Alternative theories being tested by Gravity probe B

[henryco]

As I have said there have been other ways of making the geodetic and frame dragging measurements, such as the dynamics of the double pulsar, but these have theoretical degeneracies in them, so the question is still open.
Garth

Hello Garth,

Do you have a reference on this or can you tell us about this degenerescence or on how the frame dragging was measured with the double pulsar: is it the effect of the spin of the compagnion star that is measured on the pulsar trajectory or spin period or something else?

thanks
F H-C

 

[Garth]

All these tests to date have only measured the trajectories of planets, stars and photons through a vacuum and compared them with the geodesics of GR.

Einstein's Field Equation

R_{\mu \nu} - 1/2g_{\mu \nu}R = 8\pi GT{\mu \nu}

has only actually been tested in the vacuum case

R_{\mu \nu} = 8\pi GT{\mu \nu}.

Any theory with an action that reduces to that of GR in vacuo will also predict the same geodesics.

One example of such a theory can be found here and can be downloaded for free here.

Discussion about the actions of these two theories can be found here and also free in Section 2 in the eprint here. References to further papers are also to be found in those papers.

Tests of the Equivalence Principle and the gravitational red shift of light fall into another category, but again there is a degeneracy between these two theories that will first be resolved by GP-B.

Not long now!

Garth

 

[sylas]

Hi Garth,

In the lead up to the release of initial results, I've looked over the links you gave to various predictions.

My comments/questions are as follows.

Zhao's MVSR theory, according to your cited link, predicts zero geodetic effect. You have it recorded as 6.6144. Can you check the paper and either fix the prediction, or explain what I've missed?

I read Robertson as predicting an identical geodetic effect, and a 1/4 gravetomagnetic effect. You see to have given them both as 1/4 the GR prediction.

We agree on Junhao and Xiang. I don't see any mention in their paper of the gravetomagnetic effect; but the style of their theory seems to suggest rotation of the mass will have no effect. Is this right?

I can't see any mention of Gravity Probe B in Collins' paper. How did you obtain the values in that case? Were you able to apply the theory and calculate?

Henry-Couannier seems pretty clear. No frame-dragging.

Cheers -- Sylas

 

[Garth]

I'll check, yes you are correct on Zhao and Robertson! Whoops!

The Collins' prediction came from Collins himself on this thread in post #25 ('rusty').

Garth

 

[Garth]

The corrected (And thank you Sylas!) predictions of the following alternative theories are as follows:

They have been published in refereed journals, or on the Physics ArXiv, and make specific and falsifiable alternative predictions of the outcome of the Gravity Probe B experiment.


Einstein's General Relativity(GR)
Barber's Self Creation Cosmology (SCC),
Moffat's Nonsymmetric Gravitational Theory (NGT),
Hai-Long Zhao's Mass Variance SR Theory (MVSR),
Stanley Robertson's Newtonian Gravity Theory (NG),
Junhao & Xiang's Flat Space-Time Theory (FST).
R. L. Collin's Mass-Metric Relativity (MMR) and
F. Henry-Couannier's Dark Gravity Theory (DG).

The predictions are:

1. GPB Geodetic precession (North-South)
GR = 6.6144 arcsec/yr
SCC = 4.4096 arcsec/yr
NGT = 6.6144 - a small \sigma correction arcsec/yr
MVSR = 0.0 arcsec/yr
NG = 6.6144 arcsec/yr
FST = 4.4096 arcsec/yr
MMR = -6.56124 arcsec/yr
DG = 6.6144 arcsec/yr

2. GPB gravitomagnetic frame dragging precession (East-West)
GR = 0.0409 arcsec/yr
SCC = 0.0409 arcsec/yr
NGT = 0.0409 arcsec/yr
MVSR = 0.0102 arcsec/yr
NG = 0.0102 arcsec/yr
FST = 0.0000 arcsec/yr
MMR = -0.01924 arcsec/yr
DG = 0.0000 arcsec/yr

And from The stars of Pegasus from the Bright Star Catalogue, 5th Revised Ed. (Preliminary Version) (Hoffleit+, 1991, Yale University Observatory) as distributed by the Astronomical Data Center at NASA Goddard Space Flight Center.

IM Pegasi


RA J2000 : 22h 53m 2.3s
DEC J2000 : +16° 50' 28"
Proper motion in RA : -0.018 arcsec/y
Proper motion in DEC : -0.024 arcsec/y
mag : 5.64
MK spectral class : K1-2II-III

Of course, these alternative theories have to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment. Some of them might already have failed those tests.


Garth

 

[sylas]

I'll check, yes you are correct on Zhao and Robertson! Whoops!

The Collins' prediction came from Collins himself on this thread in post #25 ('rusty').

