## Gravity probe-B

The gravity probe-b mission had finished collection date for a long time .Why not announce any result ??

Do you think that the results will consistent with "general relativity"?
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 We intend to announce the final experimental results of GP-B through a NASA press/media event towards the end of 2007. At that time it is also our intention to have submitted a number of papers on the GP-B results for publication in peer-reviewed scientific and technical journals.
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 Recognitions: Gold Member Science Advisor But the first results are promised in April, on Saturday the 14th at the APS conference in Jacksonville Florida. Not long to wait. Garth

## Gravity probe-B

 Quote by Garth But the first results are promised in April, on Saturday the 14th at the APS conference in Jacksonville Florida. Not long to wait.
do you think we might have heard a hint or a leak if the results were similar to those of the Michaelson-Morley experiment? if the results are not within noise of what GR says they should be, that would be hard to contain, no?
 Recognitions: Gold Member Science Advisor They have kept a 'blind' element in the results by not including the proper motion of the guide star against a distant quasar until the last minute. They have kept their cards very close to their chest! However we already know the proper motion of the guide star to 0.001"/yr from The stars of Pegasus from the Bright Star Catalogue, 5th Revised Ed. (Preliminary Version) (Hoffleit+, 1991, Yale University Observatory) as distributed by the Astronomical Data Center at NASA Goddard Space Flight Center. IM Pegasi RA J2000 : 22h 53m 2.3s DEC J2000 : +16° 50' 28" Proper motion in RA : -0.018 arcsec/y Proper motion in DEC : -0.024 arcsec/y mag : 5.64 MK spectral class : K1-2II-III The Proper motion in RA will affect the E-W precession and the Proper motion in DEC will affect the N-S precession. The experiment measures the precession of the gyros to four decimal places of arcsec/yr, so the final convolution of the tracking a precession data will only increase the accuracy of the result in that fourth decimal place. On the one hand, as you say, it would be hard to contain a non-GR result for so long, but on the other hand the fact that they are taking so long over processing the data might be an indication that they have found an anomaly and are checking and double checking their results before publication. We wait and see. Garth
 It seems that in 1997 scientists already have evidence of "frame-dragging"effect!! http://web.mit.edu/newsoffice/1997/blackholes.html
 Recognitions: Gold Member Science Advisor It's the geodetic effect I am interested in! Garth
 This phenomenon, known as frame-dragging, was first predicted in 1918 as a natural consequence of Einstein's general theory of relativity, which describes the effects of gravity on space and time. But it had been unproved by experiments or observation until recently, when Italian researchers suggested the effect might be present near spinning neutron stars. The MIT team then applied a similar idea to several black holes in our galaxy------- excerpt from http://web.mit.edu/newsoffice/1997/blackholes.html

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From http://einstein.stanford.edu/content...b/gpbsty3.html

 But what does "the same direction in space" mean? For Newton the answer was easy. Space and time were absolutes. A perfect gyroscope set spinning and pointed at a star would stay aligned forever. Not so for Einstein. Space-time is warped -- and may even be set in motion by moving matter. A gyroscope orbiting the Earth finds two distinct space-time processes -- frame-dragging and the geodetic effect -- gradually changing its direction of spin.
 According to Einstein the Earth warps space-time. A second, much larger change in spin direction, the geodetic effect, follows from the gyroscope's motion through this space-time curvature. The phenomenon was foreshadowed in 1916 by W. de Sitter who predicted a minute relativistic correction to the complicated motions of the Earth-Moon system around the Sun -- an effect finally detected in 1988 through an elaborate combination of lunar ranging and radio interferometry data. For a gyroscope the predicted effect is a rotation in the orbit-plane of 6,600 milliarc-seconds per year -- quite a large angle by relativistic standards. Gravity Probe B will measure the change to 1 part in 10,000 or better, the most precise qualitative check yet of any effect predicted by general relativity.
The geodetic precession is closely related to Thomas precession (if that helps any).

It's of interest to Garth because his dark-horse (though peer-reviewed) theory of gravity, SCC http://arxiv.org/abs/gr-qc/0212111 makes an experimental prediction different from GR that will be tested by gravity probe B.

You can probably find a lot of threads on SCC here at PF if you look - being published in a reputable journal, it's "fair game" for discussion on PF.

 Quote by pervect The geodetic precession is closely related to Thomas precession (if that helps any).
This statement intrigues me.

