Frame-dragging

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Template:Expert According to Albert Einstein's theory of general relativity, space and time get pulled out of shape near a forcibly-accelerated or rotating body in a phenomenon referred to as frame-dragging. The rotational frame-dragging effect was first derived from the theory of general relativity in 1918 by the Austrian physicists Joseph Lense and Hans Thirring, and is also known as the Lense-Thirring effect. More generally, the subject of field effects caused by moving matter is known as gravitomagnetism.

Lense and Thirring predicted that the rotation of an object would alter space and time, dragging a nearby object out of position compared to the predictions of Newtonian physics. This is the frame-dragging effect. The predicted effect is incredibly small—about one part in a few trillion—which means that you have to look at something very massive, or build an instrument that is incredibly sensitive.

More familiar and already-proven effects of special relativity include the conversion of mass into energy (as seen in nuclear reactions) and back, and the Lorentz transformations which make objects near lightspeed seem to grow shorter and heavier from the point of view of an outside observer. Recent measurements of satellites in Earth orbit have shown frame dragging and represented another successful prediction of General Relativity.

1 Frame dragging effects
2 Attempts to test the existence of frame-dragging and its accurate measurement in 2004 using the LAGEOS satellites
3 See also
4 References
5 External links

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Frame dragging effects

Rotational frame-dragging (Lense-Thirring effect) is the inevitable result of the general principle of relativity, applied to rotation. The relativisation of rotational effects means that a rotating body ought to pull light around with it, in a manner somewhat reminiscent of old "aether-dragging" models. It is now the best-known effect, partly thanks to the Gravity Probe B experiment.
Accelerational frame dragging is the similarly inevitable result of the general principle of relativity, applied to acceleration. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).
Velocity frame dragging is even less well known and much more controversial. Its effects (or similar effects) do seem to appear in general relativity, but it is not usually listed as a "valid" example of frame-dragging. The reasons for this are complicated.
More complex effects can be constructed from these basic building blocks, to produce a variety of effects involving combinations of rotations and accelerations, time-variant acceleration ("jerk") and more complex rotations.

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Attempts to test the existence of frame-dragging and its accurate measurement in 2004 using the LAGEOS satellites

Using recent observations by X-ray astronomy satellites, including NASA's Rossi X-ray Timing Explorer, a team of astronomers announced in 1997 that they had seen evidence of frame-dragging in disks of gas swirling around a black hole. The team included Dr. Wei Cui of the Massachusetts Institute of Technology, and his colleagues, Dr. Nan Zhang, working at NASA's Marshall Space Flight Center, and Dr. Wan Chen of the University of Maryland in College Park.

The gyroscope-based Gravity Probe B experiment aims to detect any frame-dragging effects on the direction of spin of its gyroscopes as it orbits around the Earth. It was successfully launched on April 20, 2004 for an 18-month experiment. If this experiment is successful, it is expected to yield the most accurate measurements yet performed in this field. Indeed, an accuracy of better than 1% is expected.

Another consequence of the gravitomagnetic field of a central rotating body is the so-called Lense-Thirring effect (Lense and Thirring 1918). It consists of small secular precessions of the longitude of the ascending node <math>\Omega</math> and the argument of pericenter <math>\omega</math> of the path of a test mass freely orbiting the spinning main body. For the nodes of the LAGEOS Earth's artificial satellites they amount to ~30 milliarcseconds per year (ms/<math>{yr}</math> or ms <math>{yr}^{-1}</math>). Such tiny precessions would totally be swamped by the much larger classical precessions induced by the even zonal harmonic coefficients <math>J_{\ell},\ \ell=2,4,6...</math> of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential. Even the most recent Earth gravity models from the dedicated CHAMP and GRACE missions would not allow to know the even zonal harmonics to a sufficiently high degree of accuracy in order to extract the Lense-Thirring effect from the analysis of the node of only one satellite.

Ciufolini proposed in 1996 to overcome this problem by suitably combining the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II in order to cancel out all the static and time-dependent perturbations due to the first two even zonal harmonics <math>J_2,\ J_4</math> (Ciufolini 1996). Various analyses with the pre-CHAMP/GRACE JGM-3 and EGM96 Earth gravity models were performed by Ciufolini et al. over observational time spans of some years (Ciufolini et al. 1996; 1997; 1998). The claimed total accuracies were in the range of 20-25% (Ciufolini 2004). However, subsequent analyses by Ries et al. (2003a) and Iorio (2003) showed that such estimates are largely optimistic. Indeed, a more conservative and realistic evaluation of the impact of the uncancelled even zonal harmonics <math>J_6,\ J_8,\ J_{10},...</math>, according to the adopted EGM96 model, yield a systematic error of about 80% at 1-sigma level. Moreover, also the systematic error due to the non-gravitational perturbations mainly affecting the perigee of LAGEOS II was underestimated.