Garth

Found it! Thanks. And I am glad we are on the same page in the other predictions. I've posted a kind of parallel thread to this one in another forum where I am active -- TheologyWeb. (http://www.theologyweb.com/campus/showthread.php?t=94632). It's not a physics forum, but the matter came up in other discussions and there are a number of folks who really enjoy this kind of story, so I made the thread for it.

In my table I omitted Moffatt's theory because I was not able to quantify the expected shift. He gives bounds, but they refer to the stress-energy tensor and I was not able to carry through any calculation to even get a bound on the difference. I added Ron Hatch's "Modified Lorentz Ether Theory", because it is of special interest to some of the folks at TheologyWeb. We have an enthusiastic geocentrist there (yes, really) and he cites Hatch (indirectly) for arguments based on GPS, Aether and so on. Hatch is not a geocentrist, of course.

Rusty has posted twice at this forum, and the two posts seem inconsistent with each other. In his first post, he gave the numbers you have quoted (and which I also have used in the other forum). But about two weeks later Rusty posted msg #11 of "The gpb test of GR" in which he seems to say he gets the same result for geodetic effect. I've posted to that thread to ask him... but I guess he is not active here.

Cheers -- Sylas

 

[Garth]

Yes I had missed that, well caught, but in that Rusty's post he doesn't say anything about his geodetic effect, does he?.
Nothing like keeping your options open!

I included Moffat because NGT is published on the ArXiv and in Phys. Rev. D41, 3111 (1990). and J. Math. Phys. 36, 3722 (1995) and like the Brans Dicke theory allows a small variation in the frame-dragging result, which may be detected. Another such theory is Chern-Simons gravity whose frame dragging result has just been published.

I do not include Hatch because it is only a private publication.

Garth

 

[Garth]

A new prediction, published today for Chern-Simons (CS) gravity, which arises as a model independent extension of 4-dimensional compactifications of string theory. Here I have also included for completeness the Brans-Dicke theory.

These have all been published in refereed journals, or on the Physics ArXiv, and make specific and falsifiable alternative predictions of the outcome of the Gravity Probe B experiment. Einstein's General Relativity(GR)
Brans-Dicke theory (BD)
Barber's Self Creation Cosmology (SCC),
Moffat's Nonsymmetric Gravitational Theory (NGT),
Hai-Long Zhao's Mass Variance SR Theory (MVSR),
Stanley Robertson's Newtonian Gravity Theory (NG),
Junhao & Xiang's Flat Space-Time Theory (FST).
R. L. Collin's Mass-Metric Relativity (MMR) and
F. Henry-Couannier's Dark Gravity Theory (DG).
Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).

The predictions are:

1. GPB Geodetic precession (North-South)
GR = 6.6144 arcsec/yr
BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr
SCC = 4.4096 arcsec/yr
NGT = 6.6144 - a small \sigma correction arcsec/yr
MVSR = 0.0 arcsec/yr
NG = 6.6144 arcsec/yr
FST = 4.4096 arcsec/yr
MMR = -6.56124 arcsec/yr
DG = 6.6144 arcsec/yr
CS = 6.6144 arcsec/yr

2. GPB gravitomagnetic frame dragging precession (East-West)
GR = 0.0409 arcsec/yr
BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr
SCC = 0.0409 arcsec/yr
NGT = 0.0409 arcsec/yr
MVSR = 0.0102 arcsec/yr
NG = 0.0102 arcsec/yr
FST = 0.0000 arcsec/yr
MMR = -0.01924 arcsec/yr
DG = 0.0000 arcsec/yr
CS = 0.0409 arcsec/yr + CS correction

And from The stars of Pegasus from the Bright Star Catalogue, 5th Revised Ed. (Preliminary Version) (Hoffleit+, 1991, Yale University Observatory) as distributed by the Astronomical Data Center at NASA Goddard Space Flight Center.

IM PegasiRA J2000 : 22h 53m 2.3s
DEC J2000 : +16° 50' 28"
Proper motion in RA : -0.018 arcsec/y
Proper motion in DEC : -0.024 arcsec/y
mag : 5.64
MK spectral class : K1-2II-III

Of course, these alternative theories have to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment. Some of them might already have failed one or more of those tests.Garth

 

[Kris Krogh]

Hi Garth,

The data you have for IM Pegasi have been superseded by more accurate measurements from the HIPPARCOS satellite, which you can find here:

http://archive.ast.cam.ac.uk/hipp/hipparcos.html

The HIPPARCOS catalog gives the proper motion as:

PM(ra) (mas/yr): -20.97
PM(dec) (mas/yr): -27.59
Err(PMra) (mas/yr) 0.61
Err(PMdec) (mas/yr): 0.57

Also, here are some papers describing a quantum-mechanical theory of gravity making a different prediction for Gravity Probe B:

http://lanl.arxiv.org/abs/astro-ph/9910325
http://lanl.arxiv.org/abs/astro-ph/0409615
http://lanl.arxiv.org/abs/astro-ph/0508290
http://lanl.arxiv.org/abs/astro-ph/0606489

This is based on the optics of de Broglie waves rather than space-time curvature. The geodetic precession is the same as in GR, but the frame-dragging effect is zero -- the same thing you've listed for DG. (You could call this WG, for wave gravity.)

Best wishes,

Kris Krogh

 

[Garth]

Thank you Kris, and and very warm welcome to these Forums!

Excellent, that is just what I wanted, I will update the list of predictions. Your 'Wave-Gravity' theory looks very interesting, I will study it closely.

I am interested that 'WG' also predicts the observed blue-shift of the Pioneer spacecraft signals, SCC is also able to explain them, but does so as a clock-drift between ephemeris and atomic clocks.

The HIPPARCOS catalogue is very useful, thank you. Though it seems to make the work of the VLBI team rather redundant and does it not bring into question the 'blind' element of the GP-B's team analysis?

However, the VLBI data is necessary as it keeps track of the day by day changes to IM Pegasi relative to the distant quasar to compare with the daily and orbit-by-orbit changes in the direction of the gyroscopes' spin axes relative to IM Pegasi.

As this radio star is a binary its own track across the sky is complicated and on top of that there are other perturbations such as the gyroscopes' polhode motion and the geodetic effect from the Sun to eliminate.

Kris, have you seen we discussed your paper astro-ph/0701653 refuting 'Iorio's "high-precision measurement" of frame-dragging with the Mars Global Surveyor' on the thread Gravity Probe B?

Garth

 

[Garth]

Another theory (WG) is here added to the list of predictions.

These theories and their predictions of the Gravity Probe B experiment have all been published in refereed journals, or on the Physics ArXiv. Most of them make specific and falsifiable alternative predictions of the outcomes.

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Barber's Self Creation Cosmology (SCC),
4. Moffat's Nonsymmetric Gravitational Theory (NGT),
5. Hai-Long Zhao's Mass Variance SR Theory (MVSR),
6. Stanley Robertson's Newtonian Gravity Theory (NG),
7. Junhao & Xiang's Flat Space-Time Theory (FST).
8. R. L. Collin's Mass-Metric Relativity (MMR) and
9. F. Henry-Couannier's Dark Gravity Theory (DG).
10. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
11. Kris Krogh's Wave Gravity Theory (WG)

The predictions are:

A. GPB Geodetic precession (North-South)

1. GR = 6.6144 arcsec/yr
2. BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr
3. SCC = 4.4096 arcsec/yr
4. NGT = 6.6144 - a small \sigma correction arcsec/yr
5. MVSR = 0.0 arcsec/yr
6. NG = 6.6144 arcsec/yr
7. FST = 4.4096 arcsec/yr
8. MMR = -6.56124 arcsec/yr
9. DG = 6.6144 arcsec/yr
10. CS = 6.6144 arcsec/yr
11. WG = 6.6144 arcsec/yr

B. GPB gravitomagnetic frame dragging precession (East-West)

1. GR = 0.0409 arcsec/yr
2. BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr
3. SCC = 0.0409 arcsec/yr
4. NGT = 0.0409 arcsec/yr
5. MVSR = 0.0102 arcsec/yr
6. NG = 0.0102 arcsec/yr
7. FST = 0.0000 arcsec/yr
8. MMR = -0.01924 arcsec/yr
9. DG = 0.0000 arcsec/yr
10. CS = 0.0409 arcsec/yr + CS correction
11. WG = 0.0000 arcsec/yr

So there is a degeneracy between the Dark Gravity (DG) and Wave Gravity (WG) theories. It will be interesting to see whether this may be resolved in another test, or whether the theories have fundamentally the same basis that is approached from two different directions.

We also have the tracking of the guide star IM Pegasi from the http://archive.ast.cam.ac.uk/hipp/hipparcos.html; just key in
'IM Pegassi' into the Target name of that Query Form. (Thank you Kris):RA (J1991.25) : 22h 53m 02.279"
DEC (J1991.25) : +16⁰ 50' 28.540"
Proper motion in RA : -0.02097 \pm 0.00063 arcsec/yr.
Proper motion in DEC : -0.02759 \pm 0.00043 arcsec/yr.
mag : 6.033 (HIPP)
MK spectral class : K1III SB (HIPP)

Of course, these alternative theories have to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment.

