# Alternative theories being tested by Gravity probe B

1. Dec 20, 2005

### Garth

The Gravity Probe B satellite has placed four (over redundant) gyroscopes in low polar Earth orbit to primarily test two predictions of General Relativity.

The first effect being tested is (for the GP-B polar orbit) a N-S geodetic precession, caused by the amount a gyro 'leans' over into the slope of curved space.

The second effect being tested is the E-W frame-dragging, Lense-Thirring, or gravitomagnetic effect, caused by the spinning Earth dragging space-time around with it.

Some researchers, such as Kenneth Nordtvedt, have said that the experiment was worth doing when it was first proposed but that now GR has been verified beyond resonable doubt the result of GP-B is a foregone conclusion.

I have now discovered several theories competing with General Relativity(GR) that are being tested and falsified by this experiment:
my Self Creation Cosmology).(SCC),
Moffat's Nonsymmetric Gravitational Theory (NGT),
Hai-Long Zhao's mass variance SR theory (MVSR),
Stanley Robertson's Newtonian Gravity theory (NG), and
Junhao & Xiang's Flat space-time theory (FST).

As the results will be published in the not too distant future they could be interesting!!

(Note if anybody knows of any other theories with alternative predictions for GP-B please post them as well for comparison.)

1. GPB Geodetic precession
GR = 6.6144 arcsec/yr
SCC = 4.4096 arcsec/yr
NGT = 6.6144 - a small $\sigma$ correction arcsec/yr
MVSR = 6.6144 arcsec/yr
NG = 1.6536 arcsec/yr
FST = 4.4096 arcsec/yr

2. GPB gravitomagnetic frame dragging precession
GR = 0.0409 arcsec/yr
SCC = 0.0409 arcsec/yr
NGT = 0.0409 arcsec/yr
MVSR = 0.0102 arcsec/yr
NG = 0.0102 arcsec/yr
FST = 0.0000 arcsec/yr

I cannot vouch for these other theories, they may well be considered 'crackpot' by some, however all these theories have the advantage, together with GR, that they are able to be falsified by the GP-B results.

We continue to wait and see!

Garth

Last edited: Dec 20, 2005
2. Jan 1, 2006

### Garth

The wait for the results continues into this and next new year! GP-B MISSION NEWS—NASA REPORT & DATA ANALYSIS PROCEEDING AS PLANNED
Whatever those results might be!

Garth

3. Jan 1, 2006

### Nereid

Staff Emeritus
To what extent will the parameter space that GPB and observations of the double pulsar (will) probe overlap, in terms of testing GR and alternatives?

4. Jan 1, 2006

### Chronos

The recent pulsar measurements are probably better predictors than GPB could ever hope to be. My prediction: GR will prevail again.

5. Jan 2, 2006

### Garth

This is in line with the thinking of Kenneth Nordtvedt in which case the \$700 million spent on GP-B has been wasted! However, I beg to differ.

GP-B is a controlled experiment, all the parameters that may affect the result are well determined. This cannot be said for a remote observation of a distant pulsar system.

As far as experimental/observational comparisons between SCC and GR, especially concerning the binary pulsar PSR B1913+16 (and now the double pulsar PSR J0737-3039B), there are two degeneracies and a third near degeneracy to realise.

1. SCC is conformally equivalent to canonical GR in vacuo, in a vacuum - the Schwarzschild solution - particles and photons follow the geodesics/null geodesics of GR. As all the standard tests of GR, light deflection, precession of the perihelia, time delay, test the behaviour of particles and photons through a vacuum there is no difference between these two theories in predicting the results of these tests.

(The details of the conformal transformation can be found here: The Principles of Self Creation Cosmology and its Comparison with General Relativity Section 2, especially Equation 20.)

and the details of the degeneracy of tests can be found here: Resolving the Degeneracy: Experimental tests of the New Self Creation Cosmology and a heterodox prediction for Gravity Probe B)

2. As matter becomes degenerate
p -> $\frac 13 \rho c^2$
the scalar field becomes minimally connected and again the behaviour, even when not in vacuo reduces to canonical GR; although now the full gravitational 'constant' is felt.
$G_m = \frac 43 G_{Newton}$

Because of these two degeneracies the behaviour of a binary or double pulsar system in SCC is exactly the same as in GR.

