# Gravitational shielding

The term gravitational shielding refers to a hypothetical process of shielding an object from the influence of a gravitational field. Such processes, if they existed, would have the effect of reducing the weight of an object. The shape of the shielded region would be similar to a shadow from the gravitational shield. For example, the shape of the shielded region above a disk would be conical. The height of the cone's apex above the disk would vary directly with the height of the shielding disk above the earth.[1] Experimental evidence to date indicates that no such effect exists. Gravitational shielding is considered to be a violation of the equivalence principle and therefore inconsistent with both Newtonian theory and general relativity.[2]

The concept of gravity shielding is a common concept in science fiction literature, especially for space travel. One of the first and best known examples is the fictional gravity shielding substance "Cavorite" that appears in H. G. Wells' classic 1901 novel The First Men in the Moon. Wells was promptly criticized for using it by none other than Jules Verne.[3]

## Tests of the equivalence principle

As of 2008, no experiment was successful in detecting positive shielding results. To quantify the amount of shielding, Quirino Majorana[4] suggested an extinction coefficient h that modifies Newton’s gravitational force law as follows:

${\displaystyle F={\frac {GMm}{r^{2}}}e^{-h\int \rho (r)dr}}$

The best laboratory measurements have established an upper bound limit for shielding of 4.3×10−15 m²/kg.[5] Another recent analysis suggested a lower bound of 0.6×10−15.[6] The best estimate based on the most accurate gravity anomaly data during the 1997 solar eclipse has provided a new constraint on the shielding parameter 6×10−19 m²/kg.[7] However, astronomical observations impose much more stringent limits. Based on lunar observations available in 1908, Poincaré[8] established that h can be no greater than 10−18 m²/kg. Subsequently this bound has been greatly improved. Eckhardt[9] showed that lunar ranging data implies an upper bound of 10−22 m²/kg, and Williams, et al.,[10] have improved this to h = (3 ± 5)×10−22 m²/kg. Note that the value is smaller than the uncertainty. The consequence of the negative results of those experiments (which are in good agreement with the predictions of general relativity) is, that every theory which contains shielding effects like Le Sage's theory of gravitation, must reduce those effects to an undetectable level. For a review of the current experimental limits on possible gravitational shielding, see the survey article by Bertolami, et al.[2] Also, for a discussion of recent observations during solar eclipses, see the paper by Unnikrishnan et al.[11]

## Majorana's experiments and Russell's criticism

Some shielding experiments were conducted in the early 20th century by Quirino Majorana.[4][12] Majorana claimed to have measured positive shielding effects. Henry Norris Russell's analysis of the tidal forces showed that Majorana's positive results had nothing to do with gravitational shielding.[13] To bring Majorana's experiments in accordance with the equivalence principle of General Relativity he proposed a model, in which the mass of a body is diminished by the proximity of another body, but he denied any connection between gravitational shielding and his proposal of mass variation. For another explanation of Majorana's experiments, see Coïsson et al.[14] But Majorana's results couldn't be confirmed up to this day (see the section above) and Russell's mass variation theory, although meant as a modification of general relativity, is inconsistent with standard physics as well.

## Minority views

The consensus view of the scientific community is that gravitational shielding does not exist, but there have been occasional investigations into this topic, such the 1999 NASA-funded paper which reported negative results.[15][16][17] Eugene Podkletnov claimed in two papers, one of which he later withdrew, that objects held above a magnetically-levitated, superconducting, rotating disc underwent a reduction of between 0.5 and 2% in weight.[18] Theoreticians have attempted to reconcile Podkletnov's claims with quantum gravity theory.[19][20] However, neither Podkletnov's claims, nor the similar claims of others, of "gravity reduction", "gravity shielding", or the like, have yet been successfully replicated, verified by independent review, or subjected to public demonstration.

