Alternative theories being tested by Gravity probe B

[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

 

[sylas]

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

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


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


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

Come off it Garth. The issue is not my calculation. It that we now have two difference references, using different formulae for the geodetic effect.

Thanks for your reference; I'll see if I can find it, and add it to the list I'm keeping of different predictions.

In the meantime, if you are interested, you may like to look over the reference I used, by Nandi et al. You are probably much more familiar with Brans-Dicke than I am, and I'd certainly appreciate it. The paper at Brans-Dicke corrections to the gravitational Sagnac effect (gr-pq/0006090) is proposing a fix to geodetic that is as I described previously. It's not that my calculation is "not too far out". It is that I'm calculating correctly the formulae as given in a different paper.

There is a factor 2/3 floating around. If you do get a chance to look at this paper by Nandi et al, then look at equation 110, which gives the geodetic effect; and the equation 98, which gives parameters in terms of ϖ, and the final paragraph, which summarizes the prediction.

Now perhaps this is yet another different prediction. I don't know. They claim to be using Brans-Dicke, and it is a fairly recent paper that explicitly mentions Gravity Probe B and the expected result. The paper also appeared in Phys Rev D.

Anyone else who can identify the discrepancy please feel free to help out also.

Cheers -- Sylas. 6 days and counting

 

[Garth]

Sylas I have read that paper in some depth and have a question about its method.

The basic equation they use for the Sagnac effect, equation1, is a SR effect well tested on ring laser interferometers.

However, they seem to be explaining a curvature effect by a SR flat space-time one.

In BD the correction is due to the perturbation of the curvature of space-time caused by the presence of the scalar field.

As the Sagnac effect is a time delay, is that not already taken care of in the time component of the GR formulae (i.e. the component not dependent on \gamma)? i.e. If applicable in the GR case it is only an alternative description of the same effect and should predict the same geodetic precession. (As it does for frame-dragging)

But note that your calculation of their geodetic effect, (\omega + 1)/(\omega + 2), is simply \gamma. Now \gamma measures the amount of space curvature per unit M (actually, per unit GM) so their interpretation of the geodetic effect is a purely a space curvature one, the time dilation component has dropped out! I don't think this can be correct as the essence of GR and similar metric theories of gravity is that gravitation is a space-time and not just a space curvature effect.

Any difference between the formulae might then simply be due to an inappropriate application of the Sagnac effect.

Note with the BD \omega ~ 500 their BD correction to the GR prediction is ~ (1 +/- 2.10^-3), whereas the Weinberg BD correction is ~ (1 - 10^-3)

I too am counting!
Cheers,
Garth

 

[LeBourdais]

Hello everybody,

First of all, I apologize for my way of writing in English. I hope it won't be too hard for you to understand what I say.

I am a french physicist from Montreal (B.Sc. Physics, 1974, University of Montreal, M.Sc. Physics partly completed, 1976, University of Montreal)

This thread is much interesting. I myself work on a theory of mine since a couple of years. My theory is not primarily concerned with gravitation: it is a theory that is based on a deterministic model of the physical world with nonlocal hidden variables identified explicitly. But in the end, this theory leads to a new model of gravitation. Regarding GP-B, my theory makes the same predictions as GR about geodetic effect and frame-dragging effect. But it predicts things that are different from GR and that could maybe be confirmed by that experiment, mainly:

1- flatness of 3-D geometry
2- universal "cosmological redshift" of momentum (including the momentum of gravitationally bound objects)
3- a phenomenon that leads to "shifts" in signal frequency (like the one observed in the Pioneer Anomaly)

My theory has never been published in a peer reviewed journal nor on arXiv, and I could not even publish it right now in your Independant Research Forum. So I don't expect it to be listed in your list. I just wanted to give my own predictions before the public announcement of the GP-B results, rather than giving it after

Friendly

Paul Le Bourdais

 

[Garth]

Hi Paul and bienvenue to these Forums!

You might try to put your theory onto the Theory Development Forum, the discipline may help you progress with it.

But as you say it hasn't been published and that its GP-B predictions are the same as GR we will leave it off this thread.

Garth

 

[LeBourdais]

Hi Paul and bienvenue to these Forums!

Thanks to you Garth.

You might try to put your theory onto the Theory Development Forum, the discipline may help you progress with it.

But as you say it hasn't been published and that its GP-B predictions are the same as GR we will leave it off this thread.

It's okay for me, I understand very well.

Paul

 

[Garth]

As there are only 4 days to go I here re-post all the accepted predictions for comparison with the first results due to be announced on Saturday 14th April at the April APS meeting.

