Alternative theories being tested by Gravity probe B

[Garth]

Latest June Mission Update from the GP-B team.

Nothing new to report on the results.

This GP-B update is essentially a revised and expanded version of the GP-B press release that we posted in April that tells a more readable and complete story about the goals of GP-B, what we've accomplished to date, the surprises we've encountered and how we're addressing them, and the steps we are taking towards a final results announcement at the end of the year.

1. GP-B SUCCEEDED IN COLLECTING THE DATA TO TEST EINSTEIN'S PREDICTIONS ABOUT GRAVITY

2. THE EFFECTS OF GENERAL RELATIVITY ARE CLEARLY VISIBLE

3. FIRST PEEK AT RESULTS PRESENTED AT APRIL APS MEETING; FINAL RESULTS IN DECEMBER
(geodetic precession = GR to 1% - however present estimate ("hint") of result ~30 mas too high but error is still ~100 mas)

4. THE TWO SURPRISES & THEIR IMPACT ON THE EXPERIMENT

i. Shortly after the gyros were spun up in August 2004, we discovered that the polhode motion of the gyro rotors, which was expected to exhibit a constant pattern throughout the experimental period, was changing over time, significantly complicating the calibration of the gyroscope readout angles.
ii. During the post-experiment instrument calibration testing in August-September 2005, the spin axes of the gyroscopes were found to be affected by certain class of small classical torques, known as "misalignment torques," whose effects must be rigorously separated from the relativity measurements. (Due to electrostatic patches on the rotors and their housing.)

(Italics my text)

5. NEXT STEPS-MOVING TOWARDS A FINAL RESULT
i. Fine calibration of the gyroscope/telescope scale factor
ii. Refining the analysis of the misalignment torques
iii. Extremely precise VLBI measurement data will be substituted for the current 1997 Hipparcos [star] Catalogue values for the proper motion of IM Pegasi.

We continue to wait and see!
Garth

 

[Chronos]

But these minor corrections are just that, Garth, minor. I fail to see how they can affect the conclusions. The results are GR concordant and will remain very much so, IMO.

 

[Garth]

I was just reporting what the GP-B team said at the conference, in the mist of the errors presently being reduced they saw just the hint of a non-GR signal. See http://einstein.stanford.edu/content/aps_posters/APS_talk_Everitt.pdf page 21, you will see the successive error ellipses honing down on a value about 30 mas away from the GR prediction.

Perhaps it was wishful thinking on their part - we shall wait and see!

Garth

 

[wolram]

Does every one consider this test (clean) it seems to me like trying to make some sense out of white noise, i mean it is not like a some number registers on a dial, if the test was repeated with the same results it would be more
convincing.

Or is this the one test that has been done with so much care that no other conclusions are probable.

 

[Garth]

They have a problem, which they freely admit. The presence of this noise almost ruined the experiment, however it is not white noise and the spurious signal can be extracted objectively.

The two unexpected effects are linked. First the electrostatic patches have put an extra torque on the gyro rotors that perturbs them, secondly the energy used up in this perturbation gradually reduces the polhode motion (wobble) making that more difficult to model.

However once they have accurately modeled the geometry of the patch effects, which are different for each of the four gyro rotors, they can subtract that from the precession signals and accurately model the polhode motion. It is this that they are completing at present.

You can read all about it by following the links on their website.

Garth

 

[Garth]

Just to make clear what the present situation is:

(mas = milliarcsec)
The geodetic N-S precession is predicted by GR to be - 6606 mas/yr, however there is a solar geodetic precession N-S component of + 7 mas/yr and the proper motion of IM Pegasi +28 mas/yr to take into account, resulting in a net expected N-S precession of -6571 $\pm$1 mas/yr.

The frame-dragging E-W precession is predicted by GR to be -39 mas/yr, the solar geodetic precession E-W component of -16 mas/yr and the proper motion of IM Pegasi -20 mas/yr to include, resulting in a net expected N-S precession of -75 $\pm$1 mas/yr.

From pages 20 and 21 of Francis Everitt's April APS talk, we find: A series of error ellipses on the N-S v E-W precession plot with centres respectively at (-6584 $\pm$60, -83 $\pm$22 mas/yr) June 2006, (-6597 $\pm$17, -92 $\pm$15 mas/yr) December 2006, (-6595 $\pm$12, -98 $\pm$7 mas/yr) March 2007 and (-6603 $\pm$8, -98 $\pm$7 mas/yr) March 2007.

It was this last reading for the geodetic precession that Francis Everitt reported at his April APS talk. If we also include that 'glimpse' of the E-W precession as well we have net values of:
(-6603 $\pm$8, -98 $\pm$7 mas/yr)
whereas GR predicts:
(-6571 $\pm$1, -75 $\pm$1 mas/yr).

In other words the actual readings are larger than GR predicts by 32 mas/yr in geodetic precession and 23 mas/yr in frame-dragging precession.

However, they reported an overall error, which is still being reduced, caused by residual gyro-to-gyro inconsistencies due to incomplete modeling of ~ $\pm$100 mas/yr.

This renders the present geodetic 'glimpse' as being consistent with GR to within about 1$\frac{1}{2}$%, whereas the frame-dragging precession is at present swamped by noise.

The running now stands:

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Moffat's Nonsymmetric Gravitational Theory (NGT)
4. Stanley Robertson's Newtonian Gravity Theory (NG),
5. F. Henry-Couannier's Dark Gravity Theory (DG).
6. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
7. Kris Krogh's Wave Gravity Theory (WG)
8. Hongya Liu & J. M. Overduin prediction of the http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v538n1/50681/50681.text.html?erFrom=5252751197746712308Guest#sc8 gravity theory (KK).

The predictions are now:

GPB Geodetic gross precession (North-South)

1. GR = -6606 mas/yr.
2. BD = -$(3\omega + 4)/(3\omega + 6)$ 6.606 arcsec/yr. where now $\omega$ >60.
3. NGT = -6606 - a small $\sigma$ correction mas/yr.
4. NG = -6606 mas/yr.
5. DG = -6606 mas/yr.
6. CS = -6606 mas/yr.
7. WG = -6606 mas/yr.
8. KK = -(1 + b/6 - 3b² + ...) 6606 mas/yr. where 0 < b < 0.07.

We await the GPB gravitomagnetic frame dragging gross precession (East-West) result.

1. GR = -39 mas/yr.
2. BD = -$(2\omega + 3)/(2\omega + 4)$ 39 mas/yr.
3. GSCC = -39 mas/yr.
4. NGT = -39 mas/yr.
5. NG = -39 mas/yr.
6. DG = 0 mas/yr.
7. CS = -39 mas/yr. + CS correction
8. WG = 0 mas/yr.
9. KK = -39 mas/yr.

Note: in the above list only the Kaluza-Klein gravity theory (KK) is able to produce a geodetic precession larger (negatively) than GR if 0 < b < $\frac{1}{18}$, (by a maximum of 11.5 mas when b = $\frac{1}{72}$), but it cannot produce a frame-dragging precession larger than GR.

Garth

 

[JonathanK]

About the apparent extra 32 mas/yr - there's a '96 paper by Kenneth Nordtvedt, which shows that the analysis of the lunar laser ranging data done in the '80s also gave a precession slightly greater than the geodetic precession. Nordtvedt's explanation probably wouldn't cover both anomalies, but if he's wrong… I haven't got time to look into it, but Garth, you might want to see if in relation to context the two are equivalent. It would then be a new anomaly.

The paper is "On the 'geodetic precession' of the lunar orbit", Class. Quantum Grav. 13 (1996) 1317-1321.

J.

 

[Garth]

About the apparent extra 32 mas/yr - there's a '96 paper by Kenneth Nordtvedt, which shows that the analysis of the lunar laser ranging data done in the '80s also gave a precession slightly greater than the geodetic precession. Nordtvedt's explanation probably wouldn't cover both anomalies, but if he's wrong… I haven't got time to look into it, but Garth, you might want to see if in relation to context the two are equivalent. It would then be a new anomaly.

The paper is "On the 'geodetic precession' of the lunar orbit", Class. Quantum Grav. 13 (1996) 1317-1321.

J.

Relevant papers are:
Kenneth Nordtvedt, Classical and Quantum Gravity, Volume 13, Issue 6, pp. 1317-1321 (1996)
On the `geodetic' precession of the lunar orbit

The Moon's dynamics in the geodetically rotating inertial frame is intrinsically different from its dynamics in a globally fixed frame, possessing different ratios of lunar motion to solar motion, and of tidal strength to squared solar motion. The correct prescription is that the Moon's orbit in globally fixed coordinates equals a dynamically different lunar orbit determined in the geodetically rotating inertial frame plus additional precession of that orbit as it accompanies the local frame.

and

Kenneth Nordtvedt, Icarus Volume 114, Issue 1, March 1995, Pages 51-62 http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WGF-45NJJ8B-31&_user=10&_coverDate=03%2F31%2F1995&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=be67b5191e845a480f8ca9ad31b08b62

Relativistic corrections to the perigee precession rate are found which include not only 4% enhancement of the well-discussed de Sitter "geodetic precession" term, but also a direct contribution from the solar tidal acceleration which is 10% as large.

Nordtvedt's explanation for the excess precession is solar tidal action on the Moon in orbit around the Earth, which does not apply to the GP-B gyros.

I make two further comments:

1. The analysis of the Moon's orbit is very complicated having to take into account tidal reactions as well as planetary perturbations and other effects. When trying to test for something like the geodetic precession how sure are we that all other effects have been correctly accounted for?

2. All measurements of orbits, geodesics, through empty space cannot reduce a degeneracy between GR and a conformal gravity theory in which the action reduces to that of canonical GR in vacuo.

There is therefore the possibility that the geodetic precession may be equal to GR in such observations as these above yet different from GR for the GP-B gyros. It is this point that has not been taken into account by Kenneth Nordtvedt when he said the experiment was worth doing when it was first proposed in the 1950's and begun in the 1960's, but now it is a foregone conclusion.

If the final results of the two precessions are exactly equal to GR then we can rule out such conformally equivalent gravitational theories.

However if the final GP-B results are different from the GR predictions, while other tests of the geodetic and frame-dragging precessions measuring the orbits of planetary bodies, binary pulsars, or satellites, are equal to the GR predictions, then that would indicate a conformally equivalent non-minimally connected scalar field is at work.