3. The third near degeneracy is in tests of the equivalence principle in Eotvos type experiments the violation of the EEP would be about one part in 10−17 or about three orders of magnitude smaller than the present day sensitivity of the experiment. (See Self Creation Cosmology - An Alternative Gravitational Theory section 7.

These degeneracies will be resolved by GP-B, which is the first experiment/observation that is able to distinguish between these two theories.

Note that degeneracy 1 does not apply to the cosmological solution, except in the empty universe, $\rho$ = 0 case. (When SCC converges on the GR Milne model) That is why the SCC cosmological solution is different to that of GR, it is concordant with cosmological observations but without inflation, exotic DM or unknown DE!

Garth

Last edited: Jan 2, 2006
6. Feb 19, 2006

### RandallB

Garth
Can you help me understand the Gravity B tests here? I’m having trouble understanding the expected direction of change in angles expected.

First as I read the polar orbit of GPB it is moving north to south as it is viewing IM-Pegasi the guide star being used. (In close alignment with it the guide star would always be blocked by earth during the south to north trip)

First:
GPB gravitomagnetic frame dragging precession.
The most significant measurement to be made (at least some say and IMO). It is the annual change in the orbital alignment with the guide star.
Do I read the term “E-W precession” correctly as relating the alignment moving in the direction of the rotation of earth (as there is no orbital E-W component to precess)? Thus all the theories named here are predicting the orbit to move its alignment to the east of the guide star. Is this correct?

Actually, I would expect the alignment to move west, so I was looking for a theory that agrees with a westward change. I take it then you are not aware of any theory that does.

Second:
GPB Geodetic precession
Looking at the Satellite on the IM-Pegis side of the orbit at the equator. The angle of deflection relates to the alignment of the gyro axis moving. Given three idea gyros at this point in the orbit and axis aligned; 1) E-W, 2) N-S, 3) Earth Radius, which of the three would have their alignment move and which way?
I assume one will not move at all.
Would direction of gyro rotation have any effect on direction?
And do you know a web site that does a good job of explaining why GR expects this beyond just saying “because of GR space-time curvature”.

Thanks
RB

7. Feb 19, 2006

### wolram

Congratulations Garth, i think.

8. Feb 19, 2006

### Garth

RandallB The orbit was chosen to be a polar orbit precisely to searate out the two effects: geodetic and frame-dragging.

The frame-dragging, or Lense-Thirring, or gravitomagnetic, effect is as the name suggests caused by space-time, and corresponding frames of reference, being dragged round by the revolving Earth in a West to East direction.

The geodetic effect, caused by the curvature of space-time, represents the angle missing from 3600 in the circle drawn on a curved surface, or the amount the gyro axis precesses after being parallel transported one complete orbital revolution - summed up over a year's worth of orbits. Alternatively you can think of it as the angle the gyro 'leans over into the slope' of curvature and is in the direction of motion. Therefore it is a precession in the N-S direction and clearly distinguished from the much smaller frame-dragging precession.

Note: the orbit was accurate to within 10 to secure this distinction, and that gave the launch vehicle a one second window on each day of possible launch(!)

I hope this helps.

wolfram thank you, but a little premature I think?

Garth

Last edited: Feb 19, 2006
9. Feb 20, 2006

### RandallB

OK that as I expected, the alignment of the entire orbit towards IM-Pegasi is predicted to move to the East. (Or looking at the orbital axis from the guide star view, the left side would lean towards the star)

Now this is the one I have the most trouble understanding alignment and direction on. What is “precession in the N-S direction” of a gyro axis?

In terms of the angle the gyro axis “leans over” - which of the three idea gyros I described would actually show a change.
At equator the position I described, (Pegasi side GPB moving north to south) two are perpendicular to a radius from earth thus axis ends are pointing E-W & N-S. Which if any of these ends would lean towards earth?

The third axis would be inline with a radius from earth. So for the end pointed toward earth (only on this side) which way would it move N, S, E, or W if at all?

Thanks
RB

10. Feb 21, 2006

### Garth

RB - my 'leaning' over explanation is only a 'hand waving' description to try and convey some understanding to what is going on, a full understanding requires the maths.

The precession of a spin S is given by

$$\frac{dS}{d\tau} = \Omega \times S$$

where

$$\Omega = -\frac 12 v \times a -\frac 12 \nabla \times g + (\gamma + \frac 12)v \times \nabla U$$
(see MHW equation 40.33 page 1118)

In the RHS of the last expression the first term is the SR Thomas precession caused by accelerating a vector - it 'leans over' in 4D space-time. It is zero in GR but not http://en.wikipedia.org/wiki/Self_creation_cosmology.