While Thomas precession is an effect due to the hyperbolic nature of space and is a compensation for the non commutative Einstein addition formula (see for instance: "Ungar A A - Beyond the Einstein addition law and its gyroscopic Thomas precession (Kluwer,2001)(ISBN 0792369092)"), I thought the geodetic precession had something to do with curvature?

No?
 Recognitions: Gold Member Science Advisor Yes MeJennifer - though there has been some confusion. In four-space, SR's Minkowski space-time, an object moving relative to an observer has a four-vector inclined to the four-vector of that observer. Therefore, if a force accelerates a gyroscope, its four-vector gradually leans over relative to its original direction and its spin axis will consequentially precess. This is Thomas precession. It is a SR effect. Geodetic Precession on the other hand is a GR effect. Consider the 'curved funnel' model of the space component of curvature around a gravitating mass. At any one particular distance around the central mass the space curvature can be modelled by a 'slice' of a cone. That cone can be constructed by cutting a thin cake slice out of a circle and gluing the edges together. The space curvature component of geodetic precession, described by the Robertson parameter $\gamma$, is the angle of the slice cut out of the full circle. The other component of the geodetic precession is a time dilation effect. Another way of describing the GP-B geodetic effect is to say 'it is the amount the gyros 'lean over' into the slope of the curvature of space-time' as they orbit the Earth. If that helps. In the GP-B experiment SCC predicts the same frame-dragging E-W precession but only 2/3 the N-S precession as GR. We shall know soon! Garth

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 Quote by Garth Yes MeJennifer - though there has been some confusion.
Some of the confusion here appears to be mine, which I apologize for, but I don't want to pass up the opportunity to learn something and hopefully become less confused.

 In four-space, SR's Minkowski space-time, an object moving relative to an observer has a four-vector inclined to the four-vector of that observer. Therefore, if a force accelerates a gyroscope, its four-vector gradually leans over relative to its original direction and its spin axis will consequentially precess. This is Thomas precession. It is a SR effect. ere appears to be some coordina Geodetic Precession on the other hand is a GR effect.
Suppose we have observer A, in flat space-time, in a powered circular orbit. The centripetal acceleration is supplied by his rocket. Because the direction of his acceleration is constantly changing, he will experience Thomas precession.

Suppose we have observer B, in curved space-time, in an unpowered circular orbit. From a Newtonian viewpoint, the centripetal acceleration is supplied by gravity. From a GR viewpoint, he is simply following a geodesic.

I was under the (possibly erroneous) impression that observers A and B experienced the same amount of precession in the same direction. I really ought to do a calculation to check this, but it will have to wait.

 Consider the 'curved funnel' model of the space component of curvature around a gravitating mass. At any one particular distance around the central mass the space curvature can be modelled by a 'slice' of a cone. That cone can be constructed by cutting a thin cake slice out of a circle and gluing the edges together. The space curvature component of geodetic precession, described by the Robertson parameter $\gamma$, is the angle of the slice cut out of the full circle. The other component of the geodetic precession is a time dilation effect. Another way of describing the GP-B geodetic effect is to say 'it is the amount the gyros 'lean over' into the slope of the curvature of space-time' as they orbit the Earth. If that helps. In the GP-B experiment SCC predicts the same frame-dragging E-W precession but only 2/3 the N-S precession as GR. We shall know soon! Garth
This appears to be the standard explanation of geodetic precession (and standard is good).

I ran across http://prola.aps.org/abstract/PRD/v42/i4/p1118_1 though, which seems to blur the distinction being made here, and to suggest that some of the distinction comes about because of the particular coordinate system being assumed.

Experimentally the distinction is important because the two effects occur at right angles for GP-B. They occur at right angles only for a satellite in polar orbit. In fact the polar orbit was chosen to make this happen.

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 Quote by pervect Suppose we have observer A, in flat space-time, in a powered circular orbit. The centripetal acceleration is supplied by his rocket. Because the direction of his acceleration is constantly changing, he will experience Thomas precession.
Note: observer A would experience Thomas precession even if she were accelerating in a straight line - because her 4-vector would be rotating in space-time.
 Suppose we have observer B, in curved space-time, in an unpowered circular orbit. From a Newtonian viewpoint, the centripetal acceleration is supplied by gravity. From a GR viewpoint, he is simply following a geodesic. I was under the (possibly erroneous) impression that observers A and B experienced the same amount of precession in the same direction. I really ought to do a calculation to check this, but it will have to wait.
In that situation the Thomas precession of observer A is equal and opposite in direction to the 'time dilation' component of the Geodetic precession of observer B.