We wait to see.

Garth

 

[JonathanK]

I meant look at the numbers at a shortcut (this can help!). Then only look further if the two discrepancies come out roughly the same, when allowing for orbit differences. But it might be worth waiting for all possible sources of error to be removed from the GP-B data first.

 

[Garth]

This paper on today's physics arXiv claims to correct the GR prediction for the frame-dragging precession: Correction of the Frame Dragging Formula due to the Precession of the Coordinate Axes near a Rotating Body.

The total precession gives the value with respect to chosen coordinate axes, while the precession of the coordinate axes with respect to the distant stars is usually disregarded. We address this problem in two different ways. Firstly, we consider the participation of each particle in the total precession observed from the corresponding particle. Secondly, we find the precession of the coordinate axes and its subtraction from the total precession. Both methods yield the well known value for the geodetic precession and 75% of the well known value for frame dragging effect.

So we obtained the same value for the geodetic precession as predicted by the General Relativity and 75% of the general-relativistic value for the frame dragging effect. In the case of the Gravity Probe B experiment this yields 0.030 milli arc-seconds per year.

Personally I don't believe it; the spin axes of the gyroscopes are Fermi-Walker transported along their geodesics but the basis vectors of the comoving frame are not. They are tied by a pure boost to the PPN coordinate grid, which in turn is expected to be tied to an inertial frame fixed relative to the distant quasars.

Furthermore, the present 'glimpses' of the GP-B frame-dragging result, if anything, are greater than the GR prediction!

Garth

 

[wolram]

Will there ever be closure to this test? i do not mean the scientific impossibility of proof beyond doubt, just doubts have been quashed
to a CL that is acceptable.

 

[Garth]

They originally talked of obtaining an accuracy of 0.1 mas, now I see the quote only to within 1 mas. However, even with that level of accuracy, I think they will falsify many theories, or render their perturbations away from GR too small for those theories, such as BD, to be left any significance.

However of course, as things stand at the present, they could still falsify GR, and then things really would get interesting!

We will have to wait until the end of the year to find out.

Garth

 

[JinHe]

I wrote a paper on the explanbation to GP-B data anormaly as suggested by the figure, www.lighttale.com/opin/fdtif.tif[/URL], which is taken from Dr Everitt's speech at APS meeting in Florida, 2007.

Flat Spacetime Gravity and Prediction on GP-B Data
Abstract: This paper follows the gravitational principles I proposed before: (1) Space and time are perceived and measured only by means of physical processes which are static to reference frames; (2) Freely falling mass in real surroundings always presents gravity and always has the background flat spacetime which were perceived and measured by the mass frame itself if it had approximately zero mass; (3) Spacetime is not curved and the metric form of general relativity (GR) is called refraction metric on flat spacetime which like refraction medium is effective to curve light rays. Similarly we have effective curvature, effective parallel displacement, etc. (4) The refraction metric (gravitational field) of a mass is generally obtained by holonomic or nonholonomic coordinate transformations. These principles are conceptually different from the ones of GR whose formulas of gyroscope precession in weak gravity are heuristically derived by applying a series of coordinate transformations. This paper shows that the application of rotational coordinate transformation is needed. First public peek at Gravity Probe B results (GP- shows that both geodetic and frame-dragging effects are larger than GR predictions by the amount of about 20 mas/yr. It is suggested that the gap can be fixed by applying rotational coordinate transformation. We wait for the final release of GP-B data analysis in the coming December and see if my calculation is confirmed.

Note: I am kindly asking for someone who is willing to endorse my paper on Arxiv publication. Although I gained the right for my Arxiv free-publication I gained a crackpot title in the meantime and the right is deprived of.

 

[Garth]

Although I gained the right for my Arxiv free-publication I gained a crackpot title in the meantime and the right is deprived of.

You actually earned that title when you said in you paper The Faulty Assumptions of the Expanding-Universe Model vs. the Simple and Consistent Principles of a Flat-Universe Model, -- with Additional Prediction on Gravity Probe B Data:

Freely falling particles locally have accelerations of any magnitude and any direction, which also indicates that the gravity can not be locally canceled too.

Freely falling test particles do not "locally have accelerations of any magnitude and any direction"; their accelerations are precisely determined by the Einstein tensor derived from the Riemannian and are equal in the Post Newtonian Approximation to the value in magnitude and direction given by the Newtonian gravitational acceleration at that event in space and time.

In a flat space-time model the geodetic precession is zero but the Newtonian acceleration, which would then be necessary to substitute for the effect of curvature, yields a Thomas precession exactly one half of the GR geodetic precession in the opposite direction. The GP-B result is equal to the GR prediction to within 1$\frac{1}{2}$%, which is within the present error of measurement, it has therefore falsified your theory (that in any case has not been published in a peer reviewed journal) to many orders of sigma. Any further discussion of your theory must be carried out in the Independent Research Forum, having first observed its https://www.physicsforums.com/showthread.php?t=82301.