Some of them might already have failed one or more of those tests.Garth

 

[henryco]

Another theory (WG) is here added to the list of predictions.

So there is a degeneracy between the Dark Gravity (DG) and Wave Gravity (WG) theories. It will be interesting to see whether this may be resolved in another test, or whether the theories have fundamentally the same basis that is approached from two different directions.

We also have the tracking of the guide star IM Pegasi from the http://archive.ast.cam.ac.uk/hipp/hipparcos.html; just key in
'IM Pegassi' into the Target name of that Query Form. (Thank you Kris):


RA (J1991.25) : 22h 53m 02.279"
DEC (J1991.25) : +16⁰ 50' 28.540"
Proper motion in RA : -0.02097 \pm 0.00063 arcsec/yr.
Proper motion in DEC : -0.02759 \pm 0.00043 arcsec/yr.
mag : 6.033 (HIPP)
MK spectral class : K1III SB (HIPP)
Garth

this is an april fish, isn't it ?

fred henry-couannier

 

[Garth]

this is an april fish, isn't it ?

fred henry-couannier

Hi Fred,
Please elucidate, my post #101 wasn't meant to be an April Fool joke, although I am always prone to make mistakes...(and how! ) Fred, did you read Kris' post #99?

[Edit- I have just noticed I have copied out the incorrect errors on the PM in RA and Dec, I followed the wrong line across; they should be as Kris originally said: \pm 0.00061 arcsec/yr and +/- 0.00057 arcsec/yr. respectively. ]

Garth

Garth

 

[Garth]

I have here repeated the list of predictions and the Proper Motion of IM Pegasi again with the errors in the PM(RA) and PM(Dec) corrected.

These theories and their predictions of the Gravity Probe B experiment have all been published in refereed journals, or on the Physics ArXiv. Most of them make specific and falsifiable alternative predictions of the outcomes.

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Barber's Self Creation Cosmology (SCC),
4. Moffat's Nonsymmetric Gravitational Theory (NGT),
5. Hai-Long Zhao's Mass Variance SR Theory (MVSR),
6. Stanley Robertson's Newtonian Gravity Theory (NG),
7. Junhao & Xiang's Flat Space-Time Theory (FST).
8. R. L. Collin's Mass-Metric Relativity (MMR) and
9. F. Henry-Couannier's Dark Gravity Theory (DG).
10. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
11. Kris Krogh's Wave Gravity Theory (WG)

The predictions are:

A. GPB Geodetic precession (North-South)

1. GR = 6.6144 arcsec/yr
2. BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr
3. SCC = 4.4096 arcsec/yr
4. NGT = 6.6144 - a small \sigma correction arcsec/yr
5. MVSR = 0.0 arcsec/yr
6. NG = 6.6144 arcsec/yr
7. FST = 4.4096 arcsec/yr
8. MMR = -6.56124 arcsec/yr
9. DG = 6.6144 arcsec/yr
10. CS = 6.6144 arcsec/yr
11. WG = 6.6144 arcsec/yr

B. GPB gravitomagnetic frame dragging precession (East-West)

1. GR = 0.0409 arcsec/yr
2. BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr
3. SCC = 0.0409 arcsec/yr
4. NGT = 0.0409 arcsec/yr
5. MVSR = 0.0102 arcsec/yr
6. NG = 0.0102 arcsec/yr
7. FST = 0.0000 arcsec/yr
8. MMR = -0.01924 arcsec/yr
9. DG = 0.0000 arcsec/yr
10. CS = 0.0409 arcsec/yr + CS correction
11. WG = 0.0000 arcsec/yr

We also have the tracking of the guide star IM Pegasi from the http://archive.ast.cam.ac.uk/hipp/hipparcos.html:RA (J1991.25) : 22h 53m 02.279"
DEC (J1991.25) : +16⁰ 50' 28.540"
Proper motion in RA : -0.02097 \pm 0.00061 arcsec/yr.
Proper motion in DEC : -0.02759 \pm 0.00057 arcsec/yr.
mag : 6.033 (HIPP)
MK spectral class : K1III SB (HIPP)

Of course, these alternative theories have to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment.

Some of them might already have failed one or more of those tests.Garth

 

[henryco]

Hi Fred,
Please elucidate, my post #101 wasn't meant to be an April Fool joke, although I am always prone to make mistakes...(and how! )


Fred, did you read Kris' post #99?
Garth

One essential point is the derivability of Kris exponential solution from basic principles. Did i miss something or did Kriss applied a multiplicative superposition principle in his annex while its potential Phi is still additive!?...which of course is equivalent to postulate the exponential factor from the begining...and is therefore not coherent with f/f_0=1+Phi for the single shell!

