Alternative theories being tested by Gravity probe B

[LeBourdais]

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"

Hi Kris,

Do you mean to say that the spin of the four gyroscopes have been initially aligned in the same direction ?

That sounds strange

Paul

 

[Kris Krogh]

Hi Paul,

It's a good system. Without this redundancy, they would be in a bad situation now. They need be able to compare the outputs of multiple devices to correct errors. Two rotate one way, and two the other, but they all have the same axis of rotation. You can find this kind of information on the GP-B web site.

Kris

 

[cosmopot]

New clothe put on the king

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??

You know flat space is nothing but:
ds^2=dx^2+dy^2

flat Minkowski spacetime is nothing but:
ds^2=-c^2dt^2+dx^2+dy^2+dz^2
where
ds=dx if dt=dy=dz=0
and
dT=cdt =c time if dx=dy=dz=0 where dT^2=-ds^2

curved spacetime is nothing but:
ds^2=-Ac^2dt^2+Bdx^2+Cdy^2+Ddz^2
where
ds=sqrt(B)dx if dt=dy=dz=0
and
dT=sqrt(A)dt = c time if dx=dy=dz=0 where dT^2=-ds^2
Therefore, t is not time because A varies with position on curved spacetime manifold.

 

[LeBourdais]

It's a good system. Without this redundancy, they would be in a bad situation now. They need be able to compare the outputs of multiple devices to correct errors. Two rotate one way, and two the other, but they all have the same axis of rotation. You can find this kind of information on the GP-B web site.

Thanks a lot Kris ! That's really interesting. I will check on the GP-B web site.

By the way, I have received the answer to my question from GP-B Web Site Curator: for the moment now, they got no "best value" for the frame-dragging effect.

Paul

 

[Kris Krogh]

Hi Paul,

I emailed the same address in 1999, to ask when they expected to launch the probe. It was scheduled for that October, but everyone knew they were running way behind. The response was that they were on schedule, and maybe would move the launch ahead to July. (Nice creative touch.) They ended up launching in 2004.

If you believe they have no idea how this measurement compares to the expected frame dragging, you're as gullible as I've been about their scheduling of the launch, release of data and analysis. (These delays have hurt me badly.) You can't blame the GP-B people entirely, because politics and diplomacy are necessary to carry out a project like this.

Kris

 

[LeBourdais]

Hi Kris,

Of course they probably know more than they say, but something sure, they won't give a "best value" for frame-dragging before they are ready to do so. Until they do, we can only speculate.

Paul

 

[henryco]

Hi Kris,

Of course they probably know more than they say, but something sure, they won't give a "best value" for frame-dragging before they are ready to do so. Until they do, we can only speculate.

Paul

If it is in conflict with GR, they will never dare give the central value for the frame dragging...which is dramatic since, if all experimentalists behave this way as soon as they get an anomaly...progress is hopeless!
However they can at least answer my simple questions to let us make up our proper mind, and take our own responsability of what we have to say about the result:
How did they obtain the East-West plot?, what was subtracted before?
What does the graph look like for other Gyros?

i didnt got any answer, but i was trying to reach Everitt himself. May be i should better try the email of the guy that has answered your question.
What is it?

cheers,

F H-C

 

[LeBourdais]

If it is in conflict with GR, they will never dare give the central value for the frame dragging...which is dramatic since, if all experimentalists behave this way as soon as they get an anomaly...progress is hopeless!

Salut Fred,

Do you mean to say that they would have spent 800 millions dollars to send GP-B in space with the intent of not giving the results if these were contradictory with GR ?

i didnt got any answer, but i was trying to reach Everitt himself. May be i should better try the email of the guy that has answered your question.
What is it?

There is no secret about it, it's the e-mail address provided on GP-B Web site: www@relgyro.stanford.edu
The person that answered to me is the Web Site Curator.

Take it easy Fred

Friendly,

Paul

 

[jgraber]

Preliminary Frame Dragging "Glimpse"

I am posting from the APS meeting in Jacksonville.
You can see the preliminary result that was presented here,
with lots and lots of caveats,
by going to the GPb Homepage,
http://einstein.stanford.edu/index.html
and clicking on poster L1.00028,
Gravity Probe B Science Data Analysis: Filtering Strategy.
The result is called
"Glimpses of Frame Dragging"
and is in the bottom right quadrant of the poster.
One "glimpse" differs from GR by about two sigma,
but everything is still preliminary,
including the size of the sigma,
which is of order 10 mas/y
i.e. milliarcseconds per year.
I believe this particular "glimpse" is based on about 40 days data from one of the gyros.
Also, they have not yet unblinded themselves from the improved drift of the guidestar.
However, they still hope/expect to reduce their sigma to 1 or 2 mas/y by December.
Francis said there may be a small hint of a difference with GR,
but it is still much too early to talk about this seriously.
Jim Graber

 

[henryco]

I am posting from the APS meeting in Jacksonville.
You can see the preliminary result that was presented here,
with lots and lots of caveats,
by going to the GPb Homepage,
http://einstein.stanford.edu/index.html
and clicking on poster L1.00028,
Gravity Probe B Science Data Analysis: Filtering Strategy.
The result is called
"Glimpses of Frame Dragging"
and is in the bottom right quadrant of the poster.
One "glimpse" differs from GR by about two sigma,
but everything is still preliminary,
including the size of the sigma,
which is of order 10 mas/y
i.e. milliarcseconds per year.
I believe this particular "glimpse" is based on about 40 days data from one of the gyros.
Also, they have not yet unblinded themselves from the improved drift of the guidestar.
However, they still hope/expect to reduce their sigma to 1 or 2 mas/y by December.
Francis said there may be a small hint of a difference with GR,
but it is still much too early to talk about this seriously.
Jim Graber

Thank you very much for these informations...the problem is that i was not able to understand these plots mainly because of the bad resolution in the scanned axis...i still don't see what the axis in the ellipses plots represent:
the y-axis seems to be frame dragging , but the x-axis not sure: a north/south effect?
Does the expression "glimpses so far" mean that for the time being it was not possible to extract a continuous frame dragging behind those glimpses?
Are those glimpses the same resonance peeks shown in the east-west plot of the GP-B error poster?
Since you are in Jacksonville may be you have this information.

