Dear Thierry,

Finally I would like to mention that the EEP is only a principle of conservation of energy balance

time dilation is a way to maintain the energy balance in special and general relativity. EEP is just a trick to mess the things up.

Stefano - as i am unfamiliar with this particular experiment - what is the relevance of it over i.e. recent results by Dr. Chin-Wen Chou as i will attach ? With modern clocks Dr. Chou measured clocks in his laboratory ticking slower when only being centimeters lower than other clocks . Is that the topic in your concern ?

What is your statement ?

Dear Hanna,

no problem with the clocks which change frequency with height, thanks God technology reached a good point and in this regards GR is right.

My first concern is that in the GP-A (Gravity probe A) experiment 1976 Vessot and Levine made a mistake in the model adopted for the frequency shift of the oscillators. They supposedly arrived to this model to measure the frequency shift through their chain of cancellation :

Delta F/f0 = (Delta(Phi)/c2- beta2/2)

but what results from the right calculation their model was:

Delta F/f0 = [1/(1+beta)] *(Delta(Phi)/c2- beta2/2)

and the term, is a doppler one accounting for an average of 20 parts of a million.

The second concern which does not involve their experimental error are illustrated at page 14 of my script

Article NASA GP-A REVIEW UPDATED VERSION

and it is written in the page attached, extracted from the NASA report.

The conclusion is that the EEP is fake since is at variance with the energy conservation. They made several mistakes in that page in order to match the predictions of the EEP.

INFACT:

According to EEP, the contribution of the Redshift due to speed (v2/2) and the contribution of the gravitational potential should be the same. In that case the output of the experiment should be identically 0, which is not.

The redshift "they seek to test" is the difference of potential between probe and earth.

What is clearly true is instead that the term (v2/2) is the same as the difference of potential energy between the apogee and the probe.

So basically they failed to apply the energy conservation principle!!!!

And for this reason it is lapalissian that the EEP is trash!!!

Thank you for the explanation Stefano . A theory must be right in all regards or it is wrong . Whilst I am unfamiliar with the experiment in question and its results , i will give your own article a read . And i think you already know my take on the equivalence principle . I also am familiar with misapplying theories to match experimental results .. actually that's done in other arenas of science also - even biology - it must be a common phenomenon associated to humanity . But that said - i have not read/understood this problem yet - so i cannot judge . For myself i need to make first steps first - if ever :/ .

I just remember - didn't you say somewhere the experiment was repeated without repeating the mistakes ? So did experiment match prediction then ?

Dear Mohamed

"I thing, locally, the equality Mg = Mi is indisputable. "

more than locally, statically or stationary (as for the planets)... as it was in the Eotvos experiment.

Dear Thierry,

the paper you reported is the same reported in the question of my thread, at the bottom if you have the patience to open it thoroughly.

They re-made the GP-A experiment and in that case they did use the correct model for the Doppler cancelling circuit. Although they did not stress the fact that the model adopted with GP-A was the partial cause of the unexprected error.

Dear Thierry,

The main consequence is that the Schw solution is not in agreement with the EEP.

They broke the conservation laws to make these agree. But the one which wins is the schw solution for sure and EEp succumbs..

Thierry,

with the Schw. solution you make the GPS work, with EEP you do not make anything work rather than free fall.

EEP is a tragedy which violates the principles of energy conservation.

Dear Hanna,

" I just remember - didn't you say somewhere the experiment was repeated without repeating the mistakes ? So did experiment match prediction then ? "

yes the data of the experiment with the new model adopted was quite aligned with the prediction of the Schwarzschild(ren) solution in regards to gravitational redshfit and time dilation.

The point is that they continue to say "Our preliminary results agree with the validity of the EEP ", which is not the EEP as WEP and LLI and LPI, but it is simply the verification of the LPI local position invariance.

The experiments can be shown not to comply EEP. Infact what is defined as the redshift term, which identifies the difference between the gravitational potential of the probe is not the same as the v2/2, except than in a particular point which is the null beat point. IN all other cases what is the same as v2/2 is the difference of potential energy between the apogee and the probe. So in this regards the proof of EEP is singled out.

