I8    The Einstein-Thirring-Lense Effect


Newton's experiment with the hanging water bucket seems to show that the water in the bucket knows if it is rotating or not. Ernst Mach criticized Newton's conclusion in1883 that absolute space exists and asserted that a rotating mass must influence an inertial frame in its vicinity. The two Austrian Physicist Hans Thirring and Josef Lense showed in 1918 that Einstein’s GTR solves this problem: A rotating mass slightly drags the metric of space-time along with it, twisting it a little or in the extreme case, creating a vortex-like structure in space-time. A free-falling object from the OFF no longer moves, therefore, in a ‘straight’ line toward the center of a spherical central mass if it is rotating:



This ‘dragging’ of space (keyword ‘frame dragging’) must be noticeable for a satellite orbiting the earth around the poles through a small rotation of its orbital plane:

according to Newton                                                   according to Einstein-Thirring-Lense

(Franz Embacher has kindly granted use of this graphic from his presentation on the Lense-Thirring effect, which can be
downloaded from http://homepage.univie.ac.at/Franz.Embacher/Rel/ . This site is a true treasure!)


In October 2004, I. Ciufolini and E.C. Pavlis of the University of Lecce presented their analysis [40] of the orbital data of two satellites (LAGEOS and LAGEOS 2). These satellites were specifically intended as targets for Laser Ranging (see I7). From the fluctuations and irregularities in the orbits geologists have gained much information on the detailed structure of earth’s gravitational field as well as the density distribution in the earth's interior. Ciufolini and Pavlis have, with great effort, eliminated mathematically all other influences on the orbits of these satellites (for example, the radiation pressure of the sun!) in order to finally isolate the tiny (31 milli-arcseconds per year) Lense-Thirring effect. They believe they have succeeded to an accuracy of approximately ± 10%.

Scientists from NASA and Stanford University want to measure this effect with 1% accuracy with the satellite ‘Gravity Probe B’ using a different method. You can find detailed information on the Internet. It is fascinating how this experiment once again tests the limits of what is technically feasible! The actual measurements were completed in August 2006 and the evaluations should now (January 2007) be complete. After a critical review by experts, the outcome will be presented in April 2007. Just after the experiment of Ciufolini and Pavlis nobody expects that the GTR will be refuted. However, if Einstein’s GTR can be confirmed at the 1% level, it will mean the end of some competing theories.

Gravity Probe B uses four gyroscopes constructed from high-precision polished quartz spheres. The changes in the gyro’s axis relative to the satellite are determined. This is aligned, using a small telescope, as stably as possible to the star HR 8703 in the constellation Pegasus, whose motion is very well known. The following two effects are simultaneously measured:

  1. The ‘geodetic’ effect, which we met in I1 as the precession of the perihelion of Mercury and consists of a tilting of the gyro axis in the orbital plane. It should be about 6.6 arc seconds. The accuracy of the Gravity Probe B should be better than 0.01%.
  2. The Lense-Thirring effect, which consists of a tilting of the gyro axis perpendicular to the orbital plane. It should be about 0.041 arc seconds. This effect could be measured to an accuracy of about 1%.

I would encourage you once again to have a look in the Internet at the reports, pictures and other material prepared for this latest test of the GTR. Use the search keywords mentioned above, as they are longer lived as actual concrete addresses.

Addendum January 2009: The experiment was not able to attain its lofty goal. The signal due to a ‘frame dragging effect’ is drowned in an unpredicted ‘noise’. Web Links: wiki and  Stanford University

The geodetic effect can be nicely illustrated with Epstein [15-177f]. We simply repeat the idea of Section I1 and draw an additional rotational axis. On the left we have Newton's ‘flat’ world, in which the gyro maintains its direction absolutely and on the right in the curved space of GTR the gyro is tilted through a small angle after one revolution: