Speed of gravity

In the aberration of gravity is an effect that would occur if one combines the Newtonian law of gravitation under certain conditions with a finite speed of gravity. This problem was finally solved by the combination of the gravitational law with the at that time developing field theories. Endpoint of this development was finally up today accepted general theory of relativity by Albert Einstein.

Laplace and the Newtonian gravitational

After the Newtonian law of gravitation may spread instantaneously changes in the gravitational field, ie, without loss of time. Pierre- Simon Laplace in 1800 was now trying to combine the Newtonian model with a finite speed of propagation of gravity by defining the gravitational field as a kind of radiation field or fluid. Changes in motion of the central mass would be here in the form of a wave of interest inform, resulting influences on the movement of the heavenly bodies of the order of v / c ( where v is the velocity of the body and c is the speed of the wave). The result is here so a similar relationship as the aberration of starlight.

The consequences can be best explained by an example: Consider the earth and the sun and we assume a propagation speed of gravity, which corresponds to the speed of light. Then would act on the earth a force in the direction of the place where the sun was 8 minutes ago, and the sun seemed a force in the direction of the place where the earth was 8 minutes ago. This delay would mean that the distance between Earth and the sun constantly magnify, that is, the orbits would be unstable. The same would be expected for the Earth and Moon.

However, this contradicts the observation: For the moon, for example,, the distance each year only about 4 cm and this can by the tidal forces between the Earth and Moon (loss of rotational energy, angular momentum loss ) are explained. The stability of the orbit can therefore only reach the Newtonian model, by assuming a higher propagation speed of the gravity. Laplace was this with 7.106 c, where c is the speed of light. This high speed of gravitational interaction, which would be necessary in the Newtonian gravitation, is an attack point that some critics in the 19th century generally against all theories with finite speed of propagation of gravity - such as Le Sage gravity or gravity observations on electric base - used.

Electrostatic fields

Aberration therefore occurs in all fields radiating from their components and are therefore subject to a certain direction, such as a radiation field to a light source. It does not occur in static fields, such as electrostatic fields, since such a field (as viewed in the rest frame of the source) is always stationary and does not spread if it is built once, so the attraction is always directed exactly to the position of the field source. Deviations occur only when accelerations are no longer negligible, which in turn leads to the emission of electromagnetic waves. The effects of moving charges in accordance with Maxwell's electrodynamics are determined by the Liénard -Wiechert potential.

First attempts to use an electrostatic field also for gravitation, were made at the end of the 19th century, with the best in the field of electrodynamics basic laws of Wilhelm Eduard Weber, Carl Friedrich Gauss, Bernhard Riemann were combined with the law of gravity. These models were used to explain the perihelion of Mercury above all, what a statement by the law of gravitation Newton's escaped - but most of these models did not provide exact values ​​. Only Maurice Lévy was in 1890 by a combination of Weber ' and Riemannian fundamental laws derive correct values. In a similar vein the trial of Paul Gerber, who succeeded in 1898, derive from a theory in which the gravitational potential propagates at a finite speed, the correct value for the perihelion advance of Mercury took aim. From the obtained formula calculated Gerber a propagation speed of the gravitational potential of about 305,000 km / s, which is practically the speed of light. Gerber's derivation of the corresponding equation (this equation formally with those of general relativity matches ), but has been classified as faulty and therefore not considered by many ( inter alia by Einstein) a viable approach for a theory of gravity into account. Also follows from his theory by a factor of 3/2 to a high value for the deflection of light in a gravitational field. With the replacement of Weber ' by the Maxwellian electrodynamics these experiments were not pursued further and are outdated.

The first attempt to explain on the basis of Maxwell's electrodynamics, gravitation comes from Hendrik Lorentz ( 1900). He was ( as before him Mossotti and publican ) based on the idea that the attraction of unlike electric charges of two more by a fraction is than the repulsion of two charges of the same name. The result would be nothing else than the universal gravitation. Lorentz was able to show that this theory is not affected by the Laplace criticism and only influences the order v ² / c ² occur, but he received for the perihelion advance a much too low. Lorentz summed up his efforts as follows:

The particular form of these terms may possibly be modified. But what has been said so far is enough to show that gravity can be attributed to actions which propagate faster than the speed of light.

Lorentz - covariant models

Henri Poincaré introduced in 1904 states that it must be ensured to maintain the principle of relativity, that no signal is faster than the speed of light, otherwise the synchronization rule for light signals and thus the local time ( relativity of simultaneity ) within the framework of special relativity and the Lorentz between ether theory would not. apply However, he could show in 1905 that no train instabilities in the sense of Laplace, may occur in a theory which takes into account the Lorentz transformation.

This can be understood by analogy to electrostatic fields: As has been shown above, there are in such fields ( betrachtetet in the rest frame of the Sun) no aberration. It can of course be no transformation in an inertial change something in the example rests the earth and the sun is moving. In such a system, although the description of the field of the sun would be considerably more complicated - it will perform a series of speed- dependent additional terms - but the result must be the same as in the rest frame of the Sun and the additional terms will cancel each other out. Because only the coordinates by a transformation of the physical events to be changed, the occurrence of events which itself is not adversely affected. Poincaré wrote:

Laplace showed namely that the spread occurs either instantaneously or much faster than that of light. However, Laplace investigated the hypothesis of finite propagation speed ceteris non mutatis; in contrast, are here this hypothesis many other added and it may be that takes place between them a more or less complete compensation. The application of the Lorentz transformation has already shown us many such examples.

Similar models were later also designed by Hermann Minkowski (1907 ) and Arnold Sommerfeld ( 1910). The research in this direction, however, were terminated by the development of general relativity.

General Theory of Relativity

The above hypotheses were eventually superseded by the general theory of relativity much further. The propagation velocity of the gravity is the velocity of light, too. It occurs no aberration in the sense of Laplace, as shown in the above field theories by units of the gravitational field of moving bodies, the effect is canceled almost exactly. The deviation of real planetary orbits of pure Keplerian orbits may instead be understood in relation to the emission of gravitational waves, which causes a gradual decrease of the orbital radii. She is a direct consequence of angular momentum and energy conservation. These must be met, since the effect is invariant under Lorentz transformation. General relativity theory thus explains not only the stability of the two-body system and the perihelion advance of Mercury, but also provides the correct value for the deflection of light in a gravitational field.

Regarding the measurement of the gravitational velocity, is set mainly as an indirect method to the detection of gravitational waves. Such evidence was actually by Russell Hulse and Joseph Taylor by observations of the double pulsar PSR 1913 16, whose orbit is reduced by a factor equal to the energy loss by emission of gravitational waves.

Published in 2002 Sergei Kopeikin and Edward Fomalont a work in which they claimed to have the speed of gravity measured indirectly by means of VLBI, the result between 0.8 and 1.2 c lie, so well in accordance with the general theory of relativity. However, this was rejected by other experts such as Clifford Will and Steve Carlip, who think that in this experiment, not the gravitational velocity, but only the speed of light was measured. An agreement could not yet be achieved.

Swell

• Gravity