Manuel, could you share this thought experiment with us please? Because whilst i understand energy conservation not as a law but a consequence during physical processes, it is helpful to us to calculate the latter. Hanna

Dear all,

in order to have a more complete discussion on the validity of the EEP I set up the following thread:

https://www.researchgate.net/post/At_variance_with_the_EP_a_la_Einstein_isnt_it_much_more_suitable_instead_the_equivalence_between_a_centrifugal_field_and_a_gravitational_one

[This response has been transferred from another thread.]

SQ: usual don't make things up to cover your blunders!!!

Stefano, I haven't made any "blunder" whatsoever, the paper says "2.5±70" but you made the mistake of reading it as "70±2.5" when you said:

SQ: the error was in between 72.5 and 67.5 parts per million.

That is wrong, the 68% confidence range is from +72.5 to -67.5 ppm.

SQ: 1) The 2.5 per million is the number written in the final result page, that *you* mentioned

Correct, that is their mean result.

SQ: .. as being my mistake to have reported 25 instead of 2.5 !!!

No, you were the one who quoted 25 ppm several times but I only pointed out that that was the limit due to clock stability alone, I didn't say you mistook that for the result.

SQ: 2) It has nothing to do with the 25 per million uncertainty declared initially, which is the maximum reachable performance for the experiment.

They did not "declare" that value as an achieved performance ever. As you say, they said that was the best they could achieve given the clock performance alone and excluding all the other factors. A great deal of the paper relates to designing the experiment to mitigate those other factors.

GD: Their result had a statistical spread that gave an UNCERTAINTY of 70 ppm.

SQ: yes

4) Why did they look for a reason of the 70ppm when as you say their result was so satisfactory ..

Because it is important that they can explain where the excess noise contribution beyond that of the clocks came from, so that any other researchers looking to improve the test by repeating the experiment should know what areas of the experiment cause the greatest difficulty. This is professional behaviour.

Assuming the clocks gave an error of ±25 ppm and they added other factors as the RMS, those other factors contributed ±65.4 ppm giving a total of ±70 ppm. Those other contributions therefore produced more than twice the noise of the clocks themselves and dominated the end result, so for example using the same rockets but with better clocks would give no improvement overall, it would be a waste of time and money.

SQ: and got the idea that such error was due to a possible anysotropy of the speed of light.

That would have been the most direct interpretation had their result fallen outside the uncertainty. As it was, their result of 2.5 ppm is well within the uncertainty so there was no indication of any anisotropy or any other deviation from GR at all. It provides a way for other researchers to compute the same parameter regardless of their test methods so that different experiments can be compared. Again this is standard professional behaviour.

George,

Infact there are unknown contributions which more than doubled the overall uncertainty of the measurements.

Let's go step by step.

NASA: "we can aim for a maximum sensitivity in the determination of the value of a of 1 X 10-14/4 X 10-10 or 25 parts per million"

the maximum value of the redshift which is calculated according to the gravitational potential at 10K km is 7*10-10 which at the apogee, but around that value the uncertainty is very low.

The average value of the redshift is estimated as 4x10-10

The average accuracy of the clocks in 100secs is between 1.6x10-14 and 7x10-15

which is reasonably approximated as 1 x10-14

hence the ratio gives an accuracy of 25 parts over million only based on the accuracy of the clocks.