Thank you again



F H-C

 

[henryco]

Salut Fred,

Do you mean to say that they would have spent 800 millions dollars to send GP-B in space with the intent of not giving the results if these were contradictory with GR ?

Salut Paul,

Of course not... and i apologize. But it's too frustrating for me not
to attend the APS conference and i have difficulties to correctly interpret
the information given on the posters...

Take it easy Fred

Friendly,

Paul

You are right Paul

amiclt,

Fred

 

[makc]

people simply write r, t, \phi and assume they are distance, time, angle respectively

but no one assumes that they are same distance, time, angle as in flat Minkowski spacetime, or do they?

 

[jgraber]

henryco,
the other axis is the geodetic effect.
The center of the largest ellipse is close to the expected GR value.
Jim Graber

 

[henryco]

henryco,
the other axis is the geodetic effect.
The center of the largest ellipse is close to the expected GR value.
Jim Graber

OK but as far as i know frame dragging must be continuous, not only happen from time to time as isolated glimpses (or did i miss something? somebody can confirm or invalidate this?)...otherwise this has nothing to do with GR frame dragging. What on Earth does this glimpse mean? Once we admit that this measurement is very preliminary and that no one should draw conclusion about it, there should be no problem for the experimentalist to answer this simple question: what does glimpse mean here? does it mean that from time to time there appears to be a short time burst of frame dragging (june 2006...) and that nothing is detected in between two such manifestations so far?
or is this glimpse simply due to the observer selection of a short period of time?
The first is the interpretation i must take the more serious since otherwise i would not be able to understand the question "why glimpses so far?". Moreover i understand in this case why their dominant error comes from the resonance peeks shown in the back/left plot in the error poster since such peeks can really mimic a momentaneous burst of frame dragging but obviously not a constant drift rate. If you are still in Jacksonville may be can you ask some member of the GP-B team these questions...my emails are never answered! what on Earth is going on? am i a plague-stricken?

Best regards and thank you for your help if you can get this information/confirmation.

F H-C

 

[jgraber]

The fractional data is due to two things: 1 They are not yet done analyzing it.
2. The spacecraft shut down briefly nine times during the eleven months of science data taking.
they are working on "stitching it together."
Best.
Jim Graber

 

[Kris Krogh]

Francis said there may be a small hint of a difference with GR,
but it is still much too early to talk about this seriously.
Jim Graber

Hi Jim,

Thanks very much for the information! Does the possible small hint Francis mentioned refer to frame dragging specifically? Also, do you have any sense whether this is in the direction of a larger effect, or smaller than expected?

As F H-C mentioned, on the two charts of the modeled Gyro 3 torque, we can't read any of the labels or numbers on the axes, or the other fine print. Can you fill us in? Also, do the ellipses indicate bounds on possible values?

Best wishes,

Kris Krogh

 

[LeBourdais]

As F H-C mentioned, on the two charts of the modeled Gyro 3 torque, we can't read any of the labels or numbers on the axes, or the other fine print.

Hi Kris,

If we look at the upper chart ("Torque Modeling Example : Motion of Gyroscope 3"), the dashed line is referred to as the "estimated relativistic motion" and it is clearly not flat. Therefore, whatever the numbers on the axes, I guess we can conclude that their "best value" for frame-dragging is not zero. Am I missing something ?

Paul

 

[magnetar]

Gravity probe-b backs general relativity!

http://physicsweb.org/articles/news/11/4/11/1

 

[henryco]

Hi Kris,

If we look at the upper chart ("Torque Modeling Example : Motion of Gyroscope 3"), the dashed line is referred to as the "estimated relativistic motion" and it is clearly not flat. Therefore, whatever the numbers on the axes, I guess we can conclude that their "best value" for frame-dragging is not zero. Am I missing something ?

Paul

hi paul

I would say:
1) it depends if the y-axis actually shows a pure east-west deviation, doest it (i can't decode the y-scale)?
2) even an actual east-west effect can have another origin than frame dragging (for example if we are in the vicinity of resonance peeks as shown in the error poster)...
3) The latter remark is reinforced if the (even preliminary) fitted drift rate is at several sigmas from GR prediction! If i now decode well the scales on the "glimpses plot" there are four glimpses at respectivily and approximately 2,3,8,8 standard deviations from the GR prediction !

Cheers,

Fred

 

[Kris Krogh]

Hi Paul,

You have a point there, at least as far as this particular graph is concerned. I contacted the web page curator, and I think she'll put up a more readable version of this poster for us tomorrow.Magnetar,

That article says the geodetic effect of general relativity has been measured. But that's already been measured more accurately in other ways. The important one for me is frame dragging. They say Gravity Probe B hasn't measured that yet.

 

[jgraber]

Hi everyone,
Sorry I can only post on coffee breaks when I am near the APS temporary hotspot. As I understand the "glimpses" each ellipse is a one sigma radius, and GR is very near the center of the earliest, crudest glimpse, and about two radii (i.e. approx two sigma) from the smallest, latest "glimpse", which is still based on a very limited amount of not yet fully processed data. As I understand it, the data in that plot are total motions, including nonrelativistic effects as well as the two GR effects. The speakers mentione three or four of order 40-80 mas/y total that add to the Geodetic Effect and at least one of order 40mas/y that adds to the Frame Dragging Effect. Because of these additions, the GR prediction is offset from the values usually quoted. The values on the "glimpse" chart have minus signs and increase in absolute value downward and to the left. They increase (or decrease) by 20 per grid line and the central values are 80 for the vertical (Frame Dragging) axis and 6580 for the horizontal (Geodetic) axis. The latest "Glimpse" is slightly offset in the direction of larger values, so IF you take it at face value, which is wildly over optimistic in my opinion, it would indicate that both effects are slightly larger than the GR prediction by about 10 mas/y compared to 6600 and 40. However, there will be new, much more reliable numbers in December or so, and the only sensible course in my opinion is to wait until then. remember, there are systematic as well as statistical errors, and the experiment is quoting their current overall sigma as 90-100 mas/y. This is small compared to the Geodetic effect, but totally swamps the Frame Dragging effect. They say the Geodetic effect is totally obvious from the rawish data, but the Frame Dragging Effect must be dug out of the noise. Remember, they found two major unexpected noise sources, and for several months were afraid that they would not be able to report any frame dragging result. It is only because of the large amount of redundancy in the data and the fact that the two GR effects and the two unexpected noise sources have four different mathematical characteristics that they expect to be able to recover something close to the originally expected accuracy.
Jim

 

[LeBourdais]

Thank you very much Jim ! It gives me a better picture of what's going on.

Paul

 

[Kris Krogh]

Jim,

Thanks very much for your insights! That all seems to add up. Would it be possible to confirm with someone there from GP-B that the best of this data would hint at a slightly larger than expected frame-dragging effect? (If it hints at anything.)

Best wishes,

Kris

 

[Garth]

I have just returned from the APS Meeting at Jacksonville and a holiday in Florida.

As has been well discussed the first results have verified the GR geodetic prediction to 1% but there is no handle on the frame-dragging prediction, basically because unexpected signals so far swamp it, except for 'glimpses'.

By the end of the year the correct removal of these effects will give a robust reading to both precessions.

The running now stands:

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 following are still in the running:

GPB Geodetic precession (North-South)
1. GR = 6.6144 arcsec/yr.
2. BD = (3\omega + 4)/(3\omega + 6) 6.6144 arcsec/yr. where now \omega >60.
4. NGT = 6.6144 - a small \sigma correction arcsec/yr.
6. NG = 6.6144 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.

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

1. GR = 0.0409 arcsec/yr.
2. BD = (2\omega + 3)/(2\omega + 4) 0.0409 arcsec/yr.
4. NGT = 0.0409 arcsec/yr.
6. NG = 0.0102 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.Those that have fallen by the wayside:

3. SCC = 4.4096 arcsec/yr.
5. MVSR = 0.0 arcsec/yr.
7. FST = 4.4096 arcsec/yr.
8. MMR = -6.56124 arcsec/yr.
13. PSG = 0.0000 arcsec/yr.

Garth

 

[LeBourdais]

As has been well discussed the first results have verified the GR geodetic prediction to 1% but there is no handle on the frame-dragging prediction, basically because unexpected signals so far swamp it, except for 'glimpses'.

By the end of the year the correct removal of these effects will give a robust reading to both precessions.

Hi Garth,

Thank you for this status.

Sorry for your theory.

Best wishes
Paul

 

[Garth]

Hi Garth,

Thank you for this status.

Sorry for your theory.

Best wishes
Paul

Thank you for your commiserations!

Garth

 

[magnetar]

I do not understand why so many "Alternative theories" about gravity?
why so many controversial ??

 

[sylas]

I have just returned from the APS Meeting at Jacksonville and a holiday in Florida.

Hi Garth,

Can you explain the difference between the 6614.4 and 40.9 being quoted in numerous sources before the APS meeting(including many still available in the GP-B site) and the 6606 and 39 numbers now being used? (numbers being GR expectations for geodetic and framedragging effects in milliarcsec/yr)

I'm guessing it could be a difference in the altitude of the final orbit, but I don't know.

Cheers -- Sylas

 

[Garth]

That is a good question that wasn't addressed at the meeting, I have only recently become aware of that anomaly myself.

The posters clearly show the latter (6606 and 39 mas/yr) set of values while all their previous literature showed the former (6614.4 and 40.9 mas/yr) set.

The orbit decreased in SMA by about 350 metres during the lifetime of the experiment, but that should have increased the expected precessions by about one part in 10^-4 in my estimation.

The present measured value of the geodetic precession is 6638 +/- 97 mas/yr. (Francis Everitt APS Plenary Session 14th April 07)

Note however on the Gravity Probe B Science Data Analysis: Filtering Strategy poster (Click on the title), it says of the geodetic measurement:

Current Estimates (“Glimpses”)
-6595 ± 10 milliarcsec/year
-6604 ± 7 milliarcsec/year

GP-B website:

The experiment’s final result is expected on completion of the data analysis in December of this year. Asked for his final comment, Francis Everitt said: "Always be suspicious of the news you want to hear."

Garth

 

[sylas]

That is a good question that wasn't addressed at the meeting, I have only recently become aware of that anomaly myself.

OK... I have gone back to first principles, and I think I have sorted this one out.

The information at the GP-B seems pretty sloppy. I have checked out the Fact Sheet, dated February 2005. The information therein is inconsistent.

Here are the orbit characteristics...

Orbit

Characteristics Polar orbit at 642 kilometers (400 miles), passing over one of the poles every 48.75 min.
Semi-major axis 7,027.4 km (4,366.6 miles)
Eccentricity 0.0014
Apogee altitude 659.1 km (409.5 miles)
Perigee altitude 639.5 km (397.4 miles)

The semi-latus rectum (wiki ref) is given as:
a*(1-e^2) = 7.0274*10^6*(1-0.0014^2) = 7.027386226*10^6
which is the same a, up to five figure accuracy.

