@ Low/Cornwall

They have tested the effects of gravity on time dilation with just 1 meter elevations to a great degree of accuracy, (yes just 1 meter). The question arises have they done this with STR, and gravity clearly could easily be accounted for.

Equally well at low alititudes the effects of STR outweight the effects GR greatly

Andrew, as we discussed elsewhere, the geoid which defines "mean sea level" is a surface where the gravitational potential combines with the "centrifugal force" to produce a surface on which all clocks run at the same rate. You cannot separate the two effect since geodesics are a consequence of both.

Yes I agree, but you see if you read New scientist (last edition), they say there should be a diffrence and experiments they say have proved it - so  who  is right.

I haven't seen the article but that is certainly true. Also the GRACE spacecraft measure the Earth's gravity dynamically, storms and seasonal changes in sea water can be detected, see for example the animation on the right hand side of the link.

https://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment#Measurement_principle

Measurements performed with the Laser Sagnac interferometers show that the angular frequency of Earth rotation changes on a continuous basis reflecting tidal motions of the atmosphere and other meteorological phenomena. The time dependent form of the gravity field (described by the geoid shape) is thus very complicated. The corrections to the clocks rates due to the atmospheric processes are much finer than those resulting from earthquakes and readjustment of mass distribution at the surface of our planet. They are, however, becoming important with the increasing demand on accuracy of clock synchronization.

There are indeed numerous papers on this subject, one of the possible examples is the recent text places at arXiv

https://arxiv.org/pdf/1209.2889.pdf

We should recognize, however, that the shape of geoid is not fixed. It is varying in time; this fact is confirmed by the measurement performed with laser ring Sagnac interferometers. They offer several advantages in continuous monitoring of the rotation rate.

Thank you very much for this paper, it is very well written. I still have some doubts about applying the special relativity theory in the rotating frame of reference. The text below

http://inspirehep.net/record/927038/files/arXiv%3A1109.2488.pdf

explains some of the sources of my doubts.

In conclusion when addressing the problems of clock rates on the rotating planet we should consider the General Theory of Relativity.

Dear Andrew Worsley,

Velocities on the surface of the Earth at different latitudes are ranging from 0 km / h at the poles to about 1666.7 km / h at the equator. In practice, these velocities are treated according to the principles of Newtonian physics. In this case do not appear differences in the real time clocks at different latitudes. If we treat these speeds according to the principles of Einstein's physics, very small differences real time clocks (which can be calculated) would occur. I think you'd be a problem to such differences confirmation in the measurements, because they should be used extremely sensitive clocks, for which I have no information whether they exist.

Regards,

Milivoj B. Gavrilov

@remi/george/Low/all

Herein the article in New scientist that states clocks should go slow at the equator compared to the Norht Pole and that there should be 5 nanaoseconds diffrence beteween London and Paris.

https://www.newscientist.com/article/mg23331184-900-atomic-clocks-make-best-measurement-yet-of-relativity-of-time/

They quote a  (best ever) paper that gets a null result, and then say this upholds the results.

So can anybody explain this contradiction 

@Andrew/Adrian/and all

I was always under the impression that in a rotating frame we have to use the general relativity. In summary, I would like to propose the following answer:

1. In order to assure the synchronization of clocks at two different points on the surface of a rotating triaxial ellipsoid with the accuracy required by GPS and telecommunication applications, we have to consider simultaneously the differences in both speed and geopotentials.

2. Sometimes there are attempts to consider both effects separately...

3. Formally, it is not possible to separate the effects of speed difference and geopotential difference; both effects are interconnected through the nonlinear tensorial Einstein equation.

4. With the increase of demand on accuracy of the synchronization, we have to include a more detailed information about the structure of a gravity field.

@ Low/ Adrian/George

So that means there is a time difference, yes or no some would staunchly disagrre

Difference between what? You need to be more specific. If the planet was all water, clocks would run at the same speed everywhere on the surface even if the planet was rotating. The real planet has rock and water and both flow. You also need to be clear about whether you mean on the surface or at fixed radius from the centre. Bottom line is that the theory works perfectly and allows the dynamic maps produced by GRACE to show the actual gravitational field.

That is true, but also the natural variations of the earth's gravitational field are sufficiently large that they can be measured from space, an amount much larger than the uncertainties in the tests of GR under controlled lab conditions. If Andrew specifies the exact conditions, then GR will give an unequivocal answer but "do they vary" is too woolly for a "yes or no" answer.

@George/LOW/All

https://www.google.co.uk/search?q=gravitational+geodesic&rlz=1C1OPRB_enGB569GB591&espv=2&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj2oLCl0ZXTAhWpLMAKHePnCCcQ_AUIBigB&biw=1154&bih=790#tbm=isch&q=Eatrth+graviratuional+geod&imgrc=i4Lm0Kpvg7RFiM:

The problem is this, we can confirm the exact time within 1 meter for gravitational time dilation on Earth, but no one seems to be able to do that with STR. There seems to be a huge problem with STR.

