Speed of gravity
Exact values | |
---|---|
Canis Major Dwarf Galaxy) to Earth | 25000 years |
across the Milky Way | 100000 years |
from the Andromeda Galaxy to Earth | 2.5 million years |
General relativity |
---|
In
Introduction
The speed of gravitational waves in the
Static fields
The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.
The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.
Newtonian gravitation
Laplace
The first attempt to combine a finite gravitational speed with Newton's theory was made by Laplace in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid. Changes in the motion of the attracting body are transmitted by some sort of waves.[6] Therefore, the movements of the celestial bodies should be modified in the order v/c, where v is the relative speed between the bodies and c is the speed of gravity. The effect of a finite speed of gravity goes to zero as c goes to infinity, but not as 1/c2 as it does in modern theories. This led Laplace to conclude that the speed of gravitational interactions is at least 7×106 times the speed of light. This velocity was used by many in the 19th century to criticize any model based on a finite speed of gravity, like electrical or mechanical explanations of gravitation.
From a modern point of view, Laplace's analysis is incorrect. Not knowing about
The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge. In a field equation consistent with special relativity (i.e., a Lorentz invariant equation), the attraction between static charges moving with constant relative velocity is always toward the instantaneous position of the charge (in this case, the "gravitational charge" of the Sun), not the time-retarded position of the Sun. When an object is moving in orbit at a steady speed but changing velocity v, the effect on the orbit is order v2/c2, and the effect preserves energy and angular momentum, so that orbits do not decay.
Electrodynamical analogies
Early theories
At the end of the 19th century, many tried to combine Newton's force law with the established laws of electrodynamics, like those of Wilhelm Eduard Weber, Carl Friedrich Gauss, Bernhard Riemann and James Clerk Maxwell. Those theories are not invalidated by Laplace's critique, because although they are based on finite propagation speeds, they contain additional terms which maintain the stability of the planetary system. Those models were used to explain the perihelion advance of Mercury, but they could not provide exact values. One exception was Maurice Lévy in 1890, who succeeded in doing so by combining the laws of Weber and Riemann, whereby the speed of gravity is equal to the speed of light. However, those hypotheses were rejected.[8][9]
However, a more important variation of those attempts was the theory of Paul Gerber, who derived in 1898 the identical formula, which was also derived later by Einstein for the perihelion advance. Based on that formula, Gerber calculated a propagation speed for gravity of 305000 km/s, i.e. practically the speed of light. But Gerber's derivation of the formula was faulty, i.e., his conclusions did not follow from his premises, and therefore many (including Einstein) did not consider it to be a meaningful theoretical effort. Additionally, the value it predicted for the deflection of light in the gravitational field of the sun was too high by the factor 3/2.[10][11][12]
Lorentz
In 1900,
The special form of these terms may perhaps be modified. Yet, what has been said is sufficient to show that gravitation may be attributed to actions which are propagated with no greater velocity than that of light.
In 1908, Henri Poincaré examined the gravitational theory of Lorentz and classified it as compatible with the relativity principle, but (like Lorentz) he criticized the inaccurate indication of the perihelion advance of Mercury.[14]
Lorentz covariant models
Henri Poincaré argued in 1904 that a propagation speed of gravity which is greater than c would contradict the concept of local time (based on synchronization by light signals) and the principle of relativity. He wrote:[15]
What would happen if we could communicate by signals other than those of light, the velocity of propagation of which differed from that of light? If, after having regulated our watches by the optimal method, we wished to verify the result by means of these new signals, we should observe discrepancies due to the common translatory motion of the two stations. And are such signals inconceivable, if we take the view of Laplace, that universal gravitation is transmitted with a velocity a million times as great as that of light?
However, in 1905 Poincaré calculated that changes in the gravitational field can propagate with the speed of light if it is presupposed that such a theory is based on the Lorentz transformation. He wrote:[16]
Laplace showed in effect that the propagation is either instantaneous or much faster than that of light. However, Laplace examined the hypothesis of finite propagation velocity ceteris non mutatis [all other things being unchanged]; here, on the contrary, this hypothesis is conjoined with many others, and it may be that between them a more or less perfect compensation takes place. The application of the Lorentz transformation has already provided us with numerous examples of this.
Similar models were also proposed by
General relativity
Background
General relativity predicts that
Suddenly displacing one of two gravitoelectrically interacting particles would, after a delay corresponding to lightspeed, cause the other to feel the displaced particle's absence: accelerations due to the change in quadrupole moment of star systems, like the
In GR gravity is described by a 4x4 tensor, which, in the weak gravity limit, it can be described by the gravitoelectromagnetism approximation. In the following discussion the diagonal components of the tensor would be termed gravitoelectric components, and the other components will be termed gravitomagnetic.
