The NASA Gravity Probe B (GP-B) orbiting gyroscope test of General Relativity, launched from Vandenberg Air Force Base on 20 April, 2004, tests two consequences of Einstein's theory:

The mission has required the development of cryogenic gyroscopes with drift-rates 7 orders of magnitude better than the best inertial navigation gyroscopes. These and other essential technologies, for an instrument which once launched must work perfectly, have come into being as the result of an intensive collaboration between Stanford physicists and engineers, NASA and industry. GP-B entered its science phase on August 27, 2004 and completed data collection on September 29, 2005. Analysis of the data has been in continuing progress during and since the mission. This paper will describe the main features and challenges of the experiment and announce the first results.

- the predicted 6.6 arc-s/year geodetic effect due to the motion of the gyroscope through the curved space-time around the Earth;

- the predicted 0.041 arc-s/year frame-dragging effect due to the rotating Earth.

The Confrontation between General Relativity and Experiment gives an excellent summary of various test of GRT. The predictions tested by GP-B relate to gravitomagnetic effects. The field equations of general relativity in post-Newtonian approximation with a choice of a preferred frame can in good approximation (g_{ij}=-δ_{ij}) be written in a form highly reminiscent of Maxwell's equestions with g_{tt} component of metric defining the counterpart of the scalar potential giving rise to gravito-electric field and g_{ti} the counterpart of vector potential giving rise to the gravitomagnetic field.

Rotating body generates a gravitomagnetic field so that bodies moving in the gravitomagnetic field of a rotating body experience the analog of Lorentz force and gyroscope suffers a precession similar to that suffered by a magnetic dipole in magnetic field (Thirring-Lense efffect or frame-drag). Besides this there is geodetic precession due to the motion of the gyroscope in the gravito-electric field present even in the case of non-rotating source which might be perhaps understood in terms of gravito-Faraday law. Both these effects are tested by GP-B.

In the following something general about how TGD and GRT differs and also something about the predictions of TGD concerning GP-B experiment.

** 1. TGD and GRT? **

Consider first basic differences between TGD and GRT.

- In TGD local Lorentz invariance is replaced by exact Poincare invariance at the level of the imbedding space H= M
^{4}× CP_{2}. Hence one can use unique global Minkowski coordinates for the space-time sheets and gets rids of the problems related to the physical identification of the preferred coordinate system. - General coordinate invariance holds true in both TGD and GRT.
- The basic difference between GRT and TGD is that in TGD framework gravitational field is induced from the metric of the imbedding space. One important cosmological implication is that the imbeddings of the Robertson-Walker metric for which the gravitational mass density is critical or overcritical fail after some value of cosmic time. Also classical gauge potentials are induced from the spinor connection of H so that the geometrization applies to all classical fields. Very strong constraints between fundamental interactions at the classical level are implied since CP
_{2}are the fundamental dynamical variables at the level of macroscopic space-time. - Equivalence Principle holds in TGD only in a weak form in the sense that gravitational energy momentum currents (rather than tensor) are not identical with inertial energy momentum currents. Inertial four-momentum currents are conserved but not gravitational ones. This explains the non-conservation of gravitational mass in cosmological time scales. At the more fundamental parton level (light-like 3-surfaces to which an almost-topological QFT is assigned) inertial four-momentum can be regarded as the time-average of the non-conserved gravitational four-momentum so that equivalence principle would hold in average sense. The non-conservation of gravitational four-momentum relates very closely to particle massivation.

**2. TGD and GP-B**

There are excellent reasons to expect that Maxwellian picture holds true in a good accuracy if one uses Minkowski coordinates for the space-time surface. In fact, TGD allows a static solutions with 2-D CP_{2} projection for which the prerequisites of the Maxwellian interpretation are satisfied (the deviations of the spatial components g_{ij} of the induced metric from -δ_{ij} are negligible).

Schwartscild and Reissner-Norströom metric allow imbeddings as 4-D surfaces in H but Kerr metric assigned to rotating systems probably not. If this is indeed the case, the gravimagnetic field of a rotating object in TGD Universe cannot be identical with the exact prediction of GRT but could be so in the Post-Newtonian approximation. Scalar and vector potential correspond to four field quantities and the number of CP_{2} coordinates is four. Imbedding as vacuum extremals with 2-D CP_{2} projection guarantees automatically the consistency with the field equations but requires the orthogonality of gravito-electric and -magnetic fields. This holds true in post-Newtonian approximation in the situation considered. This indeed suggests that apart from restrictions caused by the failure of the global imbedding at short distances one can imbed Post-Newtonian approximations into H in the approximation g_{ij}=-δ_{ij}. If so, the predictions for Thirring-Lense effect would not differ measurably. The predictions for the geodesic precession involving only scalar potential would be identical.

