Alternative theories being tested by Gravity probe B

[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

 

[Garth]

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

Thank you Paul!

Garth

 

[Garth]

As there is now a calculation on the physics ArXiv of the GP-B predictions of Absolute Relativity I will re-instate it. My previous comment about Thomas Precession in that theory still holds, but the eprint published predictions stand to be falsified, or otherwise, by the final results expected at the end of this year. The geodetic N-S prediction is 30 mas more negative than GR and the frame-dragging E-W prediction is 20 mas more negative than GR.

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 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).
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 = -6636 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. NGT = -39 mas/yr.
4. NG = -39 mas/yr.
5. DG = 0 mas/yr.
6. CS = -39 mas/yr. + CS correction
7. WG = 0 mas/yr.
8. KK = -39 mas/yr.
9. AR = -59 mas/yr.

Garth

 

[henryco]

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



Frederic is obviously hedging his bets!
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

Hi Garth

I don't understand why you have (temporarily as it appears since you again indicate my correct zero frame dragging prediction in the most recent post), modified my predictions here? Wasn't it clear that the amendment was only to avoid people take serious the old (2005) erroneous prediction that was still in astro-ph/0509090 ?
Regards

Fred

 

[Garth]

Hi Garth

I don't understand why you have (temporarily as it appears since you again indicate my correct zero frame dragging prediction in the most recent post), modified my predictions here? Wasn't it clear that the amendment was only to avoid people take serious the old (2005) erroneous prediction that was still in astro-ph/0509090 ?
Regards

Fred

Sorry Fred, I've been cutting and pasting to try and collect everybody's predictions together, and I copied an out-of-date version of your prediction.

Garth

 

[henryco]

The present predictions are:

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).
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 = -6636 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. 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.
9. AR = -59 mas/yr.

We continue to wait for Christmas!

Garth

Hi GArth,

You again put this wrong prediction.
It's a long time since i have corrected this which was just a calculus mistake (but by the way i could notice that many experts do the same kind of mistakes and this made me realize my own mistake !).

My predition is still:
zero frame dragging and the same geodetic effect as in GR! no effect due to the motion of the Earth around the sun or relative to the CMB

Also an extension of the theory could give other kinds of effects (not frame dragging) and even give the same prediction as GR but this is no more the minimal DG theory!

Best regards

F H-C

 

[Garth]

Sorry Fred, one last time to try and get it right!

The present predictions are:

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 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.60, -83 LaTeX graphic is being generated. Reload this page in a moment.22 mas/yr) June 2006, (-6597 LaTeX graphic is being generated. Reload this page in a moment.17, -92 LaTeX graphic is being generated. Reload this page in a moment.15 mas/yr) December 2006, (-6595 LaTeX graphic is being generated. Reload this page in a moment.12, -98 LaTeX graphic is being generated. Reload this page in a moment.7 mas/yr) March 2007 and (-6603 LaTeX graphic is being generated. Reload this page in a moment.8, -98 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.8, -98 LaTeX graphic is being generated. Reload this page in a moment.7 mas/yr)
whereas GR predicts:
(-6571 LaTeX graphic is being generated. Reload this page in a moment.1, -75 LaTeX graphic is being generated. Reload this page in a moment.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 ~ LaTeX graphic is being generated. Reload this page in a moment.100 mas/yr.

This renders the present geodetic 'glimpse' as being consistent with GR to within about 1LaTeX graphic is being generated. Reload this page in a moment.%, 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 Kaluza-Klein gravity theory (KK).
9. Jin He's Absolute Relativity theory (AR).The predictions are now:

GPB Geodetic gross precession (North-South)

1. GR = -6606 mas/yr.
2. BD = -LaTeX graphic is being generated. Reload this page in a moment. 6.606 arcsec/yr. where now LaTeX graphic is being generated. Reload this page in a moment. >60.
3. NGT = -6606 - a small LaTeX graphic is being generated. Reload this page in a moment. 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 = -6636 mas/yr.We await the GPB gravitomagnetic frame dragging gross precession (East-West) result.