The geoid with gravitation is this (see attached) -and that is another huge problem it is not extended in width at the the equator. So does not compensate for the latitude difference in time which is expected from STR

AW: The geoid with gravitation is this (see attached)

The images show how the actual field differs from the oblate spheroid you would expect from a rotating sphere.

AW: and that is another huge problem it is not extended in width at the the equator.

It shouldn't be, the effect of the velocity of rotation is included in the mean reference surface, so what you see is just the local differences from that due to variable density, weather, mountains, etc..

I think the problem is that what you are looking for is so obvious, it is already accounted for.

@ george.

You seem to contradict yourself, at one point you agree there is no time difference between the North pole and the equator and go to great lengths to explain why, and then when New scientist says there is a time difference between the North pole and the equator( and produces null results) you say the answer is obvious.

Then the Earth is oblate, and when it is demonstrated that the geoid is not, then this is all taken account of. The problem is obvious you cannot answer the question  and you you just go with what the establishment tells you.

AW: New scientist says there is a time difference between the North pole and the equator( and produces null results)

Perhaps you should read the paper that New Scientist reported, the link takes you to the abstract and the "PDF" link at the top right gives you the full paper.

They compare the frequencies at the different sites but they then look for a diurnal variation in the difference signal. The paper clearly states that equation (5) includes the static gravitational effect but since they are looking at variations, that cancels out, and they also remove the effect of the tides (more water implies higher gravity) which peak twice a day. The result that is null (or to be accurate less than 1.1*10-8)is a once-per-day component of the variation.

AW: Then the Earth is oblate, and when it is demonstrated that the geoid is not, 

The geoid is oblate, but the real planet has mountains and seas. The maps you posted show how the actual field deviates from the hypothetical oblate spheroid.

AW: .. you just go with what the establishment tells you.

No, I read the actual scientific paper, you've just guessed based on the vague popularisation.

https://arxiv.org/abs/1703.04426v1

No, I read the paper and am able to come to no real conclusion. They do not say whether there  is the expected 5 nanosecond delay, only that they get a null result. Do they or do they not get a five nanosecond delay.

 Given that they are able to get gravitational time dilation to 1 meter, this suggests that there is some obfuscation on STR, but not GTR.

Is there is no conclusion to the question? 

AW: They do not say whether there is the expected 5 nanosecond delay,

Andrew, they do say that they get the "static" difference but they are testing Lorentz Invariance, not testing gravitational dilation by repeating the Pound-Rebka experiment.

AW: only that they get a null result.

They get a null result for violation of Lorentz Invariance to an accuracy of ~10-8 which was the aim of the work.

AW: Do they or do they not get a five nanosecond delay.

They do but it is not what the experiment was performed to test so they did not spend time doing a full error analysis of that, the experimental method was designed to make it irrelevant to what they were measuring.

AW: Given that they are able to get gravitational time dilation to 1 meter, this suggests that there is some obfuscation on STR, but not GTR.

That is nonsense, the paper is clear and unequivocal.

AW: Is there is no conclusion to the question?

Yes, the conclusion is that you do not understand how experiments are performed in practice, have you never done any lab work?

@Andrew Worsley

After reading the original paper I see that it is indeed a very well written experimental study. 

I have, however, some questions of purely theoretical nature concerning eq. (6). It will be useful indeed if the corresponding mathematical expressions for $\vec(u}_A$ and $\vec(u}_B$ are written explicitly. With the present notation it is not easy to evaluate the approximation used to describe violation of the Lorentz Invariance.


This doubt rules in favor of your opinion concerning the SRT term. 

Ideally all the transformations used to get eq. (6) could be written in a form of the superposition of rotation operators.

The general relativity term in eq. (5) seems to be fine but the explicit form of the time dependent Geopotential will greatly facilitate reading of this text.

@Janusz,

Thanks for your comment.

I am trying to develop an alternative to the principle of relativity which I wiil term "the principle of equivalence". The basis of which is this, that dark energy exists and the individual components are going at the speed of light (which is a constant to all observers) hence no preferred state of motion can be attributed to it.

Thye corollary is that all stable gravitional bodies that are in balance with dark energy ( but not every observer), wiil view themselves as having zero motion.

@Andrew,

Thank you for presenting an excellent question.

I'm still working on mathematical details in order to derive equation (5) for $\Delta$ in the analytical form. It will contain all information about the time dependent gravity of our planet and the relations which according to the original paper are calculated using the software described as SOFA. I would definitely prefer to deal with the analytical equations instead of putting my trust in a computer program. Despite some extensive searches I was not able to find the corresponding derivations.

Your idea is interesting; I agree with the comment that it is better to avoid using the term "equivalence principle" because it is associated with the philosophical foundations of General Relativity. It is not clear, however, how you can define the gravity field for objects moving with the speed of light?

For all accounts you can treat treat GTR as separate from STR and time depedency separately from space in  GTR as from the link.

7). It does not offer infinite time dilation at the event horizon,

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

Article Finite Gravitational Time Dilation In Black Holes Using Dyna...