There are some reasons to think that gravimagnetic fields might have a surprise in store. The physicists M. Tajmar and C. J. Matos and their collaborators working in ESA (European Satellite Agency) have made an amazing claim of having detected strong gravimagnetism with gravimagnetic field having a magnitude which is about 20 orders of magnitude higher than predicted by General Relativity (arXiv.org gr-gc 0603032; arXiv.org gr-gc 0603033; Phys. Rev. Lett. 62 (8), 845-848; Phys. Rev. B 42(13), 7885-7893). A possible TGD based explanation of the effect is discussed here.

To sum up, TGD predicts that the geodesic precession should come out as in GRT but that Thirring lense effect might differ from the prediction of GRT.

For more details see the chapter TGD and GRT of "Classical Physics in Many-Sheeted Space-Time".

## 6 comments:

Thanks for the thoughtful post. I haven't checked the results, but from the gossip I gather they don't have (2) sorted out, and the errors are huge. Anyway, something else to think about.

Dear Kea, item 2) is the really interesting thing since here TGD can differ from GRT since Kerr metric is probably not imbeddable to H. Also the imbeddability in post-Newtonian approximation is questionable if one assumes vacuum extremal property as a I began to realize when I began to look in detail small deformations of the simplest imbedding for Schwartschild metric.

The most natural gravitomagnetic field differs in many respects from a dipole field.

a) Gravitomagnetic field has 1/r^3 dependence so that the distance dependence is same as in GRT.

b) Gravitomagnetic flux flows along z-axis in opposite directions at different sides of z=0 plane and emanates from z-axis radially and flows along spherical surface. Hence the radial component of B_g would vanish whereas for the dipole field it would be proportional to cos(theta).

This picture is consistent with the TGD based model for the asymptotic state of rotating star which involves also ordinary gauge fields with essentially similar behavior of magnetic parts of gauge fields. This is actually obvious since CP_2 coordinates are fundamental dynamical variables and the field line topologies of induced gauge fields and induced metric are therefore very closely related.

c) The dependence on the angle theta of spherical coordinates is 1/sin(theta) (this conforms with the radial flux from z-axis whereas for the dipole field B^theta has the dependence sin(theta). At z=0 plane the magnitude field can coincide with the dipole field so that satellites moving at the gravitomagnetic equator would not distinguish between GRT and TGD since also the radial component of B_g vanishes here.

d) For other orbits effects would be non-trivial and in the vicinity of the flux tube formally arbitrarily large effects are predicted because of 1/sin(theta) behavior. Perhaps TGD could be tested using satellites near gravitomagnetic North pole!

Matti

Interesting stuff - did you hear of Heim Theory and the attempt of Droscher and Hauser to explain the Tajmar effect with EHT or Extened Heim Theory (also a geometry structure theory)? Apparently using a coupling constant between photons and the 'gravito-photons' of EHT derived in 1996, the effect from bosons was shown to agree with the Tajmar effect. Heim theory is a quantum gravity theory that uses 8 time-like dimensions in addition to the usual 4-D space-time ones to explain all forces in a similar geometrical way to GR. THere are 3 species of gravity in EHT - one of these gives the gravito-photons that mediate the Tajmar effect and another gives quintessence or dark energy. Tajmar cites D&H's EHT as one of 2 or 3 possible explanations of his effect, now getting tentatibe confirmation from New Zealand and maybe 'anomalies' on Gravity Probe B.

Oh yeah - thought you sounded familiar - used to also be on Qunatum Mind long ago, eh? Yes, since then I got into Heim theory and started on a book on consciousness, genome, physics etc.

I have heard about Heim theory and tried to understand it from some article but with not much success. I have proposed that in TGD framework the large Planck constant would explain the enormous discrepancy of Tajmar effect with predictions of GRT.

Yes. I spent some time in Quantum Mind and I am still working intensively with TGD inspired theory of consciousness and of quantum biology.

Just yesterday I learned about really incredible experimental results supporting the TGD based view about plasmoids as primitive life forms. Interstellar dust might be living and these primitive life forms can be created also in laboratory. See my latest blog for TGD inspired comments about this.

Matti

Yes, Heim theroy is fascinating. Droscher and Hauser are preapring a revieew paper for publication on a journal next year - they hope this will be a better into to the theory than before for the interested scientist. As for TGD - though sort of interesting I only have time for one TOE at the mo, and that's Heim. He also had a take on consciousness - his extra timelike dimensions could be associated with order and meaning and other traits of life. Consciousness could reside in a combination of these subspaces. That also led him to extra-corporal extended being that could survive extinction of the physical body. Your blog is interesting alright ... some deep math-physics there.

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