The opportunities offered by the new generation of Earth gravity models from CHAMP and, especially, GRACE allowed to discard the perigee of LAGEOS II, as pointed out by Ries et al. (2003b). In 2003 Iorio put explicitly forth a suitable linear combination of the nodes of LAGEOS and LAGEOS II which cancels out the first even zonal harmonic <math>J_2</math> (Iorio and Morea 2004). Such an observable was used by Ciufolini and Pavlis in a test performed with the 2nd generation GRACE-only EIGEN-GRACE02S Earth gravity model over a time span of 11 years (Ciufolini and Pavlis 2004). The claimed total error budget is 5% at 1-sigma level and 10% at 3-sigma level. However, Iorio (2005a, 2005b) criticized such results because of the neglected impact of the secular variations of the uncancelled even zonal harmonics <math>\dot J_4,\ \dot J_6</math> which would amount to about 13%. This would yield a total error of <math>\sim</math> 20% at 1-sigma level. Moreover, the latest CHAMP/GRACE-based Earth gravity models do not yet allow for a model-independent measurement. Indeed, the systematic error due to the static part of the even zonal harmonics amounts to 4% for EIGEN-GRACE02S, 6% for EIGEN-CG01C and 9% for GGM02S at 1-sigma level.

However, a number of recent and very detailed papers have fully confirmed the 5% to 10% error budget of the measurement published by Ciufolini and Pavlis in 2004, see, e.g., Ciufolini and Pavlis 2005, Lucchesi 2005, and Ciufolini, Pavlis and Peron 2006.

The measurement of the Lense-Thirring effect by Ciufolini and Pavlis in 2004 is based on the innovative ideas published since 1984 by Ciufolini who proposed the use of the nodes of two laser ranged satellites of LAGEOS-type to measure the Lense-Thirring effect. Indeed, the key idea of using the nodes of two laser ranged satellites of LAGEOS-type to measure the Lense-Thirring effect was first published in Ciufolini 1984 and Ciufolini 1986 and later studied in Ciufolini 1989 and Tapley, Ciufolini et al. 1989. The use of the combination of the nodes only of a number of laser ranged satellites of LAGEOS-type was first published in Ciufolini 1989, p. 3102, see also Ciufolini and Wheeler 1995, p. 336, where is written "... A solution would be to orbit several high-altitude, laser-ranged satellites, similar to LAGEOS, to measure <math>J_2, J_4, J_6</math>, etc, and one satellite to measure <math>\dot \Omega_{Lense-Thirring}</math> [i.e., the Lense-Thirring effect on the LAGEOS satellites nodes] ....". The use of the nodes of LAGEOS and LAGEOS 2, together with the explicit expression of the LAGEOS satellites nodal equations, was first proposed in Ciufolini 1996; the explicit expression of this combination of the nodes only of the LAGEOS satellites, that is however a trivial step on the basis of the explicit equations given in Ciufolini 1996, was presented by Ciufolini at the 2002 I-SIGRAV school and published in its proceedings, see Ciufolini 2002: precisely this observable was used by Ciufolini and Pavlis in 2004 for their accurate measurement of the frame-dragging effect on the LAGEOS satellites nodes, see Ciufolini and Pavlis 2004. For a study of the determination of the Lense-Thirring effect using laser-ranged satellites see also Peterson 1997. The use of the GRACE-derived gravitational models, when available, to measure the Lense-Thirring effect with accuracy of a few percent was, since many years, a well known possibility to all the researchers in this field and was presented during the SIGRAV 2000 conference by Pavlis, Pavlis 2002, and published in its proceedings, and was published by Ries et al. in the proceedings of the 1998 William Fairbank conference and of the 2003 13th Int. Laser Ranging Workshop, Ries et al. 2003a and 2003b, where Ries et al. concluded that, in the measurement of the Lense-Thirring effect using the GRACE gravity models and the LAGEOS and LAGEOS 2 satellites: "a more current error assessment is probably at the few percent level ...".

