I'll point at that Robertson's "Newtonian Gravity Theory" is actually just almost straight GEM, or a Heaviside-like gravity from the Maxwell analog. There is a a factor of 4 on the gravitomagnetic factors that comes out of GR's, well "fancy stuff". That factor of 4 would not be on a straight Maxwell-like gravity.

You get deduce that gravitomagnetic effects must be present from a simple thought experiment of considering a charged mass system in equilibrium where gravitational attraction just cancels electric repulsion. Now, watch that from a moving frame. If there are B effects, which can be seen an SR effect on the Coulomb field (in this case), there must a similiar effect on gravity. And indeed there must similiar magnetic-looking effects on *any force*. Take a spring and have the compression cancel electric attraction. The spring force must have an SR magnetic-like velocity dependent component as well.

Doing that by straightfoward means gets you Heaviside's original GEM like gravity. And that is wrong. Basically it violated the equivalence principle because the gravitational "charge" (mass) is different from the inertial mass. Keeping those the same gets you GR and that factor of 4. It's complicated, and don't ask me to show it.

Actually, I think that factor of 4 (which is 2 applied twice, once on source, once on receiving mass) comes from the same thing that puts a factor of 2 on the Newtonian potential in g_00, ie g_00 = 1 - 2GM/r (think of the 1 there as a "gauge" term that makes it 1 at infinity rather than 0, which it has to be because that's the stationary clock rate in that coordinate system).

Anyway, Robertson thought it would be interesting and useful to do the straight Heavside/no factor of 4 predictions for GPB.

ETA: The above mass-charge equilibrium illustrates why gravity has to be so complicated. Do it naively by SR considerations alone, think you've done something, then you realize you've violated the Equivalence Principle. The reason is that inertial mass, to the moving observer increases by a factor of gamma (well, in the transverse case, it's more complex), but you said the gravitational mass, being analgous to charge, was just the rest mass.

That conundrum is why gravity cannot be a mere vector field in the general case. Only a tensor field can be made to work out in all cases and have the Equivalence Principle hold and still have inertial mass appearing to increase with velocity.

This is why gravity is so darned complex.

-Richard

Will Gravity Probe B fulfill its promise?

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Can they re-run any tests now that they know about the charge patches to either get better data, or help reduce the noise?

CJSF

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Thank you ToSeek; Uncertainty in modeling of the patch error not only will degrade the accuracy of Gravitomag. measurement, but is also certainly going to reduce the confidence levels of the data, making any comparison with competing theories (that rely on gravitomagnetic differences) suspect and maybe even marginal at best.

All this may actually be a moot point since other recent reports from lunar ranging by Nordtvedt (using 35 years of lunar laser ranging data) have confirmed gravitomagnetism in the earth-moon system to 0.1 % of the GR prediction.

See here:
http://arxiv.org/PS_cache/gr-qc/pdf/0702/0702028v1.pdf

Nordtvedt has been at the forefront for years in LLR, and (although not given the publicity of more media hyped GP-B) has previously shown that the solar geodetic effect (the so-called deSitter-Folker precession which rotates the plane of the earth-moon system), confirms GR predictions to about the same accuracy (0.1 %), ......and has also put tight constraints on competing theories, (as well as confirming the non-linear coupling of earth's gravity to itself, and the constancy of G to high precision).

See here;
http://www.springerlink.com/content/2gjffbwea99mrjxa/

Needless to say, Everitt was not too happy about the Nordtvedt report on Gravitomagnetism....but the same GR gravitomagnetic term that is used for the GP-B frame dragging is also responsible for the Gravitomagnetism of two rotating massive objects.

So why not use the 'God given' gyroscopes that are already in place ? ....dang, Nordtvedt didn't even have to make the moon go superconducting or polish it to one billionth of a cm. !

G^2

G^2,

If I read that .pdf right, the moon's orbit deviates no more than roughly 1cm from GR's predicted course. If that's correct, then that is darn-tootin' good.

And from the Springerlink abstract, another thing I like is the earth and moon fall toward the sun at the same rate to within 10^-13. That is pretty good, too.

-Richard

-Richard

Yep, darn-tootin'; the accuracy of LLR is apparently down to a couple of mm.

G^2

True;
Good point that 'any force' binding them will also require a vel. dependent term in the moving frame.


I'm not so sure about that.....
To the moving observer there is also Length contraction (in the direction of motion) by the same factor gamma; the shortened length between masses means greater gravitational mass. Also the charge density increases by a similar amount due to the same length contraction....so its possible mass-charge stays in equiibrium;(haven't done the math though).

G^2

That's a tricky thing. The charge density (and current density) is frame dependent, but the total charge is invariant. Mass-energy is not invariant, and that is the difference. A sphere in the rest frame gets "squashed" looking in the moving frame, with the charge density and the E-field looking different accordingly, but the total charge is invariant.