1. GR = -39 mas/yr.
2. BD = -LaTeX graphic is being generated. Reload this page in a moment. 39 mas/yr.
3. NGT = -39 mas/yr.
4. NG = -39 mas/yr.
5. DG = 0 mas/yr.
6. CS = -39 mas/yr. + CS correction
7. WG = 0 mas/yr.
8. KK = -39 mas/yr.
9. AR = -59 mas/yr.We continue to wait for Christmas!

Garth

 

[henryco]

Sorry Fred, one last time to try and get it right!

The present predictions are:

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 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.60, -83 LaTeX graphic is being generated. Reload this page in a moment.22 mas/yr) June 2006, (-6597 LaTeX graphic is being generated. Reload this page in a moment.17, -92 LaTeX graphic is being generated. Reload this page in a moment.15 mas/yr) December 2006, (-6595 LaTeX graphic is being generated. Reload this page in a moment.12, -98 LaTeX graphic is being generated. Reload this page in a moment.7 mas/yr) March 2007 and (-6603 LaTeX graphic is being generated. Reload this page in a moment.8, -98 LaTeX graphic is being generated. Reload this page in a moment.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 LaTeX graphic is being generated. Reload this page in a moment.8, -98 LaTeX graphic is being generated. Reload this page in a moment.7 mas/yr)
whereas GR predicts:
(-6571 LaTeX graphic is being generated. Reload this page in a moment.1, -75 LaTeX graphic is being generated. Reload this page in a moment.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 ~ LaTeX graphic is being generated. Reload this page in a moment.100 mas/yr.

This renders the present geodetic 'glimpse' as being consistent with GR to within about 1LaTeX graphic is being generated. Reload this page in a moment.%, 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 Kaluza-Klein gravity theory (KK).
9. Jin He's Absolute Relativity theory (AR).


The predictions are now:

GPB Geodetic gross precession (North-South)

1. GR = -6606 mas/yr.
2. BD = -LaTeX graphic is being generated. Reload this page in a moment. 6.606 arcsec/yr. where now LaTeX graphic is being generated. Reload this page in a moment. >60.
3. NGT = -6606 - a small LaTeX graphic is being generated. Reload this page in a moment. 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 = -6636 mas/yr.


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

1. GR = -39 mas/yr.
2. BD = -LaTeX graphic is being generated. Reload this page in a moment. 39 mas/yr.
3. NGT = -39 mas/yr.
4. NG = -39 mas/yr.
5. DG = 0 mas/yr.
6. CS = -39 mas/yr. + CS correction
7. WG = 0 mas/yr.
8. KK = -39 mas/yr.
9. AR = -59 mas/yr.


We continue to wait for Christmas!

Garth

That's OK

Thank you Garth

Fred

 

[yogi]

Garth - this question was posed by Jonathan in post 210:

"The wider question this has bearing on is what possible interpretations for the geodetic effect do we have, now that it has been measured directly. Is curvature the only one?

Maybe I missed your answer -

Along the same line - assuming the measurements are a confirmation of curvature - don't we still have an unanswered question of whether the curvature is the result of static mass acting upon static space ?

 

[Garth]

Garth - this question was posed by Jonathan in post 210:

"The wider question this has bearing on is what possible interpretations for the geodetic effect do we have, now that it has been measured directly. Is curvature the only one?

Maybe I missed your answer -

Along the same line - assuming the measurements are a confirmation of curvature - don't we still have an unanswered question of whether the curvature is the result of static mass acting upon static space ?

If space-time does suffer curvature as in GR then free falling gyros will exhibit geodesic precession.

You make a cone by cutting a thin slice out of a disk and glueing the cut edges together.

Geodesic precession is caused by the missing slice, there not being quite 360⁰ in the circle.

If there is no space-time curvature then the gyros in orbit will have to be suffering some type of Newtonian gravitational force perturbing them from their otherwise straight line trajectories.

They will be accelerating from their inertial frames of reference towards the centre of the Earth.

In a space-time continuum an accelerating parallel transported vector will 'lean over' in 4D as its velocity increases.

An accelerating gyro will precess due to this effect, the effect is called Thomas Precession.

