# Speed of gravity

The speed of gravity is the speed at which changes in the location of an object propagate their gravitational effects to all other objects in the Universe.

## Newtonian mechanics

Isaac Newton's mechanical systems included the concept of a force that operated between two objects, gravity. The quantity of force was dependent on the masses of the two objects, with more massive objects exerting more force. This led to a problem: it seemed that each object had to "know" about the other in order to exert the proper amount of force on it. This troubled Newton, who commented that he made no claims to how it could work.

Given two bodies attracting each other, the question then arises as to the speed of propagation of the force itself. Newton demonstrated that unless the force was instantaneous, relative motion would lead to the non-conservation of angular momentum. This he could observe as not being true, in fact the conservation of momentum was one of the observations that led to his theory of gravitation in the first place. He therefore concluded that gravity was instantaneous.

## Field theories

Michael Faraday's work on electromagnetism in the mid-1800s provided a new framework for understanding electromagnetic forces. In these "field theories" the objects in question do not act on each other, but on space itself. Other objects react to that field, not to the distant object itself. There is no requirement for one object to have any "knowledge" of the other. With this simple change, many of the philosophical problems of Newton's seminal work simply disappeared while the answers stayed the same, and in many cases the answers were easier to calculate.

By viewing gravity as being transmitted by a field rather than a force, it is possible for gravity to be transmitted at a finite speed without running into the problems that Newton sees. If gravity is transmitted by a field, a moving object will cause the field potentials to be non-circular. Hence by using a delayed field rather than a delayed force, one can show that the force will point to where an object is currently rather than where it was in the past. Gravity is still traveling at a finite speed because a sudden change in the direction of an object will not be noticed by the object it is pulling without a delay.

A similar effect occurs in electromagnetic fields. This view has some major implications for how physicists view the world. Until the mid-19th century, the standard view among physicists is that forces are the fundamental entity and fields are merely mathematical shorthand to describe the behavior of forces. Since the late 19th century, physicists have gradually come to view fields as the more fundamental entity and forces merely manifestations of the behavior of fields. The phenomenon in which a delayed force theory will lead to wrong answers, but a delayed field theory will lead to right ones, is one reason why.

## General Relativity

The belief that fields rather than forces were the fundamental entity was one of the main motivating factors that led Albert Einstein to develop his theory of general relativity in the early 20th century to replace Newtonian gravity which was widely considered defective because it relied on the notion of instantaneous forces to transmit gravity rather than fields. In general relativity (GR), the field is elevated to the only real concern. The gravitational field is equated with the curvature of space-time, and propagations (including gravity waves) can be shown, according to this theory, to travel at a single speed, cg.

This finite speed may at first seem to lead to exactly the same sorts of problems 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 classical delayed potential theory does not. However, Tom Van Flandern has made a name for himself by insisting that this proves general relativity incorrect. Other physicists who have interacted with him argue that the objection he presents was resolved in the 19th century.

Measurements of various sorts, notably of orbiting neutron stars, have shown that cg must be very close to c, the speed of light.

## Experimental measurement

In 1999 a Russian researcher from Izhevsk Yuri Ivanov confirmed the results of Roland Eötvös experiments, according to which a copper ball should fall with an acceleration of 0,000000001 fraction faster than a water drop.

Ivanov has discovered a phenomenon which he called shady gravitational effect (Russian: теневой гравитационный эффект): the gravity of the Sun passing through the more dense envelopes of the Earth core is partially enfeebled and forms on the opposite side of the planet a sort of gravitational shadow. In the winter solstice of 2002 a torsion balance has reacted to the change of the attracting force of the Sun eight minutes before the midnight. That meaned that a speed of diffusion of the gravitation is practically momentary (according to the calculations of Laplace this speed should exceed the speed of light at least in six million times).

In September 2002, Sergei Kopeikin made an indirect experimental measurement of the speed of gravity, using Ed Fomalont's data from a transit of Jupiter across the line-of-sight of a bright radio source. The speed of gravity, presented in January 2003, was found to be somewhere in the range between 0.8 and 1.2 times the speed of light, which is consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.

Some physicists have criticised the conclusions drawn from this experiment on the grounds that, as it was structured, the experiment was incapable of finding any results other than agreement with the speed of light. This criticism originates from the belief in electromagetic field origin of the fundamental speed c so that according to those physicists the Einstein equations must depend on the physical speed of light which explains why gravity always propagate in that theory with the speed of light. Alternative point of view is that the Einstein equations describe the origin and evolution of the space-time curvature and gravitational waves which are conceptually independent of the electromagnetic field and, hence, the fundamental speed c in the Einstein equations can not be interpreted as a physical speed of light despite that it must have the same numerical value as the speed of light in vacuum if the general relativity is correct. Perhaps, the best illustrative way to distinguish two speeds is to denote the speed of gravity in the Einstein equations as cg and the speed of light in Maxwell's equations as c. Kopeikin-Fomalont experiment observed the bending of quasar's light caused by time-dependent gravitational field of Jupiter and measured the ratio c/cg. This observation shows that this ratio is unity with the precision 20%.

On the other hand, Tom Van Flandern at the U.S. Army's Research Lab at the University of Maryland, calculates the speed of gravity as ≥ 2x1010 c (that is, twenty trillion times the speed of light). If true, this could explain why gravity appears to be an instantaneous (ie, of infinite speed), rather than a finite force. Van Flandern's theories are controversial and not well accepted among physicists.

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