Garth

 

[JinHe]

You actually earned that title when you said in you paper The Faulty Assumptions of the Expanding-Universe Model vs. the Simple and Consistent Principles of a Flat-Universe Model, -- with Additional Prediction on Gravity Probe B Data: Freely falling test particles do not "locally have accelerations of any magnitude and any direction"; their accelerations are precisely determined by the Einstein tensor derived from the Riemannian and are equal in the Post Newtonian Approximation to the value in magnitude and direction given by the Newtonian gravitational acceleration at that event in space and time.

In a flat space-time model the geodetic precession is zero but the Newtonian acceleration, which would then be necessary to substitute for the effect of curvature, yields a Thomas precession exactly one half of the GR geodetic precession in the opposite direction. The GP-B result is equal to the GR prediction to within 1$\frac{1}{2}$%, which is within the present error of measurement, it has therefore falsified your theory (that in any case has not been published in a peer reviewed journal) to many orders of sigma. Any further discussion of your theory must be carried out in the Independent Research Forum, having first observed its https://www.physicsforums.com/showthread.php?t=82301.

Garth

Dear Garth,

Thanks for your suggestion.
"locally have accelerations of any magnitude and any direction", e.g. Earth, between the magnitudes of -g=-9.8m/ss and +2g=19.8m/ss, which is the correct text as written in Appendix in my astro-ph/0605213. You short-circuited my result.

As for flat spacetime gravity, there are many kinds while your suggestion is that THERE IS ONLY ONE KIND IN THE NATURE!

 

[JinHe]

Dear Garth,
As you suggested we do not talk about my papers.
Let us talk about you suggested problem of Galileo and Einstein universal acceleration in any neighborhood.

Galileo never tested if two masses of different initial speeds share the same universal acceleration locally

Now return to curved spacetime assumption. If there were one set of coordinate system, t, x, y, z, (rectangular coordinates) on curved spacetime then the geodesic motion in terms of the coordinates is
d^2x^i/ds^2 = -\Gamma ^i_jk dx^j/ds dx^k/ds
which is simply:
accelaration = connection times velocity times velocity
which says that local accelerations depends on test particle velocities.
Even though relativists can find their own definitions of velocities and accelerations on CURVED SPACETIME, the above geodesic motion must still hold and two masses of different initial speeds must not share the same universal acceleration locally.

Therefore, Galileo and Einstein universal acceleration imagination is contradictory to the assumption of curved spacetime!

 

[Garth]

This thread is to discuss published theories that are being tested by the Gravity Probe B experiment.

As you suggested we do not talk about my papers.
Let us talk about you suggested problem of Galileo and Einstein universal acceleration in any neighborhood.

NO! PF is not the place to discuss your misunderstanding of GR or to 'push' "Einstein was wrong" ideas.

Garth

 

[JonathanK]

I agree with JinHe over one thing. Sweeping statements about what flat space theories will contain are unhelpful, because they overlook possible individual features. Because GR is a very accurate description, a good flat space (or flat space-time) theory will mimic it closely in one way or another with additional devices, mathematical or conceptual. These make any theory what it is, and you can't assume you know what they'll do - they might even mimic the geodetic effect.

You may not endorse JinHe's paper Garth, but having kindly endorsed mine before it got through peer review, perhaps you'll respond to the point I've made here, which has bearing on this. A precession of the same value as the geodetic precession will arise from flat space if one simply says that the matter in an orbiting object is slowed locally by the same factor as that by which time is slowed in GR. This turns an object (such as a gyro) rather as a stream turns a millwheel, because locally its matter moves at different speeds, at different heights in the field. (But the orbital speed everywhere in the object is the same as at the centre, as in standard gravity.)

Even if you don't check the calculation in the paper "A numerical derivation of the geodetic effect without space curvature", which is at

http://www.podtime.net/sciprint/fm/uploads/files/1178319909Geodetic%20calculation.pdf

please comment on this statement, as what you’ve said relates to it:

A precession of the same value as the geodetic precession will arise from flat space if one simply says that the matter in an orbiting object is slowed locally by the same factor as that by which time is slowed in GR.

Thanks! J

 

[Garth]

Hi Jonathan!

There are three points here, and I also want to publish a correction to my statement in my post #224 above:

In a flat space-time model the geodetic precession is zero but the Newtonian acceleration, which would then be necessary to substitute for the effect of curvature, yields a Thomas precession exactly one half of the GR geodetic precession in the opposite direction.

I posted that too quickly. In fact the Thomas precession of one half of the GR geodetic precession is in the same direction as the GR geodetic precession.

The first point is about JinHe's posts. There are many alternatives to GR out there on the web, the vast majority are 'crackpot' and not only is an enormous amount of time wasted ploughing through them but to do so on PF would be confusing to others who come here to learn what physics is actually all about. That is why there are strict guidelines here. Physics is also all about testing viable alternatives, which is why I started this thread, however the problem is sifting out the wheat, possible viable alternatives to the standard theory, from the crackpot chaff. One clear hurdle is only to consider theories that have passed peer review, which again is in accordance with PF guidelines. On this thread, as there is a clear test, the GP-B experiment, whose results are being published at this time , albeit slowly, I have extended the guidelines to also include papers that have been endorsed for publication on the physics arXiv, this seems to have been accepted by the Moderators, who do a fine job I might add.