## References

1. ^ Unnikrishan, C. S. (1996). Does a superconductor shield gravity? Physica C, 266, 133-137.
2. ^ a b Bertolami, O. & Paramos, J. & Turyshev, S. G. (2006), General Theory of Relativity: Will it survive the next decade?, in H. Dittus, C. Laemmerzahl, S. Turyshev, Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity: 27-67
3. ^ James Giblin (2000). The Century that was: Reflections on the Last One Hundred Years. Simon & Schuster. p. 8. "I sent my travelers to the moon with gunpowder, something one sees every day. Where is Monsieur Wells' 'Cavorite'? Let him show it to me!"
4. ^ a b Majorana, Q., (1920). “On gravitation. Theoretical and experimental researches”, Phil. Mag. [ser. 6] 39, 488-504.
5. ^ Unnikrishnan and Gillies (2000), Phys Rev D, 61
6. ^ Caputo M., On new limits of the coefficient of gravitation shielding,J. Astrophysics and Astronomy,vol. 27, 439-441 (2006).
7. ^ Yang X.-S., Wang Q.-S., Gravity Anomaly During the Mohe Total Solar Eclipse and New Constraint on Gravitational Shielding Parameter,Astrophysics and Space Science, Vol.282, 245-253 (2002).
8. ^ Poincaré, H. (1908). "La dynamique de l'électron", Revue générale des sciences pures et appliquées 19, pp. 386-402, reprinted in Science and Method. Flammarion, Paris. An English translation was published as Foundation of Science, Science Press, New York, 1929.
9. ^ D. H. Eckhardt, Phy Rev D, 42, 1990, 2144
10. ^ Williams, et al., “Testing the Equivalence Principle on the Ground and in Space”, (2006), to be published by Springer Verlag, Lecture Notes in Physics, gr-qc/0507083
11. ^ Unnikrishnan, Mohapatra, Gillies (2002), “Anomalous gravity data during the 1997 total solar eclipse do not support the hypothesis of gravitational shielding”, Physical Review D, vol 63, available online at http://www.astro.oma.be/ICET/bim/bim138/vanruymbeke2.htm
12. ^ Martins, R. A., 2002. "Majorana’s experiments on gravitational absorption", in: Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation (ed. Edwards, M. R.), Apeiron, Montreal, pp. 219-238.
13. ^ Russell, H.N. (1921). “On Majorana’s theory of gravitation”. Astrophys. J. 54, 334-346.
14. ^ Coïsson, R.; Mambriani, G.; Podini, P. "A new interpretation of Quirino Majorana's experiments on gravitation and a proposal for testing his results", Il Nuovo Cimento B, vol. 117, Issue 04, p.469.
15. ^ N. Li, D. Noever, T. Robertson, R. Koczor and W. Brantley (August 1997). "Static Test for a Gravitational Force Coupled to Type II YBCO Superconductors". Physica C 281 (2-3): 260–267. Bibcode:1997PhyC..281..260L. doi:10.1016/S0921-4534(97)01462-7.
16. ^ R. Koczor and D. Noever, Fabrication of Large Bulk Ceramic Superconductor Disks for Gravity Modification Experiments and Performance of YBCO Disks Under e.m. Field Excitation, NASA Marshall, Huntsville, AL, AIAA 99-2147, 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 20–24 June 1999, Los Angeles, CA.
17. ^ Space.com on NASA funding Archived February 10, 2006, at the Wayback Machine.
18. ^ Podkletnov, E; Nieminen, R (December 10, 1992). "A possibility of gravitational force shielding by bulk YBa2Cu3O7−x superconductor". Physica C 203 (3–4): 441–444. Bibcode:1992PhyC..203..441P. doi:10.1016/0921-4534(92)90055-H. Retrieved April 29, 2014.
19. ^ Modanese, G. (1996, August 20). Theoretical analysis of a reported weak-gravitational-shielding effect. Europhysics Letters, 35(6), 413-418.
20. ^ Wu, N. (2004). Gravitational shielding effect in gauge theory of gravity. Communications in Theoretical Physics, 41(4), 567-572.