However if there is no space-time curvature and all the orbital dynamics is caused by a Newtonian attractive gravitational force then the amount of Thomas precession is precisely half the GR prediction of geodetic precession. Already the first results of GP-B have confirmed the GR geodetic prediction to within 1$\frac{1}{2}$%.

Other theories have postulated different causes of N-S precession for the GP-B, you will have to read the individual papers as so far I have been unconvinced.

Garth

 

[JonathanK]

Hello Garth and all,

Yogi has mentioned what I said about interpretations for the geodetic effect. I've found a way to generalise the calculation I did about this, and put it into an equation. It's easy to check, and shows clearly that curvature is not the only interpretation for the measured effect.

If matter near a mass is slowed (in flat space) by (1 - [2GM/rc^2])^1/2, then different parts of an orbiting spherical object (such as a GP-B gyro) travel at different speeds, resulting in a slight turning of the object in the plane of the orbit, which mimics the geodetic effect. In PSG minor corrections are made to an orbital speed that's the same across the whole object.

The angle of precession θ in degrees for one (circular) orbit arising from this local slowing of matter can be arrived at with

θ = 2 arctan

2[pi]r ( ([1 – (2GM/rc^2)]^1/2) – ([1 – (2GM/r'c^2])^1/2) )
----------------------------------------------------------
r' – r

(or if preferred, tan (θ / 2) = …etc), where r is the distance from the centre of the Earth to the centre of the object, and r' is the distance to a point on its upper edge, equal to r plus the radius of the object.

This gives the curvature component of the geodetic effect (in the case of GP-B 4.4 arcsecs/yr). It gets there in a very different way from GR, and uses only basic gravity parameters.

Sorry about how the above equation is set out, couldn't do sqrt boxes etc. Garth, I'd appreciate it if you'd set it out better, thank you.

The component of the geodetic effect generally thought to be due to curvature is 2/3 of the total effect. The other 1/3 has been explained in ways that apply whether space is curved or flat (for example Shapiro et al, '88).

So this provides an alternative flat space interpretation, which means the measurement of what is known as the geodetic effect doesn't prove the curved space interpretation, it simply proves that the effect exists.

I also now have a better way of explaining why like in GR, PSG has no acceleration in freefall, in reply to your point about the Thomas precession. As in GR, the very nature of space and matter provides an explanation so fundamental that no later 'adjustments' to the description are needed. It can't be gone into here, but the freefall equation (published as equation 4 in the first paper) gives the right speeds to 12 decimal places, all along the trajectory. This came directly from this conceptual basis, so the point I'm making works in more ways than one.

Thanks, good wishes, Jonathan Kerr

 

[Garth]

Jonathan I think you had better learn LaTex, at least the tex and itex version used in these Forums!

Your calculation uses the same equations as GR but interprets them differently therefore it comes up with the same prediction, but it will be impossible to test the one theory against the other using this experiment. If all the equations are the same in every prediction then I would say you are simply restating the standard GR theory in unfamiliar and perhaps unhelpful and confusing terminology.

I should have made clear in my 'missing slice' explanation of geodetic precession in post #254 that that argument only explains the spatial part of space-time curvature, which in the GR calculation accounts for $\frac{2}{3}$ of the total.

The other component is the time part of space-time curvature, time dilation, which accounts for the remaining $\frac{1}{3}$ of the total.

There is no need for this to be "explained in ways that apply whether space is curved or flat", it is already accounted for in the curvature of space-time.

Note in GR gravitation is described by the curvature of the space-time manifold, not just by the curvature of space.

Garth

 

[JonathanK]

Sorry that I don't know the Latex system you use.

Your calculation uses the same equations as GR but interprets them differently therefore it comes up with the same prediction, but it will be impossible to test the one theory against the other using this experiment.
Garth

You seem to agree with my main point, which is that there is more than one possible interpretation. As I'm sure you realize, I arrived at that equation purely from the concept of matter in flat space being slowed by a certain factor. I could easily show the simple steps that led there, but they're not what matters. They show a general principle, and one that can be verified in other parallel ways. 2/3 of the geodetic effect can definitely be interpreted in this surprisingly simple way, without curvature.

So all that remains is the question of the other 1/3. There are different interpretations within GR for that (I sent you two papers about it early this year, the Shapiro et al one from '88, and a NASA funded study that puts forward more than one interpretation - to both of our surprise, including SR as one of them!)