Secondly this thread is not about a detailed discussion of these alternatives but rather a compilation of their clear predictions of the outcome of this experiment. But of course there has to be some discussion as here. In a theory without space-time curvature the normal Newtonian gravitational acceleration has to be explained by some Newtonian type gravitational force. This force would accelerate the gyros away (downwards!) from their inertial frame of reference and that acceleration would impart a Thomas precession equal to half the GR geodetic. For such flat space-time theories to equal the GR geodetic precession they would require an extra mechanism to make up this short-fall.

Thirdly about your comment above, it is not true that "time is slowed in GR"; time always passes at the tautological rate of one second per second...

Relativistic time dilation is the result of the path length through space-time, the proper interval, being less along one path between two events than along the geodesic path between them.

Garth

 

[JonathanK]

Sorry the statement I asked you to comment on was rather loosely put - I was trying to keep it short.

Yes, I know about the way time is defined, but mentioned time partly just as a shorthand way of referring to the expression sqrt (1 - [2GM/rc^2]), which in GR is the factor difference between the "timerate" at a given point in the field and at infinity. It's also relevant to the point I'm making that a fundamental expression from GR, if applied in an unexpected way, yields the geodetic effect out of flat space. So there was also an element of showing how little is needed to produce it.

But like you, I posted too quickly - I should have said the curvature component (2/3 of the total effect), rather than the geodetic precession. If one assumes that matter is slowed in flat space by sqrt (1 - [2GM/rc^2]), in addition to any other forces affecting it, then one has explained 2/3 of the geodetic effect. (The other 1/3 has already been explained in other ways, which apply whether space is curved or flat.)

As for the Newtonian force you assume must be needed in a flat space theory, that opens questions about whether the conceptual basis of a theory can mimic GR to the extent of having no acceleration in freefall. It's a rather sweeping statement to say that no theory can possibly do this! I could show you a possible way, but it would be too involved (and might need another pub lunch). But equation 4 in my first paper describes freefall in a new way, and can be checked in about 20 minutes. It gives the speeds all along the trajectory directly, from knowing the speed at a given point.

So anway, the corrected statement I’m hoping you’ll comment on is:

A precession of the same value as the curvature component of the geodetic effect will arise from flat space if one simply says that the matter in an orbiting object is slowed locally by sqrt (1 - [2GM/rc^2]).

Thanks, J

 

[Garth]

I am now going away on conference for a few days, so I cannot give a full response. However, if you can fully emulate the time dilation effect in a fully consistent way then you would get the same component, the question is how could you distinguish experimentally between the two theories? If there is no difference between the two then the GP-B will not be testing your theory against GR.

Garth

 

[JonathanK]

An interferometer with one arm vertical in the field. This test goes right to the heart of PSG. If light on the radial arm travels further from the centre of the field, it has a faster average speed than light on the horizontal arm. As in the Shapiro experiment with a signal grazing the sun, this has a space component and a time component, and they're equal. In PSG their effects add together, giving a different result from GR.

But there are other differences - the slowing of light and matter I mentioned mimics GR very closely in the radial direction, and makes the post-Newtonian corrections. But in the orbital direction GR doesn't have these corrections, and Newton's circular orbit speed equation stays largely unchanged. But PSG has the slowing of light and matter the same in all directions, which leads to very slight differences to solar system orbits, mass values, and measured distances. The differences to orbit speeds aren't noticed for circular orbits, as the central mass is slightly larger than thought. But the more radial motion there is in the orbit, the more noticeable this becomes - as in the hyperbolic orbits of the Pioneer and flyby anomalies (see first paper).

Also the freefall equation I mentioned should be more accurate than anything else - this is potentially testable. It agrees with numbers from Newtonian gravity arrived at via energy considerations to 12 decimal places. (I challenge anyone to guess how it was derived!)

So these provide testable differences between PSG and GR. As far as the GP-B test is concerned, I’m in a similar position to yours with GSCC, but a more accurate calculation than the one I've done for the geodetic effect, perhaps including the slight differences to solar system parameters, might yield a new prediction before the final results come through (in the meantime, perhaps you could put PSG back on the list). Any suggestions for calculations relating to this would be welcome.

Have a good conference, J

 

[JonathanK]

In a theory without space-time curvature the normal Newtonian gravitational acceleration has to be explained by some Newtonian type gravitational force. This force would accelerate the gyros away (downwards!) from their inertial frame of reference and that acceleration would impart a Thomas precession equal to half the GR geodetic. For such flat space-time theories to equal the GR geodetic precession they would require an extra mechanism to make up this short-fall.
Garth

On this PF page from last April

https://www.physicsforums.com/showthread.php?t=167699&page=2

Chris Hillman takes you up on a closely related point. He says only non-gravitational forces produce a Thomas precession, and that "the Thomas term vanishes whenever no non-gravitational forces act on the orbiting object". Let me know if I've missed something, but this seems to remove the problem for flat space theories you've set out.

 

[Garth]

The question is: "What does freely falling mean?"

Chris was expanding on what I said; we were both talking from a perspective based on the Equivalence Principle.

Thomas precession is an effect which arises when a small object moves in a circular orbit by virtue of some non-gravitational force. (Think of a stone whirled around by some schoolchild at the end of a string.)