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References

Einstein, A The Meaning of Relativity (contains transcripts of his 1921 Princeton lectures).
Thirring, H. Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19, 33 (1918). [On the Effect of Rotating Distant Masses in Einstein's Theory of Gravitation]
Thirring, H. Berichtigung zu meiner Arbeit: "Über die Wirkung rotierender Massen in der Einsteinschen Gravitationstheorie". Physikalische Zeitschrift 22, 29 (1921). [Correction to my paper "On the Effect of Rotating Distant Masses in Einstein's Theory of Gravitation"]
Lense, J. and Thirring, H. Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19 156-63 (1918) [On the Influence of the Proper Rotation of Central Bodies on the Motions of Planets and Moons According to Einstein's Theory of Gravitation]
I. Ciufolini. On a new method to measure the gravitomagnetic field using two orbiting satellites. Il Nuovo Cimento A, 109, 1709-1720, (1996).
I. Ciufolini, F. Chieppa, D. Lucchesi, and F. Vespe. Test of Lense-Thirring orbital shift due to spin. Classical and Quantum Gravity 14, 2701-2726, (1997).
I. Ciufolini, E.C. Pavlis, F. Chieppa, E. Fernandes-Vieira, and J. Perez-Mercader, J. Test of general relativity and measurement of the Lense-Thirring effect with two Earth satellites. Science 279, 2100-2103, (1998).
I. Ciufolini. Frame Dragging and Lense-Thirring Effect, General Relativity and Gravitation 36, 2257-2270, (2004).
J. C. Ries, R. J. Eanes and B. D. Tapley. Lense-Thirring Precession Determination from Laser Ranging to Artificial Satellites. Nonlinear Gravitodynamics ed. R. Ruffini and C. Sigismondi (World Scientific, Singapore, 2003a) pp. 201-211.
L. Iorio. The impact of the static part of the Earth's gravity field on some tests of General Relativity with Satellite Laser Ranging. Celestial Mechanics and Dynamical Astronomy 86 277-294, (2003).
J. C. Ries, R. J. Eanes, B. D. Tapley and G. E. Peterson. Prospects for an Improved Lense-Thirring Test with SLR and the GRACE Gravity Mission. Proc. 13th Int. Laser Ranging Workshop NASA CP 2003-212248 ed. R. Noomen, S. Klosko, C. Noll and M. Pearlman. (NASA Goddard 2003b). Preprint [1]
L. Iorio and A. Morea. The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect. General Relativity and Gravitation 36, 1321-1333, (2004). Preprint [2].
I. Ciufolini, E. C. Pavlis. A confirmation of the general relativistic prediction of the Lense–Thirring effect. Nature 431, 958 - 960 (21 October 2004); doi:10.1038/nature03007
L. Iorio. On the reliability of the so-far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites. New Astronomy in press. (2005a); doi:10.1016/j.newast.2005.01.001 [3]
L. Iorio. On the impact of the secular rates of the even zonal harmonics on the measurement of the Lense-Thirring effect: a quantitative analysis, (2005b). Preprint [4].
I. Ciufolini and E. Pavlis, On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to "On the reliability of the so-far performed tests for measuring the Lense–-Thirring effect with the LAGEOS satellites" by L. Iorio, New Astronomy, 10, 636-651 (2005). See: [5].
D. Lucchesi, The impact of the even zonal harmonics secular variations on the Lense-Thirring effect measurement with the two LAGEOS satellites, Int. Journ Mod. Phys D, 14, 1989 2023 (2005).
I. Ciufolini, E. Pavlis and R. Peron, Determination of frame-dragging using Earth gravity models from CHAMP and GRACE New Astronomy, 11, 527-550 (2006).
I. Ciufolini, Theory and experiments in General Relativity and other metric theories, Ph.D. Dissertation, Univ. of Texas, Austin (Pub. Ann Arbor, Michigan), 1984.
I. Ciufolini, Measurement of the Lense-Thirring drag on high-altitude laser-ranged artificial satellites, Phys. Rev. Lett., 56, 278 (1986).
I. Ciufolini, A comprehensive introduction to the Lageos gravitomagnetic experiment: from the importance of the gravitomagnetic field in physics to preliminary error analysis and error budget, Int. J. Mod. Phys. A 4, 3083 (1989).
I. Ciufolini, D. Lucchesi, F. Vespe and A. Mandiello, Measurement of Dragging of Inertial Frames and Gravitomagnetic Field Using Laser-Ranged Satellites, Il Nuovo Cimento A, 109, 575 (1996).
I. Ciufolini, Frame-dragging and its measurement, in Gravitation: from the Hubble length to the Planck length, Proceedings of the I SIGRAV School on General Relativity and Gravitation, Frascati (Rome), September 2002, World Scientific.
I. Ciufolini and J.A. Wheeler, Gravitation and Inertia, Princeton University Press, Princeton, New Jersey, 1995.
E.C. Pavlis, Geodetic Contributions to Gravitational Experiments in Space, in Recent Developments in General Relativity, Genoa 2000, R. Cianci, et al., eds., Springer-Verlag, Milan, p 217.
G. E. Peterson, Estimation of the Lense-Thirring Precession Using Laser-Ranged SAtellites, Ph. Dissertation, Univ. of Texas, Austin, 1997.
B. Tapley, I. Ciufolini, J.C. Ries, R.J. Eanes and M.M. Watkins, NASA-ASI Study on LAGEOS III, CSR-UT publication n. CSR-89-3, Austin, Texas (1989), and Ciufolini, I., et al., ASI-NASA Study on LAGEOS III, CNR, Rome, Italy (1989). See also: I. Ciufolini et al., INFN study on LARES/WEBER-SAT (2004).