 

[Kris Krogh]

Hi Garth,

Thanks for mentioning my paper on Iorio's claimed frame dragging measurement.

The HIPPARCOS observations of IM Pegasi were published in 1997. You're right that the VLBI measurements are still important. Without them, it wouldn't be possible to get the intended accuracy for Gravity Probe B, 1% of general relativity's frame dragging effect.

From the abstracts of papers to be given by GP-B people at this month's American Physical Society meeting, it looks like they do expect to achieve that by the end of the year. See this one:

http://meetings.aps.org/Meeting/APR07/Event/65193

Hopefully the preliminary results announced this month will be enough to distinguish between the theories on your list. (Except that DG and WG make the same prediction.)

Hi Fred,

In wave gravity, gravitational potentials are additive, not multiplicative. So they do obey the superposition principle. What are not additive are the effects of those potentials. The same could be said of general relativity, which also has nonlinear effects.

In terms of combining massive bodies, things are different, because their masses are transformed by gravitational potentials. For example, if you have two identical, massive, compact bodies and bring them together, the resulting body won't have twice the potential of one. But whatever gravitational potentials are due to each body after they are combined -- those do add linearly.

The predicted transformation of gravitational mass is shown to agree with ranging observations of the lunar orbit, and with the gravitational energy radiated by accelerating bodies.

Kris Krogh

 

[henryco]

Hi Garth,

Proper motion in RA : -0.02097 \pm 0.00063 arcsec/yr.
Proper motion in DEC : -0.02759 \pm 0.00043 arcsec/yr.[/b]
Garth

These numbers from Hypparcos are quite in disagreement with those you gave
earlier
Proper motion in RA :-0.018
Proper motion in DEC :-0.024

Did you mean that the motion of the double star system would explain such evolution ?
Didnt these values from VLBI put already into question the blind analysis of the GP-B team?

Hi Kris,

If you had a look at the DG paper, you must have noticed that we have
almost the same predictions, not only for GP-B but also regarding longitudinal Gravitational waves, and the exponential metric solution in my case. much in common !
So i understand well what you do. My concern is that you cannot at the same time say that for one shell your factor f=1+phi and apply a multiplicative
superposition method: f1.f2.f...fn which is only coherent with f=exp(phi) from the beginning (a single shell) and not f=1+phi:
I suppose your phi is as usual 2Gm/rc^2. so suppose you divide your single starting shell into two contributions m=m/2+m/2, the incoherency is that
you don't have f=(1+phi/2)(1+phi/2) though you might have f=exp(phi/2)exp(phi/2) if you had defined from the beginning your f as an exponential. but then you would not derive it anymore from basic principles.

The main reason for me to suspect an april Joke is that as y do, you danse salsa, play the guitar, run and have almost the same predictions in you theory
as in mine...

In my case the exponential is derived from a "kind of bi-metric" field theory equations. I think the degenaracy between our two approaches is broken by discontinuities which are quite specific to my approach and in my case are responsible for the Pioneer anomaly. I have just a little post here: http://www.arxiv.org/abs/physics/0703018 to explain
the Pioneer anomaly following the discontinuity approach.

I'm also interested by the 50''/year of classical torque induced angular deviation in the GP-B abstract you mentionned. This compares very well with
equinoxe precession per year! did some people have this in mind earlier in this thread ?

Regards,

F H-C

 

[Garth]

These numbers from Hypparcos are quite in disagreement with those you gave
earlier
Proper motion in RA :-0.018
Proper motion in DEC :-0.024

Did you mean that the motion of the double star system would explain such evolution ?
Didnt these values from VLBI put already into question the blind analysis of the GP-B team?

No, simply the Hipparchos catalogue was more accurate and measured from a different time base, we wait for the VLBI confirmation of their results!

 

[Kris Krogh]

Hi F H-C,

Thanks for raising this question about my paper. For other readers, I should explain you're referring to Appendix A of this: http://arxiv.org/abs/astro-ph/9910325 It outlines a Gedanken experiement from which exponential expressions for velocities of light and de Broglie waves in gravitational potentials are derived. (For a flat, isotropic space-time.)

It starts with a clock or meter stick, around which increasingly distant shells of matter are added. Each new shell has whatever amount of mass is needed to create equal steps in the gravitational potential between shells. It's assumed the potentials due to each shell add linearly. Given the further assumption that the relativity principle applies where gravitational potentials are uniform, it's shown their cumulative effects are described by (nonlinear) exponentials.

To use a classical analogy, you could compare this situation to a stack of rubber bricks, each compressed by those above. The weight of the pile is a linear function of the number of bricks, but the height isn't. These gravitational potentials add linearly, but their effects don't. (And shouldn't.)