Gravitational effects may be caused either by an actual force as in Newtonian gravitation theory, or their observed accelerations are the effect of the curvature of space-time as in GR. (In SCC it was a bit of both)

If they are caused by the effects of the curvature of space-time, as in pure GR, then there is no Thomas Precession, if however they are caused by some force, such as Chris' illustration of a stone whirled around on the end of a string, then there is a Thomas Precession.

Thomas Precession is an effect acting on a gyroscope that is being accelerated relative to the local inertial frame of reference.

In a flat space-time theory such as yours, where there is no curvature effect, then gravitational accelerations, which are the effect of actual forces, must cause Thomas Precession.

I hope this helps,
Garth

 

[JonathanK]

It doesn't have space-time, PSG is the gravity part of a theory of time. As I said, the (lateral) conceptual basis doesn't need an object in freefall to be accelerating - and it's the same conceptual basis that led directly to the freefall equation, which gives the right numbers.

Chris Hillman seemed to be discounting all gravitational forces from causing a Thomas precession, including the Newtonian kind you mention, but perhaps he's assuming GR when he says that. J

 

[JinHe]

astro-ph/0604084

Corrected version:
http://arxiv.org/abs/astro-ph/0604084

I expect it is the correct theory of gravity and the correct prediction for Gravity Probe B. If the theory is falsified I will change my career. Anyway there is small typo problem:
Formula (8): must be: M/2rc^2
Formula (10): must be: M(v/c)^2/2r^2

 

[Garth]

Okay Jin, as you have published a eprint on the physics ArXiv in which you quote a definite prediction, I shall include it in the list for falsification, or otherwise, when the final results are published at the end of the year. From your paper I conclude you call your theory "Absolute Relativity", which I shall use as its name here in this thread.

I must admit I am suspicious of your paper, going as it does from a flat-spacetime model of gravitation to derive a 'Bohr atom'-type model of the solar system, complete with a prediction of planetary SMAs similar to Titus-Bode's law, however we will let that pass for the moment...

The main objection is that I do not see a full calculation of the GP-B results, except the mention at equation (15), in particular I see no mention of Thomas precession, which must be there in a flat-spacetime theory if Special Relativistic effects are being accepted. However, from the introduction we have:

First public peek at GP-B results shows that both geodetic and frame-dragging effects are larger than GR predictions by the amount of about 25 mas/yr (see Figure 1 which is taken from Everitt (2007)). It is suggested that the gap can be covered by applying the above coordinate transformation, i. e., adding the motional gravity. We wait for the final release of GP-B data analysis in the coming December and see if my calculation is confirmed.

indeed...
So we will take the AR prediction as 'GR + 25 mas' in both the geodetic and frame-dragging measurements.

Note: mas = milliarcsec.

So we now have;
The geodetic N-S precession is predicted by GR to be - 6606 mas/yr, however there is a solar geodetic precession N-S component of + 7 mas/yr and the proper motion of IM Pegasi +28 mas/yr to take into account, resulting in a net expected N-S precession of -6571 $\pm$1 mas/yr.

The frame-dragging E-W precession is predicted by GR to be -39 mas/yr, the solar geodetic precession E-W component of -16 mas/yr and the proper motion of IM Pegasi -20 mas/yr to include, resulting in a net expected N-S precession of -75 $\pm$1 mas/yr.

From pages 20 and 21 of Francis Everitt's April APS talk, we find: A series of error ellipses on the N-S v E-W precession plot with centres respectively at (-6584 $\pm$60, -83 $\pm$22 mas/yr) June 2006, (-6597 $\pm$17, -92 $\pm$15 mas/yr) December 2006, (-6595 $\pm$12, -98 $\pm$7 mas/yr) March 2007 and (-6603 $\pm$8, -98 $\pm$7 mas/yr) March 2007.

It was this last reading for the geodetic precession that Francis Everitt reported at his April APS talk. If we also include that 'glimpse' of the E-W precession as well we have net values of:
(-6603 $\pm$8, -98 $\pm$7 mas/yr)
whereas GR predicts:
(-6571 $\pm$1, -75 $\pm$1 mas/yr).

In other words the actual readings are larger than GR predicts by 32 mas/yr in geodetic precession and 23 mas/yr in frame-dragging precession.

However, they reported an overall error, which is still being reduced, caused by residual gyro-to-gyro inconsistencies due to incomplete modeling of ~ $\pm$100 mas/yr.

This renders the present geodetic 'glimpse' as being consistent with GR to within about 1$\frac{1}{2}$%, whereas the frame-dragging precession is at present swamped by noise.

The running now stands:

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Moffat's Nonsymmetric Gravitational Theory (NGT)
4. Stanley Robertson's Newtonian Gravity Theory (NG),
5. F. Henry-Couannier's Dark Gravity Theory (DG).
6. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
7. Kris Krogh's Wave Gravity Theory (WG)
8. Hongya Liu & J. M. Overduin prediction of the http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v538n1/50681/50681.text.html?erFrom=5252751197746712308Guest#sc8 gravity theory (KK).
9. Jin He's http://arxiv.org/PS_cache/astro-ph/pdf/0604/0604084v5.pdf theory (AR).

