Alternative theories being tested by Gravity probe B

[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
$$G = 6.6742*10^{-11}, M = 5.976*10^24, c = 299792458$$

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
$$G = 6.6742*10^{-11}, M = 5.976*10^24, c = 299792458$$

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 $\pm$97 mas yr^-1 for the present evaluation of the geodetic precession. The size of the $\pm$97 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 $\pm$97 mas yr^-1 for the present evaluation of the geodetic precession. The size of the $\pm$97 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

 

[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!

~20mas is the crude size across both March error ellipses. I am not willing to accept any smaller value for the error at this stage!

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.

quite ...my point exactly.

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.

An interesting point, but we are not grasping at straws by any chance are we?

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."

Thank you for that quote from Francis.

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

We wait and see!

Garth

 

[JonathanK]

Hi Garth, I’m new to the forum, enjoying the discussion. Have an update about Planck scale gravity (PSG), which has been mentioned.

Like you I looked at my theory afresh after the preliminary results, did a calculation that shows clearly it was the prediction for the geodetic effect, rather than PSG itself, that was flawed. It sets out the correct prescription from the theory, by deriving the effect numerically from the original conceptual basis.

I don’t know if the geodetic effect has been derived in this way from a flat space theory before (some think it almost synonymous with space curvature). But the component thought in GR to be due to curvature, 2/3 of the total effect, came straight out of a very simple calculation for one of the gyros on GP-B. PSG creates an analogue effect, with the same numerical value. As per the first paper, the main issue was only this curvature component (the other 1/3 had various related questions that weren’t gone into). The new paper is under peer review, but is in preprint at

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

Unless the calculation or its conception is wrong, this puts PSG back on track like SCC, rather than having fallen by the wayside.

Thanks, Jonathan

 

[henryco]

~20mas is the crude size across both March error ellipses. I am not willing to accept any smaller value for the error at this stage!
Garth

Sorry but I'm just numerically translating the ellipse information that anybody can see in this plot. In a one sigma horizontal ellipse like this one, the error is half the size of the ellipse, as far as i know. So the error given in this plot by GP-B collaboration is in between 6 and 8 mas y-1...whatever the other issues such as extra 100 mas y-1 error sources that remain to be understood...

cheers,

Fred

 

[SpaceTiger]

And when the next prediction fails, will we see another modification/generalization? Come on people, don't you think your time would be better spent working on something new?

 

[marcus]

And when the next prediction fails, will we see another modification/generalization? Come on people, don't you think your time would be better spent working on something new?

Nick SpaceTiger, good to see you back!
Pervect said you were busy with PhD thesis and he was urged to step in and fill the gap. Does this mean that the thesis is done now?
or pending approval? In any case congratulations on forthcoming PhD

 

[SpaceTiger]

Nick SpaceTiger, good to see you back!
Pervect said you were busy with PhD thesis and he was urged to step in and fill the gap. Does this mean that the thesis is done now?
or pending approval? In any case congratulations on forthcoming PhD

Hi marcus! I'm afraid my thesis is still a work in progress and mentor duties will be primarily carried out by pervect and Janus, but I'll still be stopping by from time to time. Thanks.

 

[JonathanK]

To SpaceTiger: Hi, what makes the calculation so strong is that it is neither a modification nor a generalisation, as you seem to be saying. The theory hasn't been changed - instead the calculation works straight from the already published conceptual picture, and proves in an unambiguous way what the prediction should have been. The theory is still under development, but not in this area - the numerical value of the curvature component doesn't go into the calculation, it comes out of it. Jonathan

 

[SpaceTiger]

To SpaceTiger: Hi, what makes the calculation so strong is that it is neither a modification nor a generalisation, as you seem to be saying. The theory hasn't been changed - instead the calculation works straight from the already published conceptual picture, and proves in an unambiguous way what the prediction should have been.

So what makes the calculation so strong is the fact that you messed up in the first one?

 

[JonathanK]

Hi, I messed up in the first one for the following reasons!

In the first paper I pointed out a number of ways in which PSG mimics GR, but unfortunately missed one way. Having missed it, I wrote "There is no space curvature in PSG, so it should not mimic GR to the extent of causing a straight line parallel transported through a gravitational field to change its orientation. This removes the curvature component, which is two thirds of the predicted geodetic effect from GR.."

At that point I thought what some think - that only curvature will produce the geodetic effect. After the effect was measured I did a calculation using two points on the spin axis of one of the gyros on GP-B - the centre, and one end, at the surface of the sphere. Worked out their positions after half an orbit, with very slightly different speeds (due to different heights in a Planck scale refractive medium that affects matter). It's a thing that I'd tried last year but never completed - out came the curvature component of the geodetic effect, it gave 4.4 arcsecs/yr. Sad I'd missed it, but happy that it vindicates the theory, as I think it does. But I await the views of others, and would appreciate any thoughts you might have.

 

[JonathanK]

Hello,

Well it seems that if there was a problem with the calculation it would have been pointed out - Garth and probably SpaceTiger have read the paper, hopefully others. It's a very simple idea - matter is slowed in its motion through the field by the same factor as light is slowed (and for that matter as time is slowed), which is sqrt [1 - (2GM/rc^2)]. When one applies that to local matter within an orbiting object, one finds the object turns - the calculation shows this is exactly as in the geodetic effect, both numerically and in terms of direction. I'm all for GSCC, glad it's back on the list - experiment can help shape theories. For PSG it has helped shape the interpretation rather than the theory, and I'll take the lack of criticism as positive. 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? Thanks, best wishes Jonathan