Theoretical Analysis of a Reported Weak Gravitational Shielding Effect

Under special conditions (Meissner-effect levitation in a high frequency magnetic field and rapid rotation) a disk of high-Tc superconducting material has recently been found to produce a weak shielding of the gravitational field. We show that this phenomenon has no explanation in the standard gravity theories, except possibly in the non-perturbative Euclidean quantum theory. 04.20.-q Classical general relativity. 04.60.-m Quantum gravity. 74.72.-h High-Tc cuprates. A. Von Humboldt Fellow. e-mail: [email protected] In two recent experiments [1, 2], Podkletnov and co-workers have found indications for a possible weak shielding of the gravitational force through a disk of high-Tc superconducting material. In the first experiment a sample made of silicon dioxide of the weight of ca. 5 g, was found to lose about 0.05% of its weight when placed 15 mm above the disk. The diameter of the disk was 145 mm and its thickness 6 mm. The disk was refrigerated using liquid helium and was levitating over a solenoid due to the Meissner effect. When the disk was set in rotation by means of lateral alternating magnetic fields, the shielding effect increased up to 0.3%. When the disk was not levitating, but was placed over a fixed support, no shielding was observed. In the second experiment the disk had the form of a toroid with the outer diameter of 275 mm and was enclosed in a stainless steel cryostat. Samples of different composition and weight (10 to 50 g) were placed over the disk and the same percentual weight loss was observed for different samples, thus enforcing the interpretation of the effect as a slight diminution of the gravitational acceleration. While the toroid was rotating (at an angular speed of 5000 rpm) the weight loss was of 0.3-0.5%, like in the first experiment, but it reached a maximum of 1.9-2.1% when the speed was slowly reduced by varying the current in the solenoids. In both experiments, the magnetic fields were produced by high frequency currents and the maximum effect was observed at frequencies of the order of ca. 1 MHz. Measurements were effected also in the vacuum, in order to rule out possible buoyancy effects. The dependence of the shielding value on the height above the disk was very weak. Within the considered range (from a few cm to 300 cm) no sensible variation of the shielding value was observed. This weak height dependence is a severe challenge for any candidate theoretical interpretation, as it violates an intuitive vectorial representation of the shielding. We have analyzed in detail this issue in [3]. Independent repetitions of the experiment have already been undertaken, stimulated by scientific and especially technological interest. We would like to stress here the importance of precise measurements. In particular, it is essential to obtain exact spatial field maps and information about the transient stages. It is also crucial to use a different kind of balance from that used by the authors of [1, 2] and possibly a gravity gradiometer [4]. If the effect turned out to be of non-gravitational nature, its fundamental interest would be strongly reduced. On the contrary, if the effect is really a gravitational shielding its theoretical explanation calls for new and non-trivial dynamical mechanisms, as we argue in the following. For clarity we shall organize our analysis as follows. Considering two masses m1 and m2 (which represent the Earth and the sample) and a medium between them (the disk), we shall