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 (gij=-δij) be written in a form highly reminiscent of Maxwell's equestions with gtt component of metric defining the counterpart of the scalar potential giving rise to gravito-electric field and gti 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= M4× CP2. 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 CP2 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.
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 CP2 projection for which the prerequisites of the Maxwellian interpretation are satisfied (the deviations of the spatial components gij of the induced metric from -δij 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 CP2 coordinates is four. Imbedding as vacuum extremals with 2-D CP2 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 gij=-δij. 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".