The Shapiro et al paper described 1/3 of the geodetic effect as being due to "a gravitational analogue of spin orbit coupling". That's what I meant by an explanation that applies whether space is curved or flat.

You can look at exactly how GR interprets the effect, and I acknowledge that as you say this involves the curvature of spacetime, not just of space. But for this flat space interpretation, 2/3 is as I've interpreted it above, and the other 1/3 can be various things, such as (for example) a flat space effect like that described by Shapiro et al.

It's worth pointing out that PSG seems to mimic GR over the motion of both light and matter well in other areas. If it didn't there'd be less point in looking at the geodetic. If anyone would like to help with a more accurate calculation, let me know. (Might even explain the 32 mas/yr, though the error margins may make that impossible.) And any comments would be welcome.

Thanks again for your help Garth. It'd be great if you'd acknowledge that this alternative interpretation works, in this small corner of GR at least. Outside that there's a long way to go of course. J

 

[Garth]

Sorry that I don't know the Latex system you use.

Try How To LaTex.

You seem to agree with my main point, which is that there is more than one possible interpretation. As I'm sure you realize, I arrived at that equation purely from the concept of matter in flat space being slowed by a certain factor. I could easily show the simple steps that led there, but they're not what matters. They show a general principle, and one that can be verified in other parallel ways. 2/3 of the geodetic effect can definitely be interpreted in this surprisingly simple way, without curvature.

Yes, but my point is your expression for motion being "slowed down by a certain factor" is exactly the same as in GR. The question is therefore: "can you physically justify using that equation, or are you just copying it?" As you are using it you were bound to get the same result as GR for the spatial component.

So all that remains is the question of the other 1/3. There are different interpretations within GR for that (I sent you two papers about it early this year, the Shapiro et al one from '88, and a NASA funded study that puts forward more than one interpretation - to both of our surprise, including SR as one of them!)

I disagree, there is only one interpretation within GR, it is the time component of the effect of space-time curvature.

The Shapiro et al paper described 1/3 of the geodetic effect as being due to "a gravitational analogue of spin orbit coupling". That's what I meant by an explanation that applies whether space is curved or flat.

They are either misinterpreting the time component of curvature OR they are giving an alternative flat space-time explanation. In the latter case I want to know what happens to the Thomas Precession, which must be taken into account if space-time is flat and the orbiting gyros are not in an inertial frame of reference. Each separate effect must be taken into consideration and correctly accounted for to get a valid prediction.

Thanks again for your help Garth. It'd be great if you'd acknowledge that this alternative interpretation works, in this small corner of GR at least. Outside that there's a long way to go of course. J

You're welcome.

If you want your Planck Scale Gravity (PSG) theory to be included on this thread you will have to give a refereed or Physics ArXiv link to a paper on it that makes a distinct prediction that can be falsified by the GP-B experiment.

If you have a link to a PSG paper published in a refereed journal you can discuss it on these Forums otherwise you can submit it to the Independent Research Forum having first observed their submission rules.

Garth

 

[JonathanK]

Well, it doesn't matter, and no need to put PSG back on the list, unless you want to. In fact the paper you kindly endorsed, which was published in a refereed journal (linked to in post #126), has a frame dragging prediction, the same as GR. So it does fill the criteria, but I'll let you get on with other things, and thanks again.

The original geodetic prediction was null, but the above equation (post #255), which you've acknowleged as giving the right result, vindicates the theory. It shows that the prediction, not the theory, was wrong, as the measured geodetic effect is in fact mimicked by the original theory, without any changes. I only found this out later, but luckily was able to show it to be true. Vindicating the theory has been my main aim here.

The equation I found is not a GR equation (as far as I know), but as you say, the factor sqrt (1 - [2GM/rc^2]) is of course an expression from GR. PSG is the gravity part of a theory of time, and in it not only is time 'slowed' by this factor, the motion of light and matter are as well. Yes, I can physically justify this - the conceptual basis does just that. According to it GR is largely right, but incomplete in its interpretation - and something in effect very similar to curved space happens in flat space. (And in it GR is of course right about that expression giving the local time rate. I believe I'm allowed to use it in that context…!)

Interestingly, the spatial calculation gave 2.2 arcsec/yr. I then allowed for time rate differences to the two points on the gyro in question, which doubled the difference to their speeds, so they ended up twice as far apart. The trigonometry then gave 4.4 arcsecs/yr, and there's a factor of 2 in the equation, reflecting this doubling. So I assumed I was uncovering an alternative interpretation from a GR one in which space is 1/3 and time is 1/3. But I’m sure you know the GR interpretation.

I disagree, there is only one interpretation within GR, it is the time component of the effect of space-time curvature. They are either misinterpreting the time component of curvature OR they are giving an alternative flat space-time explanation. In the latter case I want to know what happens to the Thomas Precession, which must be taken into account if space-time is flat and the orbiting gyros are not in an inertial frame of reference.
Garth

You’re right, I misused the word "within", when I said "for the other 1/3 there are different interpretations within GR". I'm sure that "surrounding GR" is more accurate. But Shapiro is a well-known GR supporter as far as I know. You'd have to ask him about the Thomas precession - I have no idea what he'd say. My aim has really been to interpret only the first 2/3, and say that the other 1/3 has enough controversy surrounding it for this flat space interpretation to be a possibility. It seems very reasonable to me - thank you for acknowledging that the mathematics for that 2/3 works. It seems not impossible that matter actually is slowed by that factor. Anyway, good wishes, and good luck all for December! Jonathan

 

[hejin]

GPB Decembe 2007 update!

GPB final result, 6 more months, no kidding!

 

[Garth]

Unfortunately you are not kidding!
From the GP-B update

MISSION UPDATE - DECEMBER 2007PROGRAM STATUS

Over the past three months, GP-B has continued to make outstanding progress.

In our September 25, 2007 status update, we reported that the trapped flux mapping technique had resulted in a dramatic improvement in the determinations of the polhode phase and angle for each gyroscope throughout the entire 353-day experiment period. Applying these results to a central 85-day stretch of data, from December 12, 2004 through March 4, 2005, we obtained a robust and stable measurement of the frame-dragging effect with a reasonable (~30%) error level. We are in process of progressively extending the analysis to increasingly long time intervals in order to reach the full experiment accuracy, potentially to an error margin of less than 5%. Also important is the completion of the study of -- and if necessary elimination of -- any remaining systematic effects that may bias the results of the experiment.

Our progress and results were intensively reviewed by the GP-B Science Advisory Committee (SAC) at its 17th meeting on November 2, 2007. In its subsequent report, the SAC commented on "the truly extraordinary progress that has been made in data analysis since SAC-16 [March 23-24, 2007]" and unanimously concluded "that GP-B is on an accelerating path toward reaching good science results."

It is anticipated that approximately another six months until May 2008 will be needed to complete this full coverage and arrive at a definitive final result. We believe the results will be truly significant and will withstand scrutiny at the deepest scientific level. We agree with the SAC that: "This phase must include an adequate opportunity for the SAC to review the final result in some detail before publications are prepared and public announcements are made."
To this end, we are planning on this review for the May 2008 time frame.

 

[hejin]

Geodetic result in December update

On the right collumn of the December update there is a graph showing

Einstein expectation: -6571 +- 1*
4-gyro result (1 sigma) for 85 days
(12 Dec 04 -- 4 Mar 05) -6632 +- 43

 

[Garth]

On the right collumn of the December update there is a graph showing

Einstein expectation: -6571 +- 1*
4-gyro result (1 sigma) for 85 days
(12 Dec 04 -- 4 Mar 05) -6632 +- 43

That http://einstein.stanford.edu/cgi-bin/highlights/showpic.cgi?name=GR-85-day_result.jpg is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.

This is at about a 68% confidence level, we wait for the 3$\sigma$ 4-gyro results next year, but so far it does look interesting!

It will be especially interesting to see what happens to the frame-dragging result, which is at present swamped by noise.

Garth

 

[fasterthanjoao]

Despite having kept up-to-date with this thread since the beginning, I have no productive input except that the recommendation that this thread and the work of the contributors should be entered into a PF cosmological hall of fame. Very good.