The second term is the Lense-Thirring effect $$g = g_{0j}e_j$$ is the perturbation of the metric caused by the spinning of the Earth.

The third term is the geodetic effect. v is the along spin axis of the satellite's orbit, normal to its plane.

When you work it out for a polar orbit the geodetic precession is in a
N-S direction.

Garth

Last edited by a moderator: Apr 22, 2017
11. Feb 21, 2006

### RandallB

This is the part that isn’t clear in anything I’ve been able to find. At the end of the day the GPB will be making a measurement on the gyros that have been running for however long and expect them to have have moved from their normal alignments. What will those physical changes in the direct measurements be?

As in my example of three gyros with their spins around x, y, and z coordinates after running a long time, classical Newtonian expectations would say that there would be absolutely no change at all (as if the earth was not rotating). The axis end pointed toward the earth center (while over the equator, the opposite end of the axis would always point at the guide star) would not tip N, S, E, or W at all. The 4 ends of the other axis point N, S, E, & W and no end should tip towards the earth (thus away from the guide star).

None of the six theories predict such a null result. But all predict various amounts of change in the same direction. What is not clear is what direction of tilt will be physically observed by the measurements to be made on GPB. Someone on the team must have defined in clear measurable terms exactly what direction that is to match a “geodetic precession is in a N-S direction”.

12. Feb 21, 2006

### Garth

Read the information on the GP-B website. The gyros are aligned on a star, the IM Pegasi (radio) star has a proper motion that is being tracked by VLBI, the movement of the gryos relative to the star has been tracked using SQUIDs (see the website for details) by the summer this year the one data set will be compared to the other to see how the gyros have moved, various theories predict different N-S and E-W precessions and of course almost everybody expects the experiment will verify the GR prediction, but the team have kept a very open mind on this, which is what makes the experiment so exciting.
I'm not sure what your problem is. The gyros may not move at all, or they may move in a direction that can be resolved into a N-S and a E-W component, and then we shall see whether these observed precessions match any of the sets of predictions.

Garth

Last edited: Feb 21, 2006
13. Feb 21, 2006

### RandallB

In space how do you define up down left right forward and back with no references.
Same thing here, I don’t see a defined reference.

For the gyro that is pointed at the guide star.
Option 1:
The axis end pointed at the star tips up to the North the back end will of course tip down to the south.
Option 2:
The opposite happens, the end axis pointed at the star tips down to the South the back end will of course tip up to the North.

Which option is the N-S move Option 1 or 2?
We can assume N-S means “from North towards the South” movement.
But without defining which end of the gyro is being measured how does any one know what the other is talking about.

Same kind of problem understanding the other gyro measements in 3D.

14. Feb 21, 2006

### Garth

From the plane of the satellite's orbit (N-S) and the orientation of the Earth(E-W).
The Spin vector of the gyro is defined by the Right Hand Screw convention, so long as that convention (or the opposite one) is applied consistently in the analysis there is no ambiguity.

Garth

15. Feb 21, 2006

### RandallB

So the direction of gyro rotation makes a differance.
With that Right hand vector pointed at the guide star does that mean option 2 is matchs with a positive N-S move.
And option 1 if the if the vector is away from the guide star?

16. Feb 21, 2006

### Garth

As I said it depends on the convention used.

You have to examine the GP-B papers to find the answers to your questions, or simply ask the question on their website.

Garth

17. Mar 4, 2006

### Garth

Latest news of the GP-B data analysis: Phase I complete!
Another 13 months!

Garth

Last edited: Mar 4, 2006
18. Mar 5, 2006

### Chronos

Indeed, Garth. Let the data speak for itself. I do not lean either way, and I am certain you feel the same way. It will be difficult to sieve through the data . . . I hope you will be critical of that process.

Last edited: Mar 5, 2006
19. Mar 7, 2006

### jgraber

Has anyone done a parameterized post-Newtonian analysis? Can one express the expected results in terms of the usual Eddington alpha, beta gamma and higher order parameters? Any refs?
Best,
Jim

20. Mar 7, 2006

### jgraber

I should have googled first. Apparently it tests gamma and alpha-one ( a non-conservative parameter), according to Will.
No doubt that is why Nordstrom thinks the money has been wasted, as gamma has already been strongly constrained and most people believe in the conservation laws.
Best,
Jim