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).
13. Kerr's Planck Scale Gravity: now accepted for publication Predictions of Experimental Results from a Gravity Theory (PSG)

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.
13. PSG = 0.0000 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.
12. KK = 0.0409 arcsec/yr.
13. PSG = 0.0409 arcsec/yr.

The guide star IM Pegasi has a proper motion given by 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.

Signing off for now...

Garth

 

[LeBourdais]

24 Hours to go !

Good luck everyone

Paul

 

[henryco]

24 Hours to go !

Good luck everyone

Paul

Hi everybody,

You correct me if I'm wrong but GP-B annouced

- Having measured the geodetic effect at the percent level of accuracy
- Have not been able to extract the frame dragging signal yet (they give a 200% error and want to work until december to deliver the final results)

Concerning the frame dragging effect i would have appreciated if they had given at least a preliminary central value...however if i take (too much?)serious the GP-B experimental error poster, the west-east drift rate is reported for gyro2. Though i can see peaks (resonances) oscillating in between the -0.3 and +0.4 arcsec/year , the red plot where the resonances are mitigated seems to indicate that the frame dragging is compatible with zero!(for sure it is incompatible with the GR prediction! )...if some GP-B expert is around, please correct my feeling if I'm wrong.

Best regards

F H-C

 

[sylas]

Concerning the frame dragging effect i would have appreciated if they had given at least a preliminary central value...however if i take (too much?)serious the GP-B experimental error poster, the west-east drift rate is reported for gyro2. Though i can see peaks (resonances) oscillating in between the -0.3 and +0.4 arcsec/year , the red plot where the resonances are mitigated seems to indicate that the frame dragging is compatible with zero!(for sure it is incompatible with the GR prediction! )...if some GP-B expert is around, please correct my feeling if I'm wrong.

Best regards

F H-C

There's no point giving a central value. The errors are reported as being around 100 mas/y, which is two and a half times the GR prediction. In other words, if it is compatible with 0 then it is also compatible with GR. Expertise in GR is not required and indeed completely irrelevant. Expertise in GR can only tell you what the GR predition is; what you need now is expertise in tracking the experimental errors and removing systematic effects. You're wrong in saying anything "for sure" about confirming or refuting the GR prediction of framedragging.

Cheers -- Sylas

 

[Kris Krogh]

Can someone give me a link or links to where the GP-B results are reported?

Many thanks,

Kris Krogh

 

[MeJennifer]

Expertise in GR is not required and indeed completely irrelevant.

Indeed but that is not what Frederic referred to, he referred to GP-B experts.

Actually, I would prefer not to have GR experts "explain" the errors, I like to have a completely theory independent view on these errors.

I don't think anyone is interested in another "Eddington" determining which errors are relevant and which not.

 

[sylas]

Indeed but that is not what Frederic referred to, he referred to GP-B experts.

Oops! My apologies. I echo his request, then! I'd love to hear from a GP-B expert also.

What I want to know is why there is a difference between the prediction in the http://einstein.stanford.edu/content/press_kit/hi_res.pdf (6606 NS, 39 EW).

All numbers in milliarcseconds/year.

I'm guessing orbit parameters; since about an extra 3.5 km in altitude would give that kind of difference, I think. But I need a GP-B expert to confirm for me.

Cheers -- Sylas

 

[henryco]

There's no point giving a central value. The errors are reported as being around 100 mas/y, which is two and a half times the GR prediction. In other words, if it is compatible with 0 then it is also compatible with GR. Expertise in GR is not required and indeed completely irrelevant. Expertise in GR can only tell you what the GR predition is; what you need now is expertise in tracking the experimental errors and removing systematic effects. You're wrong in saying anything "for sure" about confirming or refuting the GR prediction of framedragging.

Cheers -- Sylas

Sorry sylas but i have nothing to say "for sure" ! ...since I'm not a prophet...though i must admit I'm very confident in my approach
since on many other (theoretical and experimental) grounds i find it really more satisfying than GR and this I'm ready to discuss in details with anybody (by the way i already had many such discussions in french forums and private communications but very few in english since i don't feel really at ease with my english)... Do you or other people you know find my work or behaviour suspicious in any way ? ...i'm ready to answer any question!

I was just noticing here that generally, whatever the error, it is meaningfull to give a central value and most of the time it is given in any measurement..so i was just wondering what the absence of this central value means here (unfortunately i could not attend the APS meeting). I thought that may be the answer was in the plot of the L1 session i was asking clarification about. Please let me reformulate the question.