The maximum value of 7*10-10 and the minimum value of 1.13*10-10

The 6.8x10-15 is the additional uncertainty on the redshfit, as statistically calculated at page 83, the uncertainty becomes 14*10-15

HENCE: the expected uncertainty, after considering these additional sources of error should now be double than the initial:

50 parts over one million

a) 14/7*10-5 = 2*10^-5 for the highest

b) 14*10-5 = 14*10^-5 for the lowest point

delta f/f = 7*10-10 +/- 14*10-15

and

delta f/f = 1.1*10-10 +/- 14*10-15

NASA: "all frequency errors at the 2 X 10-15 level or greater in our error budgets are considered to be significant"

NASA: "The first-order doppler effect must be accounted for at the 10-9 level if we are to achieve the expected accuracy in the redshift measurement. "

the 2.5*10-10 is given as the average overall value

NASA:" The fact that the microwave signals traverse large distances over which substantial changcs in gravity field occur means that this comparison of oscillators is a measurement of very non-local effects. Furthermore it relies on the assumption of the isotropy of the one-way velocity of light. To predict the behavior of the data from this rather complex system we will assume that the oscillators, electromagnetic Signals, velocities, and gravitational fields are all interacting in the self-consistent manner described by General Relativity "

I can agree that the overall unexpected inaccuracy was not

45ppm as I first calculated but 20ppm.

In other words we do not find in the report a justification of 20ppm

Stefano, try to understand, their result was a discrepancy of just 2.5 ppm against the GR prediction as clearly stated on their page 92. Everything you are arguing about above is only the confidence level, not an "unexpected inaccuracy" and not their result.

If you want to see where that figure comes from, again start with page 92 where it states the "one sigma probability limits" (random error) of 63 ppm and a possible "apparatus bias" (systematic error) of 29.4 ppm. Combine those and you get sqrt(632 + 29.42) = 69.5 ppm which they round to 70 of course.

I've attached the page and highlighted the figures for you.

George,

>

so according to what you say, they should have decleared that they reached the accuracy level of 2.5 ppm.

In other words they should have declared that they managed to confirm GR to 2.5 *10-6

This unfortunately is not the case. They declared the self consistency of the theory to 70ppm as also reported in every publication.

But this is not the point of the discussion we can go on forever.

What is important is the error they made in the model of the cancelling circuit whch is not trivial.

The right model is not the one they presented in 1979 and consisted in the reference model adopted.

They did not take into account an additional term their circuit did not manage to cancel out. In other words the first order Doppler was not totally cancelled out but a significant part remained.

GD: Stefano, try to understand, their result was a discrepancy of just 2.5 ppm against the GR prediction as clearly stated on their page 92.

SQ: so according to what you say, they should have decleared that they reached the accuracy level of 2.5 ppm.

No, they declared that their result was a discrepancy of 2.5 ppm but the uncertainty was 70 ppm

SQ: In other words they should have declared that they managed to confirm GR to 2.5 *10-6

No. The uncertainty means that while their result was 2.5 ppm, the random noise might have been up to 70 ppm so based on their paper we have 68% confidence that the actual value lies in the range +72.5 to -67.5 ppm. Try this page, see if you can follow what I'm saying from here:

https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

SQ: They declared the self consistency of the theory to 70ppm as also reported in every publication.

Yes, exactly, and scientists reading that know exactly what it means. You seem to be confusing the value of 2.5 and the value of 70.

SQ: What is important is the error they made in the model of the cancelling circuit whch is not trivial.

I can't comment without a reference to the paper from which you took the graphic. What you've said about the original paper has been seriously misrepresenting the numbers.

George,

>

the result is nothing but the ratio between the MODEL ADOPTED/CALCULATED

and the output DATA ACQUIRED from the signals and is expressed as

1+ the error

"their average" of the values was not 0 as it should have expected, but 2.5ppm simple as that. That average does not mean anything, what counts is the dispersion of the values.

The 2.5 is a systematic error, while the 70 is the random part.

it is the estimated random noise of the clocks and other measurements which reach 50ppm and something else which cannot be attributed to noise but it was in the final measurements.

the uncertainty is in the interval -67.5ppm and 72.5ppm

the expected range of values of the comparison is

1+ 72.5ppm and

1- 67.5ppm

The discrepancy between the model adopted and the actual model emerges clearly from the following:

a) In the first image it is the model calculated and adopted in the official report of NASA for the GP-A experiment.