The formula for geodetic precession is 1.5(GM)^{1.5}c^{-2}R^{-2.5}, where R is the semi-latus rectum (ref: Gravitation and cosmology, S. Weinberg (1972) [pp237-8]).

Plug in
<br /> G = 6.6742*10^{-11},<br /> M = 5.976*10^24,<br /> c = 299792458<br />

and we get 1.0155*10^{-12} rad/sec, or 6.60559 arcsec/yr.

However, the same press release, with these same orbit parameters, gives 6.6144

I'm guessing they had already calculated 6.6144 from a projected orbit; and then recalculated for the actual orbit, but did not properly update all the recorded predictions.

The value 6.6144 implies an orbit about 3.7 km smaller in radius.

Now… what formulae do I need to use for the Lense-Thirring effect?

Cheers -- Sylas

 

[Garth]

OK... I have gone back to first principles, and I think I have sorted this one out.

The information at the GP-B seems pretty sloppy. I have checked out the Fact Sheet, dated February 2005. The information therein is inconsistent.

Here are the orbit characteristics...The semi-latus rectum (wiki ref) is given as:
a*(1-e^2) = 7.0274*10^6*(1-0.0014^2) = 7.027386226*10^6
which is the same a, up to five figure accuracy.

The formula for geodetic precession is 1.5(GM)^{1.5}c^{-2}R^{-2.5}, where R is the semi-latus rectum (ref: Gravitation and cosmology, S. Weinberg (1972) [pp237-8]).

Plug in
<br /> G = 6.6742*10^{-11},<br /> M = 5.976*10^24,<br /> c = 299792458<br />

and we get 1.0155*10^{-12} rad/sec, or 6.60559 arcsec/yr.

However, the same press release, with these same orbit parameters, gives 6.6144

I'm guessing they had already calculated 6.6144 from a projected orbit; and then recalculated for the actual orbit, but did not properly update all the recorded predictions.

The value 6.6144 implies an orbit about 3.7 km smaller in radius.

Concur; does that mean their first set of values was simply a mistake?

Now… what formulae do I need to use for the Lense-Thirring effect?

Cheers -- Sylas

Here it is:

\Omega_{f-d} = \frac{GI}{c^2R^3}[\frac{3\underline{R}}{R^2}(\omega.\underline{R}) - \omega]

Garth

 

[sylas]

Concur; does that mean their first set of values was simply a mistake?Here it is:

\Omega_{f-d} = \frac{GI}{c^2R^3}[\frac{3\underline{R}}{R^2}(\omega.\underline{R}) - \omega]

Garth

Thanks Garth... yes, I know that formula. It is a vector equation, and it varies over the whole orbit. So we have some work to try and get a magnitude from it. I was hoping for a straight formula for the magnitude.

I also need a value for I, which is the moment of inertia for the Earth. I can calculate assuming a solid sphere; but distributions of mass are not uniform, so this is only an approximation.

The vectors are \omega, which is in a fixed direction along the Earth's axis, and R, which is the location of the probe. This part has a maximum value over the poles, the dot product is just a product of magnitudes. The direction is the opposite of \omega by the sign differences, so at the poles but in brackets has magnitude 2\omega. But over the equatot, the dot product drops to zero and the magnitude is \omega in the opposite direction.

The suggests a mean magnitude of \omega/2. I think.

Using I = 0.4MR_e^2 as a solid sphere, I get

0.2*GMR_e^2R^{-3}c^{-2}\omega

as a magnitude. My spreadsheet gets very roughly in the ball park with this, at 0.049

But I'm still out by much too much.

Any GP-B experts can help me out?

Thanks -- Sylas

 

[sylas]

Followup to my previous post! I have now found a figure for the moment of inertia of the Earth, and am able to get close to the OLD value for the framedragging effect. But I'll go through it all from the beginning with new numbers.

To get accurate values, I have tried to use data to five or six figures of accuracy, or whatever is available. I use SI units, unless explicitly given otherwise.

I've checked out the following sources.

• A NASA Planetary fact sheet for the Earth.
• The paper A General Treatment of Orbiting Gyroscope Precession, by Ronald J.Adler and Alexander S. Silbergleit (arXiv:gr-qc/9909054)
• The International Earth Rotation and Reference Systems Service: Useful constants.

Geodetic effect

The geodetic effect is 1.5*(GM)^1.5c^-2r^-2.5, where r is the semilatus-rectum of the probe orbit. This is the semimajor axis times (1-e²), as indicated in a previous post.

The radius of the orbit of GP-B is measured as 7027.4 km (semi-major axis). The eccentricity is e = 0.0014, so the semilatus rectum is 7027.386 km. Adler and Silbergeit use 7028 km with a circular orbit; this was calculated before launch.

The value of GM (gravitational constant times Earth mass) is known with great precision; much more than either G or M individually. The value of G*M is 3.986004418*10¹⁴ m³s^-2 in IERS.

NIST currently gives G as 6.67428*10^-11, which would give M as 5.9721864*10²⁴. The NASA page gives Earth mass as 5.9736*10²⁴; this corresponds to G = 6.6727*10^-11.

To convert from radians per second to milliarcseconds per year, the factor is 6.50908*10¹⁵. That uses a tropical year of 365.24219 days (IERS). The speed of light is 299792458

The only meaningful source of error here is in r, the radius of the orbit. The largest value for the geodetic precession requires r to be small, and the conversion factor to be large. The conversion factor for milliarcseconds/year uses the length of a tropical year, being 365.24219 days; there's no basis for using anything greater.