At least, is it true that the left/down plot in the L1 poster session :

L1.00027: "Gravity Probe B Experiment Error" by Barry Muhlfelder, G. Mac Keiser, John Turneaure
( Garth, you will find this poster online at http://einstein.stanford.edu/ )

shows the final east-west drift rate for gyro 2 after subtraction of some well understood dominant systematical effects (it remains these resonance peaks which magnitudes are used as the main error estimators) or is it something else ? What do the plots for other gyros look like?

best regards,

F H-C

 

[cosmopot]

Curved spacetime -> Black Holes -> BigBang

I wrote lots of papers and chatted on many forums but no one challenge my points:
1. GR is nothing but curved spacetime;
2. On curved spacetime, coordinates are not the accurate values of spatial distance or temporal interval or spatial angle.
3. To have those accurate values we need to perform integration with metric form being integrand. However, I did not see anyone do so to achieve distance, or angle, or time interval on curved spacetime. Instead, people simply write r, t, \phi and assume they are distance, time, angle respectively.

I am driven crazy by this fact with which many great figures (Einstein, Hilbert, John Baez, Steve Carlip, Francis Everitt being associated.

You can not say spacetime is curved because you have the terminology with some quantities: metric, cutvature, covariance. For example, quantum mechanics uses distance, radius which do not mean we can have definite orbits of micro-particles!

Is there anyone answering my question??

 

[Kris Krogh]

I agree with F H-C that the central value for this data should have some meaning. (Not only because our theories make the same predictions.) It certainly would be interesting to see the east/west drift rates for the other three gyros.

Also, the "Next Steps" section of the same poster describes the current error as 50-100 marcsec/yr. Previously, the GP-B people have used a single number like this to describe combined errors for both the east/west and north/south directions. If that's the case here, the east/west component might be still lower.

At least from a naive inspection, this chart does appear to show the east/west (frame-dragging) effect is close to zero, rather than the 41 marcsec/yr predicted by general relativity.

 

[Kris Krogh]

The NASA press release also puts the current estimated GP-B error at 50-100 marcsec/yr, as opposed to a specific 100.

 

[LeBourdais]

The NASA press release also puts the current estimated GP-B error at 50-100 marcsec/yr, as opposed to a specific 100.

The very fact that the GP-B estimated error has itself a great margin of error (75 ± 25 marcsec/yr) excludes the possibility of giving any meaning to a central value. Am I wrong ?

 

[Kris Krogh]

The very fact that the GP-B estimated error has itself a great margin of error (75 ± 25 marcsec/yr) excludes the possibility of giving any meaning to a central value. Am I wrong ?

General relativity predicts 41 marcsec/yr. Suppose the measurement were -75 ± 75 marcsec/yr. That would rule out general relativity, while a zero precession would remain possible. So the central value does have meaning.

A previous GP-B web page said the best current estimate of the gyro motion relative to the guide star would be presented. The chart in the "GP-B Experiment Error" poster shows an east/west drift rate averaging about zero. I'm hoping that's relative to the guide star's motion, as previously measured -- but maybe it's not. With the guide star moving, certainly the drift is not zero in absolute terms.

Maybe that chart is the result after subtraction of any cumulative drift. But I hope they will follow through and tell us the central value for the drift, and not only the error.

 

[sylas]

The link that henryco has given for the poster on errors is goes to the GP-B site, from which you must navigate to the poster. The direct link for the poster is GB-P Experiment Error: A Work in Progress (L1.00027).

Also, the "Next Steps" section of the same poster describes the current error as 50-100 marcsec/yr. Previously, the GP-B people have used a single number like this to describe combined errors for both the east/west and north/south directions. If that's the case here, the east/west component might be still lower.

I gather that the error is an absolute error of comparable magnitude both North-South and East-West; this would mean that the East-West signal is swamped by the errors, and the North-South is obtained to about 1% or thereabouts.

At least from a naive inspection, this chart does appear to show the east/west (frame-dragging) effect is close to zero, rather than the 41 marcsec/yr predicted by general relativity.

Hm. Yes, I see what you guys are getting at. Here's a grab of the chart.

What is this measuring? If it is simply the East/West drift, then indeed the red line is well below the GR prediction of 0.039 (or 0.041, depending on what predictions you read!).

But directly below the grap is that sentence "Impact on experiment error 100 marcsec/yr". This value of 100 is 0.1 on the left hand axis, which is way off the whole scale. I'm not getting this.

Cheers -- Sylas

 

[Kris Krogh]

Hi Sylas,

To give you an example, the guide star moves east/west about -28 marcsec/yr, and -21 marcsec/yr north/south. The Gravity Probe B folks have described it as moving 35 marcsec/yr. That's the total magnitude -- squaring and summing the two values and taking the square root.

If the total current error were 50 marcsec/year in magnitude, it's conceivable the east/west component is significantly less. Maybe were're getting down in the range of 41 marcsec/yr predicted by general relativity.

Cheers,

Kris

 

[LeBourdais]

General relativity predicts 41 marcsec/yr. Suppose the measurement were -75 ± 75 marcsec/yr. That would rule out general relativity, while a zero precession would remain possible. So the central value does have meaning.

