Speed of gravity

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In mathematical physics, particularly in the context of classical theories of gravitation, the speed of gravity refers to the speed at which gravitational radiation propagates. This is the speed at which news or field updating information is propagated as a wave.

If no other theory is specified, it is generally understood that the theory in question is our current gold standard theory of gravitation, namely general relativity.

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[edit] Newtonian gravitation

Isaac Newton's formulation of a gravitational force law requires that each object `knows' the instantaneous position of all other gravitating objects through their gravitational attraction. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when one somehow moves a gravitating object, the field is everywhere immediately updated.

This aspect of his theory troubled Newton, who felt that such updating information should propagate at some finite speed. He experimented with the effect of introducing such a finite updating speed, and found that this would destroy the remarkable agreement of his original theory with all astronomical observations available in his own time. (Discrepancies between Newtonian gravitation and observation were not widely recognized until the 19th century, long after Newton's death.)

[edit] General relativity

In general relativity, the gravitational potential is identified with the metric tensor and the gravitational force with the Christoffel symbols of the space-time manifold. Tidal gravitational field is associated with the curvature of space-time. General relativity predicts that gravitational radiation should exist and propagate as a wave at the speed of light. To avoid confusion, we should point out that a slowly evolving source for a weak gravitational field will produce, according to general relativity, similar effects to those we might expect from Newtonian gravitation. In particular, a slowly evolving Coulomb component of a gravitational field should not be confused with a possible additional radiation component; see Petrov classification. Nonetheless, any of the Petrov-type gravitational field obeys the principle of causality, so that the slowly evolving "Coulomb component" of the gravitational field can not transfer information about position of the source of the gravitational field with the speed faster than the speed of light.

This finite speed of gravitational interaction in general relativity may at first seem to lead to exactly the same sorts of problems with the aberration of gravity that Newton was originally concerned with. Although the calculations are considerably more complicated, one can show that general relativity does not suffer from these problems just as electromagnetic retarded Lienard-Wiechert potential theory does not.

It is not very easy to construct a self-consistent gravity theory in which gravitational interaction propagates at a speed other than the speed of light, which complicates discussion of this possibility. However, the mainstream view is that there is no known observational or experimental evidence which suggests that the speed of gravity differs from the speed of light.

[edit] Aberration argument

It is often held, e.g. by Tom Van Flandern, that the speed of gravity must be at least 20 billion times that of light. This argument draws an analogy to the aberration of light, which causes the Sun to appear in a position slightly displaced from its actual position. Introducing a speed of light time delay into Newtonian gravitation would result in unstable planetary orbits.

But in general relativity, gravitomagnetism effects cancel out the effects of aberration. The weak stationary field limit of general relativity reproduces Newtonian gravity with instantanous action at a distance, despite the fact that the full theory gives a speed of gravity of c.

No current observations are inconsistent with general relativity.

[edit] Experimental measurement?

In September 2002, Sergei Kopeikin and Edward Fomalont announced in a conference in Seattle, Washington that they had made an indirect measurement of the speed of gravity, using their data from VLBI measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of a bright radio source - quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.

Several physicists, including Clifford M. Will and Steve Carlip, have criticised these claims on the grounds that they have allegedly misinterpreted the results of their measurements. However, Kopeikin and Fomalont continue to vigorously argue their case. (See the citations below for the details of the arguments pro and con.)

It is important to understand that none of the participants in this controversy are claiming that general relativity is "wrong". Rather, the debate concerns whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions.

[edit] External links


[edit] References

    • Kopeikin, Sergei M. (2001). "Testing Relativistic Effect of Propagation of Gravity by Very-Long Baseline Interferometry". Astrophys. J. 556: L1-L6. arXiv:gr-qc/0105060.
    • Asada, Hidecki (2002). "The Light-cone Effect on the Shapiro Time Delay". Astrophys. J. 574: L69. arXiv:astro-ph/0206266.
    • Will, Clifford M. (2003). "Propagation Speed of Gravity and the Relativistic Time Delay". Astrophys. J. 590: 683-690. arXiv:astro-ph/0301145.
    • Fomalont, E. B.; and Kopeikin, Sergei M. (2003). "The Measurement of the Light Deflection from Jupiter: Experimental Results". Astrophys. J. 598: 704-711. arXiv:astro-ph/0302294.
    • Kopeikin, Sergei M. (2003). "The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002". Phys. Lett. A 312: 147-157. arXiv:gr-qc/0212121.
    • Kopeikin, Sergei M. (2004). "The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment". Classical and Quantum Gravity 21: 3251-3286. arXiv:gr-qc/0310059.
    • Samuel, Stuart (2003). "On the Speed of Gravity and the v/c Corrections to the Shapiro Time Delay". Phys. Rev. Lett. 90: 231101. arXiv:astro-ph/0304006.
    • Kopeikin, Sergei and Fomalont, Edward (2006). "On the Speed of Gravity and Relativistic v/c Corrections to the Shapiro Time Delay". Phys. Lett. A: in press. arXiv:gr-qc/0310065.
    • Carlip, S. (2004). "Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy". Class. Quant. Grav. 21: 3803-3812. arXiv:gr-qc/0403060.
    • Kopeikin, Sergei M. (2005). "Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy". Class. Quant. Grav. 22: 5181-5186. arXiv:gr-qc/0510048.
    • Pascual-Sánchez, J.-F. (2004). "Speed of gravity and gravitomagnetism". Int. J. Mod. Phys. D 13: 2345-2350. arXiv:gr-qc/0405123.
    • Kopeikin, Sergei (2006). "Gravitomagnetism and the speed of gravity". Int. J. Mod. Phys. D: in press. arXiv:gr-qc/0507001.
    • Samuel, Stuart (2004). "On the Speed of Gravity and the Jupiter/Quasar Measurement". Int. J. Mod. Phys. D 13: 1753-1770. arXiv:astro-ph/0412401.

    Promoting Van Flandern's claims:

    • Van Flandern, T.; and Vigier, J.P. (2002). "Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions". Found. Phys. 32: 1031-1068.
    (See Meta Research for further citations.)

    Criticizing Van Flandern's claims:

    • Carlip, S. (2000). "Aberration and the Speed of Gravity". Phys. Lett. A 267: 81-87. arXiv:gr-qc/9909087.
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