The predictions are now:

GPB Geodetic gross precession (North-South)

1. GR = -6606 mas/yr.
2. BD = -$(3\omega + 4)/(3\omega + 6)$ 6.606 arcsec/yr. where now $\omega$ >60.
3. NGT = -6606 - a small $\sigma$ correction mas/yr.
4. NG = -6606 mas/yr.
5. DG = -6606 mas/yr.
6. CS = -6606 mas/yr.
7. WG = -6606 mas/yr.
8. KK = -(1 + b/6 - 3b² + ...) 6606 mas/yr. where 0 < b < 0.07.
9. AR = -6631 mas/yr.

We await the GPB gravitomagnetic frame dragging gross precession (East-West) result.

1. GR = -39 mas/yr.
2. BD = -$(2\omega + 3)/(2\omega + 4)$ 39 mas/yr.
3. GSCC = -39 mas/yr.
4. NGT = -39 mas/yr.
5. NG = -39 mas/yr.
6. DG = 0 mas/yr.
7. CS = -39 mas/yr. + CS correction
8. WG = 0 mas/yr.
9. KK = -39 mas/yr.
10. AR = -64 mas/yr.

We wait for the end of the year!

Garth

 

[JinHe]

GPB September update arrived!

I am earnest to let you know but I have not read the detail.

 

[Garth]

No new results to report yet, MISSION UPDATE — SEPTEMBER 2007

In the last three and one half months, we have made significant progress in understanding and addressing both surprises, as well as combining the insights generated by both the geometric and algebraic methodologies towards a final result.

For example, the trapped flux mapping has now been completed for all four gyroscopes and results processed for each throughout the year. One very remarkable result is that we have succeeded in improving by a factor of ~500 the determination of the polhode phase and angle for each gyroscope throughout the duration of the experiment. In particular, the polhode motion for each gyro is now “phase-locked” and known to 0.1 radian (6 degrees) over the course of the experimental year.

As a result, a previous discrepancy between the scale factor calibration computed by the geometric and algebraic methods has been completely eliminated, and these two scale factor determinations are now in full agreement, within the current limits of measurement.

Furthermore, the improved knowledge of the polhode phase has laid the foundation for greatly improved determinations of the patch-effect torques. One of the intriguing puzzles at an earlier stage of the analysis was that the clocking of the gyroscope housings with respect to the rolling spacecraft frame appeared to vary with time, and from gyro to gyro, in a manifestly unphysical way. In other words, the rolling spacecraft is like a flywheel, and the gyro readout planes are very stably locked to it, so there cannot be any physical variation…yet, such variation appeared to be present in the data. Fortunately, the improved polhode phase determinations have effectively eliminated this apparent variation. Moreover, this modeling and estimation of the misalignment torque coefficient, which constitutes the main disturbance of gyro motion, has now been improved by a factor of five.

We are now proceeding with a detailed incorporation of the new results and a corresponding derivation of improved relativity results for review with our Science Advisory Committee (SAC) and with NASA in preparation for our 17th SAC meeting, which is scheduled here at Stanford on the 2nd of November.

Progress continues - but slowly!

Garth

 

[yuiop]

Hi,
I have a perhaps niaeve question about time dilation with respect to the GP-B experiment.
As I understand it, a clock on the probe would gain time due to reduced gravitational potential at high altitude and lose time due to the motion of the North/South orbit with respect to a clock in a ground station at one of the poles. I am curious if there any time dilation effect due the frame dragging of the Earth's gravitational field as the probe passes over the equator. On first inspection of Hafele/ Keating type experiments a clock does not appear to affected by the relative motion of a gravitational field. In the H/K experiments a clock on the ground that is stationary with respect to the gravitational field is slower than a Westbound clock and faster than a Eastbound clock. In other words the clocks only seem to gain or lose time due to rotational motion relative to a distant "fixed" star and are indifferent to the Earth's gravitational rotation. So does frame dragging affect time dilation or does it only affect gyroscopic precession?

 

[Garth]

Hi kev!

Time dilation does not affect the E-W frame-dragging precession. It does not even depend on the orbital velocity, only on the properties of space-time (the theory) and the angular momentum of the Earth.

Garth

 

[yuiop]

Hi Garth. The angular momentum effect you mention is new to me. Are you referring to angular momentum of the Earth about its own axis, or of the Earth about the Sun, or both?

What difference would you expect to see in elapsed time per orbit (as measured by a clock aboard the sattelite) with:

A) No sidereal rotation of the earth.
B) Earth rotating normally.

How would the elapsed times compare to a clock at the same altitude on an imaginary huge tower at the North pole? (The tower clock is mounted on a counter-rotating platform that cancels out the East-West rotation of the Earth.)

 

[Garth]

In GR it is the Earth's angular momentum that quantifies the dragging of space-time around the spinning Earth, which causes the E-W effect called the frame-dragging precession or Lense-Thirring effect.

Differences between different theories in the elapsed time on-board the satellite do not affect their frame-dragging precession predictions, as I said, but they do affect the predicted geodetic precession; this is one effect being tested by that N-S precession.