Hi Kris,

The central value here has a meaning only for the combination of three effects (frame-dragging, “polhode” motion and "patches" torques) and the contribution from each of these effects is obviously not still known.

As they say on the "Gravity Probe B" site :

The GP-B instrument has ample resolution to measure the frame-dragging effect precisely, but the team has discovered small torque and sensor effects that must be accurately modeled and removed from the result.

Paul

 

[Kris Krogh]

Hi Paul,

When these extraneous influences like the polhode motion are estimated, of course that's done separately from the frame-dragging they are trying to measure. The latter is whatever is left when everything else has been accounted for.

This preliminary result is of the form x ± 100 marcsec/yr or x ± 50 marcsec/yr, where x has to be some specific number. (It can't be anything from -1000 to +1000, or you'd have an uncertainty of ± 1000.) Question is, what is x?

Best wishes,

Kris

 

[LeBourdais]

This preliminary result is of the form x ± 100 marcsec/yr or x ± 50 marcsec/yr, where x has to be some specific number. (It can't be anything from -1000 to +1000, or you'd have an uncertainty of ± 1000.) Question is, what is x?

Hi Kris,

You surely have read in my thoughts About one hour ago, I sent an e-mail at the contact address provided on the GP-B official site and I asked the question:

The margin of error for GP-B is told to be 50-100 marcsec/yr. The question I would like to ask is the following: is there any best value for the frame-dragging effect ? That is, can we say the result for the frame-dragging effect is X more or less 50-100 marcsec/yr, X being the best value. If so, is that value of X available ?

I hope I will get an answer

Best wishes,

Paul

 

[Kris Krogh]

Thank you Paul!

 

[LeBourdais]

Does anyone know the spin axis orientation for each of the four gyroscopes ?

 

[henryco]

Hi Kris,

You surely have read in my thoughts About one hour ago, I sent an e-mail at the contact address provided on the GP-B official site and I asked the question:



I hope I will get an answer

Best wishes,

Paul

Hi everybody

I also sent an email but received no answer so far.
This plot is very intriguing since it is clearly there to show us and explain to us what is the main source of uncertainty: the 100 marcsec/year.
This is why i believe that the resonance peeks we can see regularly spaced on the plot actually give us the order of magnitude of this error and indeed the higher peeks reach the 40 marcsec level (what else in this plot could justify the 100 marcsec given just below it?). If they don't understand at all what is the origin of these peeks, they can give the most pessimistic error: approximately 2.5 times 40 marcsec. ANother question is: is the reported
drift rate integrated from the origin to the bin time ? Presumably not (it would be indicated) so that the integrated drift rate at the end time must be very close to zero!
But what is even stranger here is that whatever the magnitude of the peeks, the very low dispersion of most points about the mean value and the ability to identify the peaks, subtract them and provide us with a mitigated red fit is a clear indication that whatever value was subtracted before, the error on the mean residual is extremely better than 100marcsec! and since other sources of errors are negligible compared to this one (the other errors are on the same poster) , my feeling is that they
were able to give a much better error but they decided not to give it and not to give also a central value. If the central value is at zero at the milliarcsec precision level, this might indicate a huge overestimation of the error already enough to produce a kind of earthquake in the community...so may be they want to work 8 more monthes to be sure since this would be a revolutionary
result! Is there some GP-B expert around?

regards

Fred

 

[LeBourdais]

Hi everybody

I also sent an email but received no answer so far.

Salut Fred

I think it's a good thing that more than one people ask them for the same question.

Best wishes

Paul

 

[CarlB]

Even though the results are preliminary, some theories appear to have been eliminated. Anyone care to write up a synopsis?

 

[sylas]

Even though the results are preliminary, some theories appear to have been eliminated. Anyone care to write up a synopsis?

Anything that did not give about 6.6 for the geodetic precession is falsified. We can ignore the frame-dragging predictions as so far not able to be tested.

Here is Garth's list.

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.

Based on this we have models 3, 5, 7 and 8 as falsified.
The paramaterized models 2, 4 and 12 simply have a new constraint on the free parameter.

The remaining models are:

• GR (1)
• Parameterized models, which are the same as GR in the limit. 2,4,10,12: BD, NGT, CS, KK.
• Models with frame dragging at 25% of what GR expects. 6: NG
• Models with no frame-dragging. 9,11: DG, WG.

Cheers -- Sylas

 

[Kris Krogh]

Hi Paul,

The spin axes of all four gyros were aligned with IM Pegasi. These are its coordinates, posted previously by Garth:

RA (J1991.25) : 22h 53m 02.279"
DEC (J1991.25) : +160 50' 28.540"

Kris