Two gravitoelectrically interacting particle ensembles, e.g., two planets or stars moving at constant velocity with respect to each other, each feel a force toward the instantaneous position of the other body without a speed-of-light delay because
A moving body's seeing no
In other words, since the gravitoelectric field is, by definition, static and continuous, it does not propagate. If such a source of a static field is accelerated (for example stopped) with regard to its formerly constant velocity frame, its distant field continues to be updated as though the charged body continued with constant velocity. This effect causes the distant fields of unaccelerated moving charges to appear to be "updated" instantly for their constant velocity motion, as seen from distant positions, in the frame where the source-object is moving at constant velocity. However, as discussed, this is an effect which can be removed at any time, by transitioning to a new reference frame in which the distant charged body is now at rest.
The static and continuous
Aberration of field direction in general relativity, for a weakly accelerated observer
The finite speed of gravitational interaction in general relativity does not lead to the sorts of problems with the
It is in fact 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.[20]
Formulaic conventions
In
Measurements
For the reader who desires a deeper background, a comprehensive review of the definition of the speed of gravity and its measurement with high-precision astrometric and other techniques appears in the textbook Relativistic Celestial Mechanics in the Solar System.[21]
PSR 1913+16 orbital decay
The speed of gravity (more correctly, the speed of
Jovian occultation of QSO J0842+1835 (contested)
In September 2002,
Several physicists, including Clifford M. Will and Steve Carlip, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, Hideki Asada in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.[24]
It is important to keep in mind that none of the debaters in this controversy are claiming that general relativity is "wrong". Rather, the debated issue is whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions.
Kopeikin and Fomalont, however, continue to vigorously argue their case and the means of presenting their result at the press conference of the American Astronomical Society (AAS) that was offered after the results of the Jovian experiment had been peer-reviewed by the experts of the AAS scientific organizing committee. In a later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time
Stuart Samuel also showed that the experiment did not actually measure the speed of gravity because the effects were too small to have been measured.[28] A response by Kopeikin and Fomalont challenges this opinion.[29]
GW170817 and the demise of two neutron stars
The detection of GW170817 in 2017, the finale of a neutron star inspiral observed through both gravitational waves and gamma rays, at a distance of 130 million light years, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after peak gravitational wave emission; assuming a delay of zero to 10 seconds, the difference between the speeds of gravitational and electromagnetic waves, vGW − vEM, is constrained to between −3×10−15 and +7×10−16 times the speed of light.[30]
This also excluded some alternatives to general relativity, including variants of scalar–tensor theory,[31][32][33][34] instances of Horndeski's theory,[35] and Hořava–Lifshitz gravity.[36][37][38]
Notes
References
- ISBN 978-0-618-75354-3.
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- ISBN 978-0-8053-8662-2.
- ^ Taylor, Edwin F.; Wheeler, John Archibald (1991). Spacetime Physics (2nd ed.). p. 12.
- ^ Verrier U. Le (1859). "Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète". C. R. Acad. Sci. 49: 379–383.
- ^ Laplace, P.S.: (1805) "A Treatise in Celestial Mechanics", Volume IV, Book X, Chapter VII, translated by N. Bowditch (Chelsea, New York, 1966)
- ^ Brown, Kevin S. "Laplace on the Speed of Gravity". MathPages. Retrieved 9 May 2019.
- ]
- ISBN 978-0-19-858174-1.
- ^ Gerber, P. (1898). . Zeitschrift für Mathematische Physik (in German). 43: 93–104.
- ^ Zenneck, pp. 49–51
- ^ "Gerber's Gravity". Mathpages. Retrieved 2 Dec 2010.
- ^ Lorentz, H.A. (1900). . Proc. Acad. Amsterdam. 2: 559–574.
- ^ Poincaré, H. (1908). "La dynamique de l'électron" (PDF). Revue Générale des Sciences Pures et Appliquées. 19: 386–402. Reprinted in Poincaré, Oeuvres, tome IX, S. 551–586 and in "Science and Method" (1908)
- ^ Poincaré, Henri (1904). "L'état actuel et l'avenir de la physique mathématique". Bulletin des Sciences Mathématiques. 28 (2): 302–324.. English translation in Poincaré, Henri (1905). "The Principles of Mathematical Physics". In Rogers, Howard J. (ed.). Congress of arts and science, universal exposition, St. Louis, 1904. Vol. 1. Boston and New York: Houghton, Mifflin and Company. pp. 604–622. Reprinted in "The value of science", Ch. 7–9.
- S2CID 120211823. See also the English Translation.
- Bibcode:2007ggr..conf..193W.
- ^ Will, Clifford & Gibbons, Gary. "On the Multiple Deaths of Whitehead's Theory of Gravity", to be submitted to Studies In History And Philosophy Of Modern Physics (2006).
- S2CID 12941280.