b) in the second there is the model of the GP-A experiment re-calculated in 2001

( GRAVITY PROBE A "REVISITED" https://arxiv.org/pdf/gr-qc/0010108.pdf )

c) in the third image there is the model I recalculated in 2014 by considering the simplified version of the problem: trajectory vertical and no motion of earth. I presented the "neglected factor" which is a non cancelled first order doppler.

d) in the fourth image there is the model of the GP-A re-presented in 2017 , in which the neglected factor is present again

(GRAVITY PROBE A "RE-PROPOSED" Probing the gravitational redshift with an Earth-orbiting satellite https://arxiv.org/pdf/1710.10074.pdf )

in b) c) d) the additional term which multiplies the initial forumla appears:

in b) and d) it is (1+beta) (DE moving detector)

in c) it is a Doppler effect 1/(1-beta) (DE moving source)

Hi Stefano,

I think we're nearly there.

GD: The uncertainty means that while their result was 2.5 ppm,

SQ: the result is nothing but the ratio between the MODEL ADOPTED/CALCULATED and the output DATA ACQUIRED from the signals and is expressed as 1+ the error

That is correct.

SQ: "their average" of the values was not 0 as it should have expected, but 2.5ppm simple as that.

Correct again, though you wouldn't "expect" zero error, you expect there to be a deviation because of the noise.

SQ: That average does not mean anything, what counts is the dispersion of the values.

The value of 1+2.5ppm is their actual result so mean a lot. If that had been significantly more than 70 ppm, it would have indicated a possible departure from the theory. As long as it is within the noise, there is no contra-indication, so that is the most important part of their publication in terms of testing the theory.

The standard deviation on the other hand measures the quality of the experiment and is how different experiments are compared and tells us to what degree we can trust the theory.

SQ: The 2.5 is a systematic error, while the 70 is the random part.

No, there you don't quite understand the terms. The 2.5 ppm discrepancy is the result, not one of the error factors. A systematic error is one that applies uniformly to all readings.

For example if the clocks are vibrated, you would expect reading to have some scatter, that's a "random error", and it can be reduced by averaging over a large number of readings. On the other hand, if the clock was very stable but hadn't been calibrated before the experiment, it might be running 10 ppm fast say. That error would apply to every reading so cannot be reduced by averaging, that is a "systematic error". I haven't gone into the paper in depth but looking at the last page, the impression I get is that the 63 ppm quoted is the standard deviation of the data hence the random error while the 29.4 ppm could be their systematic error based on 25 ppm for the clock drift and about 15 ppm for other factors.

GD: the random noise might have been up to 70 ppm so based on their paper we have 68% confidence that the actual value lies in the range +72.5 to -67.5 ppm.

SQ: it is the estimated random noise of the clocks and other measurements which reach 50ppm and something else which cannot be attributed to noise but it was in the final measurements.

I'm not sure what you mean by that or where you got the 50 ppm figure, they say clearly that the 70 ppm is the combination of 63 and 29.4.

SQ: the uncertainty is in the interval -67.5ppm and 72.5ppm the expected range of values of the comparison is 1+ 72.5ppm and 1- 67.5ppm

Yes, that's right, and the actual value measured was 1+2.5 ppm. As bare numbers that is:

1 sigma range (systematic and random) : 0.9999325 to 1.0000725

Measured : 1.0000025

Given the 70 ppm uncertainty we can construct the ranges for deciding on the outcome

1 sigma range to confirm the theory : 0.999930 < x < 1.000070

5 sigma range to falsify the theory : x < 0.999650 or x > 1.000350

Anything between those ranges would be "inconclusive". Obviously the actual result of x = 1.0000025 is in the 'confirm' band.

Thanks for the additional references.

SQ: in b) c) d) the additional term which multiplies the initial forumla appears:

SQ: in b) and d) it is (1+beta) (DE moving detector)

SQ: in c) it is a Doppler effect 1/(1-beta) (DE moving source)

Note that for beta

George,

>

yes, infact I've never said that the experiment should give a worse prediction than 70ppm, but on the contrary, by considering the accurate model, without that error, in the model the uncertainty might be lower.