The GP-B abstract doesn't describe a 50''/year effect. That's 50'' over the life of the science experiment, which I think was about 18 months. They say the torque was caused by charged patches on the rotor surfaces, when the spin axis of the spacecraft became misaligned.

If GP-B confirms one of the predictions on Garth's list precisely, we'll know that wasn't from "cherry picking" the data. So in that limited sense it's still a double-blind experiment.

Best wishes,

Kris Krogh

 

[henryco]

Hi Kris,

The GP-B abstract doesn't describe a 50''/year effect. That's 50'' over the life of the science experiment, which I think was about 18 months. They say the torque was caused by charged patches on the rotor surfaces, when the spin axis of the spacecraft became misaligned.

Yes but this 50"/year should also be converted into some angle that could directly be compared with an equinox precession.
The conversion should involve the cosine of the angle between the gyroscopes spin axis and the ecliptic plane...does somebody know this for GP-B ?

best regards,

F H-C

 

[Garth]

Are you saying this 50"/yr precession has been observed by the GP-B, or are you just speculating? They haven't said anything yet about their findings.

Garth

 

[Kris Krogh]

Hi F H-C,

The GP-B spacecraft was designed to keep its roll axis pointed toward IM Pegasi. The gyro rotors spun on the same axis. This 50'' problem occurred when the orientation of the spacecraft (and gyro housing) changed. It doesn't represent any kind of steady precession. Apparently they've found a way to deal with it.

 

[Garth]

Hi F H-C,

The GP-B spacecraft was designed to keep its roll axis pointed toward IM Pegasi. The gyro rotors spun on the same axis. This 50'' problem occurred when the orientation of the spacecraft (and gyro housing) changed. It doesn't represent any kind of steady precession. Apparently they've found a way to deal with it.

Thank you Kris.

From the April APS Programme:

L1.00020 Evidence for Patch Effect Forces on the Gravity Probe B Gyroscopes,
DALE GILL, SAPS BUCHMAN, Stanford University
During the course of the GP-B on-orbit experiment the effect of anomalous forces were observed in the motion of the gyroscope rotors. A likely explanation for the origin of these forces is the existence of patch effect charges on the surface of the rotor. The effects observed were:
a) increased misalignment torques; 1 arcsec/deg/day, b) forces along the direction of the spin axis; 10−7 m/s2, c) spin-down rates in excess of residual gas induced spin-down; 0.4-1.5 μHz/hr, d) charge measurement effects, e) modulation of control effort and position in excess of the ones caused by rotor geometry. While varying from gyroscope to gyroscope all effects are consistent with patches of 20-100mV with extent up to dipole configuration. This poster will present data from analysis of on-orbit performance and ground based experimentation to show that the effects arise from variations in the work function of the rotor’s niobium coating. This poster will include details of the process for application of the coating onto the rotor. The results of a ground based experiment to map variation in the work function of flight spare rotors will also be presented. Finally some possibilities to mitigate these effects on future instruments will be presented.

Also:

L1.00027 Gravity Probe B Experiment Error,
BARRY MUHLFELDER, G. MAC KEISER, JOHN TURNEAURE, Stanford University
The GP-B experiment error results from both statistical and systematic sources. Excluding all systematic effects, the on-orbit gyroscope readout noise provides an experiment error noise floor limit of 0.2 marcsec/yr. We have also evaluated the effects of more than 200 systematic sources including: thermal sensitivities of the readout system, non-linearities in the telescope readout, roll phase uncertainty, and spacecraft anomalies. The impact of these and other systematic effects has been mitigated by the development of a variety of techniques. Study of the flight data revealed two unanticipated gyroscope behaviors. These two behaviors, a slowly varying readout scale factor and a specific type of Newtonian torque, are now well understood, and have been incorporated into the data analysis model. Residual errors associated with these and other gyroscope behaviors are included as part of the overall systematic error. The consistency of the results for the four independent gyroscopes provides a crosscheck of gyroscope specific error. Proper summing of all errors for the four gyroscopes gives the experiment error. We will present the most current numerical assessment of all GP-B error sources and will give the associated experiment error.

Garth

 

[henryco]

Hi F H-C,

The GP-B spacecraft was designed to keep its roll axis pointed toward IM Pegasi. The gyro rotors spun on the same axis. This 50'' problem occurred when the orientation of the spacecraft (and gyro housing) changed. It doesn't represent any kind of steady precession. Apparently they've found a way to deal with it.

Hi Kris,

They say: a likely explanation for the origin of these forces is...so may be the better is to wait (not long now) for the final results ...
regards,

F H-C

 

[Garth]

I have found a GP-B geodetic prediction, with an undetermined parameter b, for the five-dimensional extension of GR theory known as Kaluza-Klein gravity (KK), which I have added to the list.