The calculation is

1.5 * (3.986004418 * 10^{14})^{1.5} * 299792458^{-2} * (7.027386 * 10^6)^{-2.5} * 365.24219 * 86400 * 360 * 3600 * 1000 / 2 / \pi

This gives the geodetic precession as 6603.77 milliarcseconds/year. I can't see any possible way to make this any bigger.

To make matters worse, Adler and Silbergeit also give a correction factor to take account of the Earth's oblate shape. This factor is given as:
1-\frac{9}{8}*J_2*(R/r)^2)

Here R is the radius of the Earth and J₂ is the quadrupole moment.

For the radius of the Earth, Adler and Silbergeit use 6378 km, NASA gives 6378.1 km, and the IERS gives 6378.1366 km.

For J₂, Adler and Silbergeit use 1.083*10^-3, and the IERS gives 1.0826359*10^-3. The accuracy here will not matter much.

This factor reduces the geodetic prediction, by (1-1.00*10^-3), to give a final prediction of 6597.14 milliarcsec/year

How anybody ever got 6614.4 I don't know.

There is an additional precession due to the Sun; but this is in a different plane, and is going to have more effect on framedragging. It is discussed in Adler and Silberguit as well, with a magnitude of 19 milliarcsec/yec, but mostly perpendicular to geodetic precession.

Frame dragging

As derived above (and Adler and Silbergeit confirm) the magnitude of the effect works out to be GJr^{-3}c^{-2}\omega / 2

The moment of inertia for a solid body is J = kMR^2, where k is a "moment of inertia ratio". This ratio is 0.4 for a uniform sphere, but it will be more if the mass density is greater near the surface, and less if the mass density is greater near the center.

Adler and Silbergeit use k = 1/3.024 = 0.3307. The NASA fact sheet gives k = 0.3308.

Using the value of GM from IERS, GJ would be kGMR², which is about 5.3640*10²⁷, using the NASA value for the radius R of the Earth.

The IERS gives a value for J directly, which is 8.0365*10³⁷; and with their value of G as 6.6742*10^-11, this gives GJ = 5.3638*10²⁷.

The length of a sidereal day 23.9345 hours (NASA sheet) so the rotation velocity ω is 7.2921 * 10^-5 rad/sec. In IERS it is 7.292115*10^-5.

The framedragging effect is
GJr^{-3}c^{-2}\omega/2

This works out to
5.3638*10^{27} * (7.0274 * 10^6)^{-3} * 299792458^{-2} * 7.292115*10^{-5} * 365.24219 * 86400 * 360 * 3600 * 1000 / 2 / \pi / 2

which gives 40.81 milliarcsec/year,

As before, there is a correction factor; this time equal to
1+\frac{9}{8}*J_2*(R/r)^2(1-\frac{3}{7}*MR^2/J))

This works out to 1-2.97*10^{-4}, which brings the prediction back down to 40.80 milliarcseconds/year.

This close to the 40.9; but now I don't know how they are obtaining 39.

Cheers -- Sylas

 

[Garth]

That's a very impressive piece of work, thank you Sylas.

Why don't you e-mail Alex Silbergleit at: gleit@relgyro.stanford.edu with these questions? And then let us know the answer of course.

Garth

 

[henryco]

That's a very impressive piece of work, thank you Sylas.

Why don't you e-mail Alex Silbergleit at: gleit@relgyro.stanford.edu with these questions? And then let us know the answer of course.

Garth

Hi everybody,

Thank you for your efforts to help clarify several points. I still can't decode the axis informations from the plot named Torque modeling example: motion of gyro 3 in the L10028 poster. Can someone who attended the APS conf or GP-B expert help us ?

regards,

F H-C

 

[Garth]

Hi everybody,

Thank you for your efforts to help clarify several points. I still can't decode the axis informations from the plot named Torque modeling example: motion of gyro 3 in the L10028 poster. Can someone who attended the APS conf or GP-B expert help us ?

regards,

F H-C

The unexpected torques on the rotors were from:
1) A time dependent polhode precession due to the gyros not being exactly spherical. The time dependency is modeled by a dissipation of kinetic energy over time.
2) A misalignment torque due to a variation of electric potential over the surface, which can arise due to the polycrystalline structure.
It can be affected by presence of contaminants and is modeled as dipole layer. The patch fields are present on rotor and housing walls and cause forces and torques between these surfaces.

On the Torque modeling example: motion of gyro 3 in the L10028 poster the legend is very unclear, but the x-axis is E-W orientation milliarcsec/yr and the y-axis I believe is Polhode phase angle error.

Garth

 

[henryco]

The unexpected torques on the rotors were from:
1) A time dependent polhode precession due to the gyros not being exactly spherical. The time dependency is modeled by a dissipation of kinetic energy over time.
2) A misalignment torque due to a variation of electric potential over the surface, which can arise due to the polycrystalline structure.
It can be affected by presence of contaminants and is modeled as dipole layer. The patch fields are present on rotor and housing walls and cause forces and torques between these surfaces.

On the Torque modeling example: motion of gyro 3 in the L10028 poster the legend is very unclear, but the x-axis is E-W orientation milliarcsec/yr and the y-axis I believe is Polhode phase angle error.

Garth

Thank you garth. I have asked other questions to the GP-B website curator
and were told that an upgrade will soon be available on their site with clearer
plots... For the time being i don't see how i could read the amount of relativistic motion from this plot where the dashed line represents the estimated relativistic motion.
I also asked how the error plot was obtained on the error poster ...
They also told me that the audio file of their presentations will soon be available online



F H-C


Regards,

F H-C

 

[henryco]

The unexpected torques on the rotors were from:
1) A time dependent polhode precession due to the gyros not being exactly spherical. The time dependency is modeled by a dissipation of kinetic energy over time.
2) A misalignment torque due to a variation of electric potential over the surface, which can arise due to the polycrystalline structure.
It can be affected by presence of contaminants and is modeled as dipole layer. The patch fields are present on rotor and housing walls and cause forces and torques between these surfaces.