 

[Garth]

That http://einstein.stanford.edu/cgi-bin/highlights/showpic.cgi?name=GR-85-day_result.jpg is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.

This is at about a 68% confidence level, we wait for the 3$\sigma$ 4-gyro results next year, but so far it does look interesting!

As I posted in the We are in a Schwarzschild black hole--T or F? thread:

Now that is interesting, the GP-B website has withdrawn that diagram and replaced it with one that makes no such claims!

Garth

 

[Garth]

If you want to see for yourselves you can still find the original intriguing diagram in a series of slides of a lecture given by Francis Everitt at Cornell University on the 12th November 2007. http://colloquia.physics.cornell.edu/11-12-2007/cornellpres_files/v3_document.htm .

The pertinent slides are slide 3: http://colloquia.physics.cornell.edu/11-12-2007/cornellpres_files/v3_slide0341.htm

That last one clearly shows the inconsistency with the GR prediction to the 1 $\sigma$ confidence level.

Again we wait for the 3 $\sigma$ confidence level results with interest!

Garth

 

[Garth]

Impossibility of GP-B reliable measurement?

A critical analysis of the GP-B mission. I: on the impossibility of a reliable measurement of the gravitomagnetic precession of the GP-B gyroscopes by a Gerhard Forst.

In this paper we discuss the impossibility for the Gravity Probe B (GP-B) experiment to provide a clean and undisputable test of the gravitomagnetic precession of its four gyroscopes and of the Lense-Thirring effect. Lense-Thirring effect and geodetic precession have already been measured by Lunar Laser Ranging (LLR), laser ranged satellites, binary pulsars and accretion disks of black holes and neutron stars. In this paper we show that in the GP-B experiment there are critical problems for measuring Lense-Thirring effect and geodetic precession by the GP-B data analysis. The GP-B data analysis is extremely model dependent and relies on the assumptions about the unknown quadrupole moment induced by the gyroscopes rotation, both: (I) its size and (II) its direction with respect to the quadrupole moment due to fabrication and (III) its unknown rate of change due to variations of the gyroscopes rotation rate. The huge systematic biases in the GP-B data amount to about 1000 milliarcsec/year, but the GP-B team has claimed to be able to model 90 % of this signal, thus leaving the systematic biases at the level of about 100 milliarcsec per year, that is $\sim 300 %$ of the Lense-Thirring effect effect of the GP-B gyroscopes; any further modelling will result in a rough test of Lense-Thirring effect that will be highly model dependent and extremely affected by other huge unknown systematic biases. In this paper we show that such claims are necessarily highly model dependent and then are very much affected by huge unknown systematic biases. We give an important example of these systematic biases of which there is no mention in the discussions of the GP-B team.

Has GP-B all been a waste of time and money?

Firstly, it must be said that the team have recognised that there were two unexpected sources of error that almost render the results too inaccurate to test the two precessions, especially the much smaller frame-dragging or gravitomagnetic precession effect.

However, the team are also confident that they can, and are, modelling these errors accurately by using two cross checking independent methods.

I specifically asked the question at the April Conference about whether these methods were genuinely independent in a 'double-blind' way or whether they used the expected GR results in their derivation.

Francis Everitt was quite adamant that that was what one mustn't do and their error reduction modelling was quite independent of the expected results.

Gerhard Forst is disputing this independence, which is a serious charge to make. However I note that his email is a private not an academic address (but then so is mine...), that he isn't an endorser on the ArXiv, which is suspicious, this is his only eprint and he has no papers published in referred journals, which does not say much about his academic credibility.

Given the immense amount of experience and expertise on the GP-B team, at this stage I would rather trust them, although of course when the results are finally published so also is all the data for others to check and dispute.

I can see an undisputed result being a long way off...

Garth

 

[Kris Krogh]

Hi Garth,

I think your suspicions about Gerhard Forst are well justified. Here is a message I sent the moderator of ArXiv:


Dear arXiv-moderation,

This concerns the authorship of http://arxiv.org/abs/0712.3934 , "A critical analysis of the GP-B mission. I: on the impossibility of a reliable measurement of the gravitomagnetic precession of the GP-B gyroscopes." This paper may represent an anonymous attack.