- S2CID 250863503.
- ^ Kopeikin, S.; Efroimsky, M. & Kaplan, G. (2011). Relativistic Celestial Mechanics in the Solar System. Wiley-VCH.
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- ^ "Quest to settle riddle over Einstein's theory may soon be over". phys.org. 10 February 2017. Retrieved 10 February 2017.
- ^ "Theoretical battle: Dark energy vs. modified gravity". arstechnica.co.uk. 25 February 2017. Retrieved 27 October 2017.
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Further reading
- Kopeikin, Sergei M. (2001). "Testing Relativistic Effect of Propagation of Gravity by Very-Long Baseline Interferometry". Astrophys. J. 556 (1): L1–L6. S2CID 2121856.
- Asada, Hidecki (2002). "The Light-cone Effect on the Shapiro Time Delay". Astrophys. J. 574 (1): L69–L70. S2CID 14589086.
- Will, Clifford M. (2003). "Propagation Speed of Gravity and the Relativistic Time Delay". Astrophys. J. 590 (2): 683–690. S2CID 16402202.
- Fomalont, E. B. & Kopeikin, Sergei M. (2003). "The Measurement of the Light Deflection from Jupiter: Experimental Results". Astrophys. J. 598 (1): 704–711. S2CID 14002701.
- Kopeikin, Sergei M. (Feb 21, 2003). "The Measurement of the Light Deflection from Jupiter: Theoretical Interpretation". arXiv:astro-ph/0302462.
- Kopeikin, Sergei M. (2003). "The Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002". Phys. Lett. A. 312 (3–4): 147–157. S2CID 11664954.
- Faber, Joshua A. (Mar 14, 2003). "The speed of gravity has not been measured from time delays". arXiv:astro-ph/0303346.
- Kopeikin, Sergei M. (2004). "The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment". Classical and Quantum Gravity. 21 (13): 3251–3286. S2CID 250893542.
- Samuel, Stuart (2003). "On the Speed of Gravity and the v/c Corrections to the Shapiro Time Delay". Phys. Rev. Lett. 90 (23): 231101. S2CID 15905017.
- Kopeikin, Sergei & Fomalont, Edward (2006). "On the speed of gravity and relativistic v/c corrections to the Shapiro time delay". Physics Letters A. 355 (3): 163–166. S2CID 12121566.
- Hideki, Asada (Aug 20, 2003). "Comments on "Measuring the Gravity Speed by VLBI"". arXiv:astro-ph/0308343.
- Kopeikin, Sergei & Fomalont, Edward (2006). "Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment". Foundations of Physics. 36 (8): 1244–1285. S2CID 53514468.
- Carlip, Steven (2004). "Model-Dependence of Shapiro Time Delay and the "Speed of Gravity/Speed of Light" Controversy". Class. Quantum Grav. 21 (15): 3803–3812. S2CID 250863503.
- Kopeikin, Sergei M. (2005). "Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy". Class. Quantum Grav. 22 (23): 5181–5186. S2CID 17222421.
- Pascual-Sánchez, J.-F. (2004). "Speed of gravity and gravitomagnetism". Int. J. Mod. Phys. D. 13 (10): 2345–2350. S2CID 2402650.
- Kopeikin, Sergei (2006). "Gravitomagnetism and the speed of gravity". Int. J. Mod. Phys. D. 15 (3): 305–320. S2CID 18790529.
- Samuel, Stuart (2004). "On the Speed of Gravity and the Jupiter/Quasar Measurement". Int. J. Mod. Phys. D. 13 (9): 1753–1770. S2CID 2908984.
- Kopeikin, Sergei (2006). "Comments on the paper by S. Samuel "On the speed of gravity and the Jupiter/Quasar measurement"". Int. J. Mod. Phys. D. 15 (2): 273–288. .
- Kopeikin, Sergei & Fomalont, Edward (2007). "Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments". General Relativity and Gravitation. 39 (10): 1583–1624. S2CID 15412146.
- Kopeikin, Sergei & Fomalont, Edward (2008). "Radio interferometric tests of general relativity". Proceedings of the International Astronomical Union. 3 (S248, A Giant Step: From Milli- to Micro-arcsecond Astrometry): 383–386. S2CID 53363773.
- Zhu, Yin (2011). "Measurement of the Speed of Gravity". Chinese Physics Letters. 28 (7): 070401. S2CID 250811249.
External links
- Does Gravity Travel at the Speed of Light? in The Physics FAQ (also here).
- Measuring the Speed of Gravity at MathPages
- Hazel Muir, First speed of gravity measurement revealed, a New Scientist article on Kopeikin's original announcement.
- Clifford M. Will, Has the Speed of Gravity Been Measured?.
- Kevin Carlson, MU physicist defends Einstein's theory and 'speed of gravity' measurement.