Here is a paper that goes into detail on the mass-charge equilibrium:

http://www.arxiv.org/abs/gr-qc/0304084

Note the interesting thing. If you add the requirement that inertial mass equal gravitational mass, you get only one factor of 2 (to first order, there are higher order terms apparently) on the gravitomagnetic force. The authors say the other factor of 2 can be seen as coming from "curvature".

Note that Maxwellian gravity (without the factor of 4) would be completely Lorentz-kosher otherwise. It's only if you require the Equivalence Principle to absolutely hold that things have to get fancy........

-Richard

Yes, of course; not thinking. And thus it has become a 'nicht gedenken' experiment.

Yes, Richard; thanks for pointing that out; that is the very reference I gave you a few months ago when we were discussing the interaction of gravitomagnetism with spin, and how it must imply EP violation,....remember here: Gravity produced by machine in laboratory (in post #78; concerning Tajmar & deMatos experimental detection of the Gravitomagnetic field of a spinning superconductor).

However, I unintentionally skipped over the section on justification of Gravitomagnetism using this thought exp.( ), since my intention was to focus on the implications of the Maxwellian gravity analogs involving spin, and not proving the necessity of gravitomagnetism, (However, the author does give a good formal presentation.). I really liked his approach since it uses the linear differential form of the gravitational field analogs which are heuristically simpler and more amenable to my limited cognitive resources. Nevertheless, as far as I am concerned there is enough 'real' physical evidence for gravitomagetism (GP-B not withstanding), that I need not resort to 'gedenken' type simplifications.

That is what my 'Nordtvedt post' above was about. Gads; Nordtvedt even makes the case that gravitomagnetism is quite ubiquitous .... in the origin of inertia....

Here is a very interesting secondary source...referring to his comments ....
http://physics.fullerton.edu/~jimw/g...ertia/nord.htm
You are probably already familiar with it; if not, I recommend it considering the implications.

Nevetheless, I really do want to get back to the issue of gravitomagnetism coupling to spin since that is where the experimental evidence is lacking.

Maybe I will resurrect our last discussion in that regard when I have more time.

G^2

http://einstein.stanford.edu/

Unfortunately, there is no way on Earth to confirm that a time-variant polhode moment is the proper solution. One expects the polhode moment of an egg to vary over eighteen months, but not a set of spheres made from materials chosen because of their known (presumed?) stability. It would seem to be a worthwhile test of the varacity of this 300,000,000+dollar assumption to construct a duplicate set of spheres and see if the polhode properties on earth are the same as they are in the heavens.

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Testing for Lorentz Violation: Constraints on Standard-Model Extension Parameters via Lunar Laser Ranging
James B. R. Battat, John F. Chandler, Christopher W. Stubbs
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138

http://arxiv.org/PS_cache/arxiv/pdf/...710.0702v1.pdf

New constraint, by at least one full magnitude. This methodology assumes that the speed of light is constant in order to make the measurement; so it is not a perfect test of relativity. It does eliminate or severely constrain many alternatives.

After looking at some of the modifications they are making in the APOLLO experiment, such as measuring the effects of continental drift, it will be interesting to see how much the moon's orbital path is truly increasing. First round APOLLO science testing should be completed within a year.

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jwj

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Constraining Torsion with Gravity Probe B
Mao, Tegmark, Guth and Cabi

http://arxiv.org/PS_cache/gr-qc/pdf/0608/0608121v4.pdf

OK, that is a legitimate premise: If a torsion gravity theory is correct, One would expect this hypothetical angular momentum coupling to be time variable; that is, to effect the rotational moments of the Gravity B probe.

We know the rotational moments of the Gravity B probes did change over time, and this unexpected change is thought to be due to electrostatic coupling and a time-dependent Polhode moment. If this unexpected momentum is due to torsion coupling; The coupling of each gyroscope should vary as a function of the angle of the gyroscope relative to the local 'torsion' moment. It would be interesting to see what the net Polhode correction would be if the torsion correction is first applied to each gyroscope.

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jwj

It's ok not to know. We should try harder to find out.

http://einstein.stanford.edu/

So...when you use a "trapped flux mapping technique", how do you know how much of the deviation is due to unexpected flux, and how much is honest-to-goodness deviation in the experimental result from what was expected?

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jwj

It's ok not to know. We should try harder to find out.

Good question...probably you don't know.
I really don't put much confidence in "tweaking" the gravitomagnetic data with new 'ad hoc' experimental models ....it seems too much like someone's trying to fit the data so as to resurrect a GR prediction from the GP-B ashes...

If 30% error level is considered "reasonable" then the Lageos satellite detection by Ciulfolini beat them to the punch, at least for the gravitomagnetic part.

Maybe we should go back and investigate other approaches....like the South Pole gravitomagnetic proposal by Braginsky and Kip Thorne.

Rather than divert the OP I've put that idea on another thread here:

South Pole Experimental Detection of Gravitomagnetism

G^2

Has Gravity Probe B been a Big Flop?

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Then it will be like LIGO which has taught researchers more items they need to study and resolve to be able to successfully measure this kind of thing.

I'm thinking that Gravity Probe C should be in a low orbit around Jupiter.

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