As such your second and third questions do not have anything to do with this thread and should be asked on the S&GR forum, however a brief comment would be that a spinning Earth affects the diagonal component g_0j of the metric and should slightly reduce the on-board proper time elapsed over one orbit.

$$g_{0j} = -2\epsilon _{jkl} S^kx^l/r^3$$

In the case of the Earth's spin I would guess that this effect would be too small to be detectable.

Garth

 

[Garth]

We now have an amendment to F. Henry-Couannier's Dark Gravity Theory (DG).
THE DARK GRAVITY MODEL PREDICTIONS FOR GRAVITY PROBE B.

We found that the dark gravity model predictions crucially depend on the number of privileged coordinate systems leading to two different kinds of scenario. In any case however the geodetic effect is the same as the one in General Relativity. In case we have one single preferred frame (the CMB restframe), no frame dragging is expected. Instead a preferred frame effect arises as a periodic angular precession with a one year period, with amplitude:
$$\delta\theta_{PF} \leq 0.04$$′′
well reachable with the experimental accuracy (5.10⁻⁴′′/year) of the Gravity Probe B experiment. In case the privileged frame is a local one, centered on the solar system, the privileged frame effect will be an order of magnitude below but still reachable with GPB. On the other hand, we find that in case there is a multiplicity of comoving privileged coordinate systems, one for each space-time elementary volume, we have the same Post Newtonian predictions as in GR for the gravitomagnetic effect.

Frederic is obviously hedging his bets!

I am also removing the Absolute Relativity theory as there has been no published calculation of the previously included prediction.

So the running now stands:

Note: mas = milliarcsec.

The geodetic N-S precession is predicted by GR to be - 6606 mas/yr, however there is a solar geodetic precession N-S component of + 7 mas/yr and the proper motion of IM Pegasi +28 mas/yr to take into account, resulting in a net expected N-S precession of -6571 $\pm$1 mas/yr.

The frame-dragging E-W precession is predicted by GR to be -39 mas/yr, the solar geodetic precession E-W component of -16 mas/yr and the proper motion of IM Pegasi -20 mas/yr to include, resulting in a net expected E-W precession of -75 $\pm$1 mas/yr.

From pages 20 and 21 of Francis Everitt's April APS talk, we find: A series of error ellipses on the N-S v E-W precession plot with centres respectively at (-6584 $\pm$60, -83 $\pm$22 mas/yr) June 2006, (-6597 $\pm$17, -92 $\pm$15 mas/yr) December 2006, (-6595 $\pm$12, -98 $\pm$7 mas/yr) March 2007 and (-6603 $\pm$8, -98 $\pm$7 mas/yr) March 2007.

It was this last reading for the geodetic precession that Francis Everitt reported at his April APS talk. If we also include that 'glimpse' of the E-W precession as well we have net values of:
(-6603 $\pm$8, -98 $\pm$7 mas/yr)
whereas GR predicts:
(-6571 $\pm$1, -75 $\pm$1 mas/yr).

In other words the actual readings are larger than GR predicts by 32 mas/yr in geodetic precession and 23 mas/yr in frame-dragging precession.

However, they reported an overall error, which is still being reduced, caused by residual gyro-to-gyro inconsistencies due to incomplete modelling of ~ $\pm$100 mas/yr.

This renders the present geodetic 'glimpse' as being consistent with GR to within about 1$\frac{1}{2}$%, whereas the frame-dragging precession is at present swamped by noise.

The running now stands:

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Moffat's Nonsymmetric Gravitational Theory (NGT)
4. Stanley Robertson's Newtonian Gravity Theory (NG),
5. F. Henry-Couannier's Dark Gravity Theory (DG).
6. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
7. Kris Krogh's Wave Gravity Theory (WG)
8. Hongya Liu & J. M. Overduin prediction of the http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v538n1/50681/50681.text.html?erFrom=5252751197746712308Guest#sc8 gravity theory (KK).

The predictions are now:

GPB Geodetic gross precession (North-South)

1. GR = -6606 mas/yr.
2. BD = -$(3\omega + 4)/(3\omega + 6)$ 6.606 arcsec/yr. where now $\omega$ >60.
3. NGT = -6606 - a small $\sigma$ correction mas/yr.
4. NG = -6606 mas/yr.
5. DG = -6606 mas/yr.
6. CS = -6606 mas/yr.
7. WG = -6606 mas/yr.
8. KK = -(1 + b/6 - 3b² + ...) 6606 mas/yr. where 0 < b < 0.07.

We await the GPB gravitomagnetic frame dragging gross precession (East-West) result.

1. GR = -39 mas/yr.
2. BD = -$(2\omega + 3)/(2\omega + 4)$ 39 mas/yr.
3. NGT = -39 mas/yr.
4. NG = -39 mas/yr.
5. DG = -40 mas/yr., or -4 mas/yr., or -39 mas/yr.
6. CS = -39 mas/yr. + CS correction
7. WG = 0 mas/yr.
8. KK = -39 mas/yr.

We continue to wait for Christmas!

Garth

 

[LeBourdais]

Hello Garth,

I just want to say that you deserve my deepest respect. You have accepted the experimental verdict and I know that it is not easy. I wish that someday you make a big discovery, you really deserve it.

Paul