On the Torque modeling example: motion of gyro 3 in the L10028 poster the legend is very unclear, but the x-axis is E-W orientation milliarcsec/yr and the y-axis I believe is Polhode phase angle error.

Garth

There are also some other details i would like to know about these effects

1) The dissipative polhod motions must after some time determine the actual rotation axis of the four gyroscopes. its direction should be a priori different
and arbitrary for each one: has this information been given at the conference: the raw "initial" axis direction for each Gyro i.e. after stabilisation (when the polhode dissipative effects become small)

2) If it is true that there is a force proportional to a misalignment...
eventually this force should impose an alignment therefore a preferred direction relative to the stator and if the latter is fixed with respect to distant stars (is it?) this should prevent any relativistic motion at some level...

Sorry for these probably naive questions but since i couldn't attend the conference...

Regards


F H-C

 

[Garth]

Yes,

The unexpected signals have complicated the matter somewhat for the GP-B and that explains why it is taking so long to produce the results.

Whereas they were expecting some polhode motion, the new thing was for this to be time dependent. Therefore it has taken some time for them to model this effect correctly. However, the polhode motion is only a minor effect which is only significant when the most accurate readings are required especially for the frame-dragging effect.However what has nearly spoiled the experiment was the misalignments experienced because of electrostatic patch effects. With the spacecraft rolling about its axis pointing towards the guide star every 77.5 seconds they found a misalignment of up to 1 arcsec/deg/day, potentially larger than the relativity precessions they were looking for.

In their words:

... wide variety of unexpected scientific, technical and programmatic difficulties from minor discrepancies to design flaws and outright failures. GP-B provides several excellent examples of the process of recovery from these events...

The first thing they have to do is to model is patch effect correctly using the geometry and rate of change data to isolate the 'noise' from the signal without using the expected relativity answer in the process.

As to the detailed answers to your questions they haven't given much away, because I think they are not sure at present of that answer. They say that it is very much "a work in progress". We will have to wait until the end of the year when all will be revealed, I trust, in the promised published papers.

However I must add that I find Francis Everitt's final comment "Always be suspicious of the news you want to hear." intriguing. It is almost as if he does not want to believe in their results...

Garth

 

[fasterthanjoao]

Garth,

Whilst I've read (and unfortunately only understood part) of this thread, it's always been with interest. I've refrained from posting since most of the questions I have about the data you've been posting (thanks, by the way) Garth is that the questions tend to be answered anyway.

Your recent post on the gravity probe B results (sorry your theory didn't work out), and subsequent discussions, are particularly an interesting read from a beginners point of view as it's easy to pick up knowing what's left.

It may be a tall ask, but if you've time, could you offer a brief, simplified post (even a PM?) on the basic large scale changes/implications these theories may have? any other outrageous features you're proficient in are always worth noting! thanks.

 

[Tripathy]

The Stanford website mentions on the first phase GP-B results dated 14th April 2007:
“….. the data from the GP-B gyroscopes clearly confirm Einstein's predicted geodetic effect to a precision of better than 1 percent. However, the frame-dragging effect is 170 times smaller than the geodetic effect, and Stanford scientists are still extracting its signature from the spacecraft data. 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.”

Can anyone answer whether the result of the frame-dragging effect, derived after removal of the much larger torque and sensor effects, can still be considered to be a result obtained from a “controlled” experiment?

 

[Garth]

The Stanford website mentions on the first phase GP-B results dated 14th April 2007:
“….. the data from the GP-B gyroscopes clearly confirm Einstein's predicted geodetic effect to a precision of better than 1 percent. However, the frame-dragging effect is 170 times smaller than the geodetic effect, and Stanford scientists are still extracting its signature from the spacecraft data. 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.”

Can anyone answer whether the result of the frame-dragging effect, derived after removal of the much larger torque and sensor effects, can still be considered to be a result obtained from a “controlled” experiment?

That is a good question, which may be asked of both precession measurements even though the Geodetic precession is some 170 times larger.

The GP-B team are working very hard to model and determine the unexpected time dependent polhode and patch effect torques on the gyro rotors to within 0.1 mas so they can be subtracted from the raw data.

They claim they are doing so without using the expected results in the process, thus keeping GP-B a controlled and objective experiment.

However I have two questions:
1. How do you know that you have allowed for all other effects that might be affecting the result? In other words the tendency in any experiment is to keep subtracting sources of 'noise' until the remaining signal is what you expect, and then stop. If the result is not what is expected then you might discover another unknown source of error.

2. Might there be a degeneracy in the modelling of these torques? i.e. Having fitted the time dependent data well to one solution and use that to obtain the final result, might there be another solution that also fits the noise data well that produces a different result?

Garth

 

[Garth]

Garth,

Whilst I've read (and unfortunately only understood part) of this thread, it's always been with interest. I've refrained from posting since most of the questions I have about the data you've been posting (thanks, by the way) Garth is that the questions tend to be answered anyway.

Your recent post on the gravity probe B results (sorry your theory didn't work out), and subsequent discussions, are particularly an interesting read from a beginners point of view as it's easy to pick up knowing what's left.

It may be a tall ask, but if you've time, could you offer a brief, simplified post (even a PM?) on the basic large scale changes/implications these theories may have? any other outrageous features you're proficient in are always worth noting! thanks.

I don't claim to be an expert of these other theories, other than SCC and the Brans-Dicke theory, but I have given links to their papers, which you can read up for yourself.

