K is considered as an approximation  for the relativity theory of Einstein how explains H&K experiment, you said; You said "It is the SCHW solution which has to be applied and is successful to a very good accuracy." ...That's ok and I agree with you. But also I reached to exact solution  according to my theory to light bending by gravity and precession same the solution of GR which is depending on SRT, in case of weak gravitational field, but by different equivalence principle and transformation. Now according to Einstein's GR, quantum theory and gravity do not merge, and now we can understand why. While according to my equivalence principle and my transformation they are merge. According to relativity, local and global adjectives are not appropriately usable or used as you said, and now we can understand why. But according to my theory they are appropriately usable and used. 

The consequence of the equivalence principle of Einstein is depending on the strength of the gravitational field, while my equivalence principle depending on the potential. So there is no any contradiction between the result of the solution to H&K experiment and my equivalence, But the solution to H&K experiment which is considered as an approximation for SRT to solve the H&K experiment  in law velocities is completely in contradiction with the core of the equivalence principle of Einstein's GR, because the equivalence principle of Einstein depending on the strength of the field.

Now according to this paper http://iopscience.iop.org/article/10.1088/1367-2630/16/6/065008/meta

Franson calculated that, treating light as a quantum object, the change in a photon's velocity depends not on the strength of the gravitational field, but on the gravitational potential itself. However, this leads to a violation of Einstein's equivalence principle, and that agreed completely with my equivalence principle depending on the potential, and how also I interpreted H&K experiment according to my transformation.

F. Leyvraz,

This is precisely what makes interpretation of the HK experiment a bit difficult. 

No. The interpretation of H&K is not difficult. It is interpreted completely according to my theory in a very simple way. And the solution is not in contradiction with my equivalence principle. it is agreed completely with my transformation and my equivalence principle, and thus by my quantization of gravity.

Now the solution of my theory to H&K is considered as an approximation for relativity theory of Einstein to explain H&K experiment. While this solution is completely in violation with the core of the equivalence principle of Einstein in GR.  Because of that you say interpretation of the HK experiment a bit difficult...That according to relativity of Einstein not my theory. 

You said "It might be useful for you to get some kind of reliable information on special relativity."

But I think it might be useful for you to get some kind of reliable information on Almosallami Theory of gravity. ;)

Also I advice you to review carefully the solution of London-Paris  problem proposed by Valentin Danci in the reference https://www.researchgate.net/publication/277487328_Incorrect_relativistic_comparisons_hide_Special_Relativity%27s_clocks_paradox_-_Diagram

It's very good reference for people who do not understand relativity well.

Data Incorrect relativistic comparisons hide Special Relativity's...

Here is a calculation for an idealized flight around and idealized earth.

Stefano> What calculated by Einstein in 1911 ... is something very disputable

I will pass on that, since I am not (yet) sufficiently interested in the history of science to study the paper in detail.

What I would say is that the redshift formula must have the form used, to avoid the in-principle possibility of making a Perpetum Mobile of the first kind. The background ingredients for this were in place in 1911, in the form of the double Einstein formula, E= h\nu = mc^2 (but perhaps not as firmly accepted in 1911 as now).

If light didn't redshift we could convert its energy to massive matter, which gain energy by falling down in the gravity field, where it can be converted to more energetic photons, which we send back upwards...

Valentin> ω_r = 2π/(23 × 60^2 + 56 × 60 + 4) s^−1 , which is needed for v_r = r_e ω_r ?

How do you manage to insert greek letters and mathematical symbols?

The denominator is the rotation time of the earth, as measured by a clock on the rotating surface of the earth. It is most convenient to evaluate everything in Schwarzschild coordinates, which you may prefer to call an absolute frame. Actually, I (and everyone else) am ignoring the fact that the earth is rotating around the sun, and the sun around the galaxy, and so on. But I made a point of transforming from Schwarzschild time to the north pole clock time. It is mostly a point of principle, since the difference is small.

Valentin> I think those clocks on the ground located anywhere else than the poles would have a different time indication than the clock at North Pole. 

I once thought the same, and even gave a special relativity exercise about how much longer one could live by moving from Trondheim to Guayaquil. But apparently, the dynamics of the earth is such that all clocks at its surface ticks at the same rate. The time dilation correction and the gravity field correction may both vary, but in such a way that the sum is constant. I learned this  from a remark by Neil Ashby (maybe in his Living Reviews in Relativity), and I trust him on this point. It is probably a well known fact (to everyone who knows it well), which can be given a simple and elegant proof which I don't know of. But which may ignore tiny corrections, due to the precense of non-equilibrium features like mountains and valleys.

Valentin> Anyway, my point in all this discussion was that the H&K experiment...

No point of repeating that discussion; I think we have gone through most of that before.

Valentin> rotating in reference to what?

The behavior of the Foucault pendulum indicates that it is with respect to the "fixed stars", but the timescale is too short to say if this means the rotating frame of our galaxy, or  a distinguished frame of the universe itself.

In my calculation I actually made a choice when I selected the Schwarzschild metric (which should be corrected a little bit  -- due to the presence of a rotating earth). But in another world the geometry could instead have been described by another metric, like the Kerr metric. I think it is a dynamical question which might be answered by solving the appropriate Einstein equations, i.e. a quantitative realization of Mach's principle.

Dear Kåre and all,

"Here is a calculation for an idealized flight around and idealized earth. (HKcalculation.pdf)"

Thank you for this wonderful computation.

I have anyway a problem:

Could you tell me how many nanometers both flight traveled? How do you explain the shift? Quantum teleportation?

Thank you again.