The “Gravity Probe B” experiment, interaction between the orbital moment and gauge field, and a gravidiamagnetic effect

Abstract

At the present time, the "Gravity Probe B" (GP-B) experiment is being performed on the orbit aimed at investigation into features of motion of a rotating probe body (gyro) in the Earth's gravitational field. The results of measurements are under processing and will be compared with the predictions of GRT and its various generalizations.It is well known that classical experiments confirm GRT accurate to 0.3%. Therefore, there is reason to hope that the foregoing experiment will identify departures from GRT.In [1], it is proposed to treat possible variations of the experiment results from the GRT predictions as the presence of torsion of spacetime in the above experiment. In this work, it is assumed that a gyro could respond to torsion if a rotating planet-type body was able to produce spacetime torsion, hence the experiments with a gyro like the above GRB can be the best means for determination of the most adequate of all possible unconventional gravitation theories allowing for torsion.A nonconventional theory is necessitated by the fact that it is assumed in the conventional Poincaré -gauge gravitation theory [2, 3] that the orbital angular momentum cannot be a source of field due to the absence of translational invariance of the field equations arising in this case. This was discussed in detail in the well-known review [3]. In [1], this opinion was cited as a common folklore in modern theory of gravitational field. This difficulty was overcome in a new variant of the Poincaré-gauge gravitation theory [4, 5] and a recently developed Poincaré-Weyl-gauge gravitation theory [6, 7], where the angular momentum a m M along with the spin moment a m S occur as a source of gravitational field, including the torsional field, without violation of translational invariance of the field equations.The theory is developed on the basis of the Noether theorems allowing gauge fields dynamically realizing the laws of conservation of energy-momentum, total rotational moment (orbital and spin), and dilatation charge to be introduced. The dilatation charge is due to the invariance of the theory with respect to tension and compression of spacetime. As a result, the theory necessitates the Weyl-Kartan geometry with curvature, torsion, and nonmetricity of the Weyl type in spacetime.Within this approach, the tetrads a h μ are not true gauge fields, they represent certain functions of the introduced gauge fields: Lorentzian m a A (rotational r-field), translational k a A (t-field), and dilatational a A (d-field). An equation for the gauge field m a A is as follows:

Exact geodesic precession related solutions of the inertial navigation equations

“…1.1 [1]; this is visualized by distinguishing the first term of the series expansion for small velocities. 7) This expression coincides with the corresponding expression in Sec. 1.2 [1].…”

“…1.4, of the inertial navigation equations. (It also corresponds to the results of geodesic precession measurements in the Gravity Probe-B experiment [4][5][6][7][8]. 1) )…”

“…The solution corresponds to the object motion in a circle of radius r = |r 0 | with velocity v = tanh |ψ 0 |, zero apparent acceleration a, and nonzero gravitational acceleration g. Then Ω = Ω √ 1 − v 2 , Ω = v/r, and Ω = g/r. The attitude vector ϑ remains zero, and hence dϑ/dt = 0, but the object nevertheless measures the constant angular velocity ω = cosh ψ(cosh ψ − 1)Ω in its reference system, and 7) ωτ…”