In the BD theory a minimally connected scalar field is added to the GR field equation that has the effect of perturbing the GR space-time and therefore freely-falling particle and photon geodesics, but does not otherwise interact with them. As these perturbations have not been discovered the scalar field must be very weakly connected to matter. The presence of the scalar field affects the cosmological solution and cosmic evolution.

In SCC that scalar field is now non-minimally connected and interacts with particles inducing a scalar field force on particles but not photons. The scalar field force exactly compensates for the perturbation of space-time in vacuo, and SCC freely-falling particle and photon geodesics are the same as those of GR. The coupling constant \lambda was equal to unity. The theory passed all the tests GR does, up to but not including the GP-B geodetic precession prediction. It had interesting cosmological consequences as well as predicting the Pioneer anomaly discussed elsewhere on the Cosmology Forum.

I can see my way clear to a general self creation theory in which \lambda is left as an unknown variable.

The geodetic prediction becomes

\Omega = [(1 - \lambda/3)6.6 + 0.25] arcsec/yr.

(I have found an extra 0.25 arc/sec/yr precession due to cosmological time dilation (clock drift) that makes my original prediction 4.65 arcsec/yr not 4.4 arcsec/yr.)

Unfortunately the theory then predicts the total mass density parameter for the universe to be

\Omega_T = \frac{1}{3\lambda},

so if \lambda is small a lot of DM and DE is required and an attractive feature of the original theory is lost.

I will post more when I have published.

Garth

 

[Garth]

I have now (modestly!) included my modified General Theory of Self Creation Cosmology (GSCC) which leaves the \lambda parameter undetermined.

Note that the results published at the April APS meeting in Jacksonville include a modified GR prediction with one decimal place less accuracy. The reason for this modification is not clear, however the modified GR predictions are included in this post.

The running now stands:

1. Einstein's General Relativity(GR)
2. Brans-Dicke theory (BD)
3. Barber's General Theory of Self Creation Cosmology (GSCC), to be published
4. Moffat's Nonsymmetric Gravitational Theory (NGT)
5. Stanley Robertson's Newtonian Gravity Theory (NG),
6. F. Henry-Couannier's Dark Gravity Theory (DG).
7. Alexander and Yunes' prediction for the Chern-Simons gravity theory (CS).
8. Kris Krogh's Wave Gravity Theory (WG)
9. 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 precession (North-South)

1. GR = 6.606 arcsec/yr.
2. BD = (3\omega + 4)/(3\omega + 6) 6.606 arcsec/yr. where now \omega >60.
3. GSCC = [(1 - \lambda/3)6.606 + 0.250]arcsec/yr. where at present \lambda < 0.14.
4. NGT = 6.606 - a small \sigma correction arcsec/yr.
5. NG = 6.606 arcsec/yr.
6. DG = 6.606 arcsec/yr.
7. CS = 6.606 arcsec/yr.
8. WG = 6.606 arcsec/yr.
9. KK = (1 + b/6 - 3b² + ...) 6.606 arcsec/yr. where 0 < b < 0.07.

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

1. GR = 0.039 arcsec/yr.
2. BD = (2\omega + 3)/(2\omega + 4) 0.039 arcsec/yr.
3. GSCC = 0.039 arcsec/yr.
4. NGT = 0.039 arcsec/yr.
5. NG = 0.039 arcsec/yr.
6. DG = 0.0000 arcsec/yr.
7. CS = 0.039 arcsec/yr. + CS correction
8. WG = 0.0000 arcsec/yr.
9. KK = 0.039 arcsec/yr.

Garth

 

[MeJennifer]

Not 4.4096?

Garth, all the respect for your theory, but didn't your theory predict 4.4096 arcsec/yr? How come it now shows a number much closer to the experimental outcome?

 

[Garth]

Garth, all the respect for you theory, but didn't you predict 4.4096 arcsec/yr? How come it now shows a number much closer to the experimental outcome?

I have written more on the Self Creation Cosmology thread.

The original theory was highly determined with \lambda = 1. It had many interesting features, which I have been discussing on that thread and it made a particular prediction for GP-B, which appears not to be verified.

Therefore the day after that announcement was made on the 14th April I sat down and looked again at the theory. I realized that there was a cosmological clock drift time dilation to take into account that adds another 0.25 arcsec/yr, but which wasn't enough to save the theory.

I therefore generalised the theory by leaving \lambda undetermined. This meant losing some of the attractive features of the model but still preserving several others. The result is the prediction posted above and I am now writing up the new General Theory of Self Creation Cosmology for publication.

If the final results for GP-B are exactly those predicted by GR then I will finally say goodbye to SCC!

Garth

 

[LeBourdais]

I can see my way clear to a general self creation theory in which \lambda is left as an unknown variable.

The geodetic prediction becomes

\Omega = [(1 - \lambda/3)6.6 + 0.25] arcsec/yr.

(I have found an extra 0.25 arc/sec/yr precession due to cosmological time dilation (clock drift) that makes my original prediction 4.65 arcsec/yr not 4.4 arcsec/yr.)

Unfortunately the theory then predicts the total mass density parameter for the universe to be

\Omega_T = \frac{1}{3\lambda},

so if \lambda is small a lot of DM and DE is required and an attractive feature of the original theory is lost.

Hi Garth,

The smaller the value of \lambda, the higher the value of \Omega_T will be. Can you tell us which is the highest value of \Omega_T you would consider acceptable ? This would provide a minimum acceptable value of \lambda and a maximum acceptable value for the geodetic precession.

Paul

 

[Garth]

Hi Garth,

The smaller the value of \lambda, the higher the value of \Omega_T will be. Can you tell us which is the highest value of \Omega_T you would consider acceptable ? This would provide a minimum acceptable value of \lambda and a maximum acceptable value for the geodetic precession.

Paul

Hi Paul!

In GSCC if \lambda \neq 1 then ideally \lambda ~ 1/3, which would give \Omega_T ~ 1, concordant with the standard model, however that would be too high a value of \lambda for the present geodetic precession.

I say "present" because I think we ought to wait for the final analysis before being sure what that reading actually is. They have to accurately model the polhode and patch effect torques accurately and unambiguously first.

The present error bars on the geodetic measurement allow for \lambda < 0.14 which gives \Omega_T > 2.33.

It then depends on whether that could be concordant with the WMAP data and exactly how much DE and DM would be required and plausible.

Garth

 

[Garth]

Hi everybody,

Thank you for your efforts to help clarify several points. I still can't decode the axis informations from the plot named Torque modeling example: motion of gyro 3 in the L10028 poster. Can someone who attended the APS conf or GP-B expert help us ?

regards,

F H-C

The Gravity Probe B site now includes slides of http://einstein.stanford.edu/content/aps_posters/APS_talk_Everitt.pdf which includes a slide in high definition of that diagram; see page 21.

The 'X-axis' is the N-S result, the 'Y-axis' is the W-E result, both in mas.yr^-1 . The ellipses are the one sigma error envelopes around the readings at succeeding stages or 'floors' of error reduction.

This is as described by Jim in #171.

These readings include the Earth geodetic (EG) result, the Earth frame-dragging (EFD) result, the solar geodetic (SG) result and the proper motion (PM) of the guide star.

In the E-W direction the expected values (yr^-1) are:
GR EFD = -39, SG = -16, PM = -20 (mas) making a total net expected value of -75 mas.

In the N-S direction the expected values (yr^-1) are:
GR EG = -6606, SG = +7, PM = +28 (mas) making a total net expected value of -6571 mas.

These net expected values are marked with the two large green arrows.

However, you can see from that diagram that the latest, March 2007, ellipses are not centred on those values, the frame-dragging result is around -95 mas yr^-1 and the geodetic result around -6595 mas yr^-1, which makes it very interesting!

Caveat: Note that the size of the error on the March 2007 'glimpses' are only about 20 mas yr^-1 whereas Francis Everitt quoted 6638 \pm97 mas yr^-1 for the present evaluation of the geodetic precession. The size of the \pm97 mas error is due to "Residual gyro-to-gyro inconsistencies due to incomplete modeling ~ 100 mas yr^-1" (See slide 20 in that lecture presentation)

We wait for December for those errors to be reduced further!

Garth

 

[henryco]

The Gravity Probe B site now includes slides of http://einstein.stanford.edu/content/aps_posters/APS_talk_Everitt.pdf which includes a slide in high definition of that diagram; see page 21.

The 'X-axis' is the N-S result, the 'Y-axis' is the W-E result, both in mas.yr^-1 . The ellipses are the one sigma error envelopes around the readings at succeeding stages or 'floors' of error reduction.

This is as described by Jim in #171.

These readings include the Earth geodetic (EG) result, the Earth frame-dragging (EFD) result, the solar geodetic (SG) result and the proper motion (PM) of the guide star.

In the E-W direction the expected values (yr^-1) are:
GR EFD = -39, SG = -16, PM = -20 (mas) making a total net expected value of -75 mas.

In the N-S direction the expected values (yr^-1) are:
GR EG = -6606, SG = +7, PM = +28 (mas) making a total net expected value of -6571 mas.

These net expected values are marked with the two large green arrows.

However, you can see from that diagram that the latest, March 2007, ellipses are not centred on those values, the frame-dragging result is around -95 mas yr^-1 and the geodetic result around -6595 mas yr^-1, which makes it very interesting!

Caveat: Note that the size of the error on the March 2007 'glimpses' are only about 20 mas yr^-1 whereas Francis Everitt quoted 6638 \pm97 mas yr^-1 for the present evaluation of the geodetic precession. The size of the \pm97 mas error is due to "Residual gyro-to-gyro inconsistencies due to incomplete modeling ~ 100 mas yr^-1" (See slide 20 in that lecture presentation)

We wait for December for those errors to be reduced further!

Garth

Very interesting indeed...but, i don't see where your 20 mas yr^-1 in the MArch glimpse comes from! looking at the March ellipses i rather see something like -98 +- 7 which is more than 3 sigmas away from -75 for the two ellipses!

Anyway if there are 100mas yr^-1 gyro to gyro inconsistencies...
i would say that these center values and small errors mean nothing for the time being and i understand that they need more time to clarify the situation.

Here is my favoured scanario: the frame dragging is zero but there are some resonance peaks from time to time as shown in their error poster for gyro 2
If the resonance peaks are much larger in time as may be the case for other gyros , then they are much more difficult to separate from the zero baseline and this is why in the error poster they estimate a 100 mas y-1 for this main source error assuming much larger peaks in the other Gyros than those seen for Gyro 2.

The question is : Does Gyro 2 plot in the error poster only shows an error or an absolute measurement after removing all other sources of errors, sun geodetic an proper star motion effect ? If not something very accurate (very indeed since the final error will come mostly from the resonance peaks as they say there) was subtracted by hand to put the mean to zero...what is it?
The quite ambiguous answer i got from Everitt is:

" You are observant in noticing that the
results for gyro #2 obtained by the geometric
analysis method could be interpreted as giving a
smaller than Einstein east-west drift "

"but until
we have completed the full analysis, taking into
account the small but significant misalignment
torques, we should not attach too much importance
to that. There were certain anomalous features
in that gyroscope's performance. We believe we
understand them but remain watchful."

yes but i would say that the mean effect shown by the geometric approach here is so small compare to GR prediction that this should hardly be fortuitous... (unless strange fine tuning between systematical effects and physical effects occured!)

F Henry-Couannier