These theories and their predictions of the Gravity Probe B experiment have all been published in refereed journals, or on the Physics ArXiv. Most of them make specific and falsifiable alternative predictions of the outcomes.

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Barber's Self Creation Cosmology (SCC),
4. Moffat's Nonsymmetric Gravitational Theory (NGT),
5. Hai-Long Zhao's Mass Variance SR Theory (MVSR),
6. Stanley Robertson's Newtonian Gravity Theory (NG),
7. Junhao & Xiang's Flat Space-Time Theory (FST).
8. R. L. Collin's Mass-Metric Relativity (MMR) and
9. F. Henry-Couannier's Dark Gravity Theory (DG).
10. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
11. Kris Krogh's Wave Gravity Theory (WG)
12. 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:

A. GPB Geodetic precession (North-South)

1. GR = 6.6144 arcsec/yr.
2. BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr. where \omega >6.
3. SCC = 4.4096 arcsec/yr.
4. NGT = 6.6144 - a small \sigma correction arcsec/yr.
5. MVSR = 0.0 arcsec/yr.
6. NG = 6.6144 arcsec/yr.
7. FST = 4.4096 arcsec/yr.
8. MMR = -6.56124 arcsec/yr.
9. DG = 6.6144 arcsec/yr.
10. CS = 6.6144 arcsec/yr.
11. WG = 6.6144 arcsec/yr.
12. KK = (1 + b/6 - 3b² + ...) 6.6144 arcsec/yr. where 0 < b < 0.07.

B. GPB gravitomagnetic frame dragging precession (East-West)

1. GR = 0.0409 arcsec/yr.
2. BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr.
3. SCC = 0.0409 arcsec/yr.
4. NGT = 0.0409 arcsec/yr.
5. MVSR = 0.0102 arcsec/yr.
6. NG = 0.0102 arcsec/yr.
7. FST = 0.0000 arcsec/yr.
8. MMR = -0.01924 arcsec/yr.
9. DG = 0.0000 arcsec/yr.
10. CS = 0.0409 arcsec/yr. + CS correction
11. WG = 0.0000 arcsec/yr.
12. KK = 0.0409 arcsec/yr.

We also have the tracking of the guide star IM Pegasi from the http://archive.ast.cam.ac.uk/hipp/hipparcos.html:RA (J1991.25) : 22h 53m 02.279"
DEC (J1991.25) : +16⁰ 50' 28.540"
Proper motion in RA : -0.02097 \pm 0.00061 arcsec/yr.
Proper motion in DEC : -0.02759 \pm 0.00057 arcsec/yr.
mag : 6.033 (HIPP)
MK spectral class : K1III SB (HIPP)

Of course, these alternative theories have to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment.

Again I emphasise that some of them may well have already failed one or more of those tests.Garth

 

[Garth]

I have been in discussion with Jonathan Kerr about his paper that makes another prediction for GP-B.

Although it has not yet been published, it is at present going through the peer reviewing process.

As time is short and the first results are due to be announced in eleven days time I here include it as an 'also ran', we shall know shortly, hopefully!

The theory is called "Planck scale gravity," (PSG), and makes the following prediction:

A. GPB Geodetic precession (North-South)

GR = 6.6144 arcsec/yr.
PSG = 0.0000 arcsec/yr.

B. GPB gravitomagnetic frame dragging precession (East-West)

GR = 0.0409 arcsec/yr.
PSG = 0.0409 arcsec/yr.

As the prediction pair is unique in my list above the result should be decisive.
Of course, PSG has to pass all the other tests of GR as detailed in Clifford Will's paper The Confrontation between General Relativity and Experiment. As with the other alternative theories it may have already failed one or more of those tests.

Garth

 

[sylas]

Hey Garth... another minor correction.

12. 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).

...

12. KK = (1 + b/6 - 3b² + ...) 6.6144 arcsec/yr. where 0 < b < 0.07.

I think that should be |b| < 0.07, and thus -0.07 < b < 0.07; if I read the paper right. I could not make your link work; but the reference is also in the arxiv archive, at gr-qc/0003034.

Overduin appears to be one of the researchers directly involved in the GP-B project.

I've found this thread dealing with different predictions has captured the imagination of a number of amateur readers. Even if someone is not a physicist, this adds a bit of drama to the whole proceeding and gets people interested in the idea of science at work. Thanks!

Cheers -- Sylas

 

[Garth]

Hey Garth... another minor correction.

I think that should be |b| < 0.07, and thus -0.07 < b < 0.07; if I read the paper right. I could not make your link work; but the reference is also in the arxiv archive, at gr-qc/0003034.