The author's name is given as "Gerhard Forst," with the email address g.forst@yahoo.com . He has no prior ArXiv papers, and seems to have no peer-reviewed publications. His affiliation and address are given as:

G. Forst
FGP
Behrenstr. 1
10117 Berlin

Whatever FGP stands for, there is no mention on the web of such an organization at the given address. Was this paper endorsed? If so, can the endorser show "Gerhard Forst" is the author's real name?

There is an interesting similarity to papers by another author, who has a history of tit-for-tat disputes on ArXiv:

"On the impossibility of measuring a galvano-gravitomagnetic effect with current carrying semiconductors in a space-based experiment," http://arxiv.org/abs/gr-qc/0308053

"On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense-Thirring effect," http://arxiv.org/abs/gr-qc/0404107

"On the impossibility of using certain existing spacecraft for the measurement of the Lense-Thirring effect in the terrestrial gravitational field," http://arxiv.org/abs/gr-qc/0508012

"On the impossibility of measuring the general relativistic part of the terrestrial acceleration of gravity with superconducting gravimeters, http://arxiv.org/abs/gr-qc/0602005

"On some critical issues of the LAGEOS/LAGEOS II Lense-Thirring experiment," http://arxiv.org/abs/0710.1022

In addition to the titles, there are many other similarities. Comparing the most recent of these to the paper in question, there are these sequences:

"...no other tests performed by independent teams, without connections with Ciufolini and coworkers...have been so far reported in literature."

"...no independent team, without connections with the GP-B team, will be able to repeat the GP-B data analysis..."

In the former there are 4 sentences beginning with the word "Indeed." Such a sentence is also found in the latter. I could list further examples.

That author has himself claimed increasingly accurate measurements of the Lense-Thirring effect, which I've discussed here:

http://arxiv.org/abs/astro-ph/0701653

Both those claimed measurements and his reputation would be seriously threatened by a contrary result from Gravity Probe B. I hope the reasons are clear from my paper.



Kris Krogh

 

[Garth]

Kris,

Thank you, that is very interesting!

Actually I have read Lorenzo Iorio's papers with interest, I shall be even more critical from now on!

Happy New Year
Garth

 

[henryco]

That last one clearly shows the inconsistency with the GR prediction to the 1 $\sigma$ confidence level.

Again we wait for the 3 $\sigma$ confidence level results with interest!

Garth

Hi Garth

Your comments on these results make me consider more seriously another possible prediction in my framework which i had eliminated because it is already ruled out by the 1% precision test of the geodetic effect by LusarLaserRanging. However the DG theory make it possible for a rare event, the appearance or disappearance of a discontinuity of gravity in the neighbourhood of our earth, to occur. If this happened after the LLR tests and before the GP-B data taking, the physics of gravitomagnetism might have changed so that the geodetic test by LLR is no more relevant now!
If so, my prediction would still be:
- no frame dragging (no influence of the Earth rotation!) on GP-B gyros
- the same geodetic effect as in GR where enters the speed of GP-B relative to the earth

but now i can consider a preferred frame effect which i did not take serious before.
The formula is the same as the geodetic effect one except that it involves the speed of the Earth relative to a preferred frame which is not attached to the Earth as i assumed up to now. Whever this preferred frame is attached to the CMB, the galaxy or more locally to our sun does not matter since in all cases the dominant effect comes from that part of the speed which is the speed of the Earth relative to our sun.

Thus the additional effect for GP-B is a periodic angular precession with roughly 40 mArcsec amplitude and one year period which should give a contribution on projection to both N-S and E-W GP-B signals.
May be the 85 days represent a favorable period to see these contributions (may be the reason why GP-B has announced a E-W effect on this period and at the sametime there is as you say a strange one sigma inconsistency with GR on th NS effect ) but then
i expect it to disapear on a one year integration.



So may be could you add a second possible prediction for DG :
If preferred frame is not the Earth (sun or galaxy or CMB)

Frame dragging 0
Geodetic as in RG
Preferred frame effect: 40marcsec-amplitude one_year-periodic angular precession

Regards

Fred