On top of that GR would predict a 'space curvature ("missing slice") component' precession for observer B that was twice his 'time dilation component' precession. (See MTW page 1119 equation 40.34)

So observer B suffers 3X observer A's total precession.
 This appears to be the standard explanation of geodetic precession (and standard is good). I ran across http://prola.aps.org/abstract/PRD/v42/i4/p1118_1 though, which seems to blur the distinction being made here, and to suggest that some of the distinction comes about because of the particular coordinate system being assumed.
Although I do not have access to the paper itself I can understand what they are doing. From an orbiting coordinate system the Earth is spinning even if it is non-rotating wrt the fixed stars. It could be confusing because the two precessions in their case are equal yet have fundamentally different origins. This becomes obvious if the satellite's orbit is not in the plane of the Earth's rotation, as indeed it is not with GP-B.

Geodetic precession will be experienced by a gyroscope orbiting the equator of a non-rotating Earth, but IMHO it is confusing to call this 'frame dragging' .
 Experimentally the distinction is important because the two effects occur at right angles for GP-B. They occur at right angles only for a satellite in polar orbit. In fact the polar orbit was chosen to make this happen.
Indeed, they had a launch window of 1 second each day to put it into that orbit!

Garth

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 Quote by Garth Note: observer A would experience Thomas precession even if she were accelerating in a straight line - because her 4-vector would be rotating in space-time.

 (See MTW page 1119 equation 40.34)
Surely v x a would be zero if v were in the same direction as a? Implying no precession for an observer accelerating in a straight line (where a is always in the same direction as v) as MTW's 40.33b reduces to -(1/2) v x a for this case.

 So observer B suffers 3X observer A's total precession.
OK, I can see that now. Thanks for the correction.

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 Quote by pervect Surely v x a would be zero if v were in the same direction as a? Implying no precession for an observer accelerating in a straight line (where a is always in the same direction as v) as MTW's 40.33b reduces to -(1/2) v x a for this case.
a is actually the 4-acceleration, in equation 40.34 the components are evaluated in the PPN approximation where the 3-acceleration suffices. See MTW exercise 6.9 page 175.

Garth
 Recognitions: Science Advisor Staff Emeritus 40.33 (pg 1118) has already been re-written in a 3d vector form - it's not a 4-vector equation (and the cross product only makes sense in 3 dimensions). One could regard the Lorentz boost as a kind of rotation, but there isn't any spatial rotation in the normal 3-d sense in the case of constant acceleration in the same direction that I can see. And I've looked at exercise 6.9 as you suggest. I.e. if we accelerate in the x direction with a constant acceleration, a gyroscope with its spin axis in any of the x, y, or z directions will not precess in any spatial direction (assuming the force accelerating the gyroscope is applied at the center of mass). The most that will happen is that time dilation might affect the apparent angular momentum carried by the gyroscopes, but this is not a 3-d rotational effect.

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As I said that 3-acceleration expression suffices in the PPN approximation.
From MTW page 118
 Equations 40.33 describe in complete generality at the post-Newtonian level of approximation the precession of the gyroscope spin S relative to the comoving orthonormal frame that is rotationally tied to the distant stars.
Where we are confusing ourselves is over two sorts of acceleration.

In the case of a gyroscope fixed to the Earth's surface the significant Thomas precession is due to the gyro's acceleration when carried around by the Earth's rotation.

However, my point in #13 was referring to a linear acceleration that was the subject of MTW Exercise 6.9.

Here a constant force acting through the centre of mass produces a acceleration constant in direction however, the 4-velocity of an linearly accelerating body actually rotates in an inertial space-time frame.

Now, the four-angular momentum S of a rotating body has the property of always being orthogonal to its 4-velocity (eq. 6.21), therefore S has to precess under acceleration $\mathbf{a}$ to keep orthogonal to that 4-velocity $\mathbf{u}$:

$$\frac{d\mathbf{S}}{d\tau} = (\mathbf{u} \wedge \mathbf{a})\cdot d\mathbf{S}$$

Garth

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