You are quite correct! Thank you.

Overduin appears to be one of the researchers directly involved in the GP-B project.

That's interesting, he was in 2005: The nearly flat universe Authors:

R. J. Adler and J. M. Overduin
(1) Gravity Probe B, Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, 94305-4085, U.S.A.

I've found this thread dealing with different predictions has captured the imagination of a number of amateur readers. Even if someone is not a physicist, this adds a bit of drama to the whole proceeding and gets people interested in the idea of science at work. Thanks!

Cheers -- Sylas

It has certainly captured my imagination!

You are welcome.

Garth

 

[sylas]

I've been double checking all these numbers for myself from the cited papers, and I have another proposed correction…

2. Brans-Dicke theory (BD)

...

2. BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr. where \omega >6.

...

2. BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr.

There's no reference given for this prediction. Let me propose including Brans-Dicke corrections to the gravitational Sagnac effect (arxiv gr-qc/0006090) by K.K. Nandi, P.M. Alsing, J.C. Evans, T.B. Nayak, also accepted for Phys.Rev. D63 (2001) 084027

In that paper, the Gravity probe corrections appear right at the end. They give multiplying factors for the geodetic effect as 2/3(3/2 - 2ξ/η), and for the Lense-Thirring effect as 1 - σ/η

Now let me try out these tex tags… Looking back in the paper to eqn 98 on page 22, we have:
\begin{equation*}\begin{split}\sigma&amp;= \frac{1}{\sqrt{(2\varpi+3)(2\varpi+4)}}\\<br /> \eta&amp;= \sqrt{\frac{2\varpi+4}{2\varpi+3}}\\<br /> \xi&amp;= 1 - \eta + 2\sigma\end{split}\end{equation*}

Using these, we can calculate the geodetic effect as follows. The end of the paper gives multiplying factors (to first order) from the GR predictions. Here is the solution for the geodetic factor

\begin{equation*}\begin{split}<br /> \frac{2}{3}(\frac{3}{2}-\frac{2\xi}{\eta})&amp;= 1-\frac{4\xi}{3\eta}\\<br /> &amp;=1-\frac{4-4\eta+8\sigma}{3\eta}\\<br /> &amp;=1-\frac{4}{3}\sqrt{\frac{2\varpi+3}{2\varpi+4}}+\frac{4}{3}-\frac{8}{3}\sqrt{\frac{(2\varpi+3)}{(2\varpi+4)^2(2\varpi+3)}}\\<br /> &amp;\approx 1-\frac{4}{3}(1-\frac{1}{2(2\varpi+4)})+\frac{4}{3}-\frac{8}{3(2\varpi+4)}\\<br /> &amp;= 1+\frac{1}{3(\varpi+2)}-\frac{4}{3(\varpi+2)}\\<br /> &amp;= 1-\frac{1}{\varpi+2}\end{split}\end{equation*}

The Lense-Thirring effect multiplying factor is given by
\begin{equation*}\begin{split}<br /> 1-\frac{\sigma}{\eta}&amp;= 1 - \sqrt{\frac{2\varpi+3}{(2\varpi+4)^2(2\varpi+3)}}\\<br /> &amp;=1 - \frac{1}{2\varpi+4}\\<br /> &amp;=\frac{2\varpi+3}{2\varpi+4}<br /> \end{split}\end{equation*}

So I get the same factor for the Lense-Thirring effect, but I think the geodetic effect should be ammended to read:

2. BD = (\varpi + 1)/(\varpi + 2) 6.6144 arcsec/yr. where \varpi >6.

Or equivalently

2. BD = (1 - 1/(\varpi + 2)) 6.6144 arcsec/yr. where \varpi &gt; 6

Cheers -- Sylas

 

[Garth]

I've been double checking all these numbers for myself from the cited papers, and I have another proposed correction…
.....
There's no reference given for this prediction.

The references are: Weinberg "Gravitation and Cosmology" 1972:

The Lense-Thirring, "frame dragging" effect,
page 248 equation 9.928 and the line following:

Thus the effects of the rotation of a spherical mass on the precession of spins and perihelia are smaller in the Brans Dicke theory than in general relativity, by a factor of (2\omega + 3)(2\omega + 4).

And for the geodetic effect,
page 238 equation 9.6.24 and the next line which gives:

Thus the effect of a modification of Einstein's field equations on the geodetic precession is simply to multiply it with a factor

\frac{(1 + 2\gamma)}{3}

Now in BD (Weinberg equation 9.9.27):
\gamma = \frac{\omega + 1}{\omega + 2}

so the geodetic effect is to multiply the GR result by a factor:

\frac{3\omega + 4}{3\omega + 6}

So your calculation was not too far out.

Garth