Speed of gravity
Encyclopedia
In the context of classical theories of gravitation
, the speed of gravity is the speed
at which changes in a gravitational field
propagate. This is the speed at which a change in the distribution of energy
and momentum
of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In a more physically correct sense, the "speed of gravity" refers to the speed of a gravitational wave
.
The speed of gravitational waves in the general theory of relativity is equal to the speed of light
in vacuum, c. Within the theory of special relativity
, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any massless particle. Such particles include the gluon
(carrier of the strong force), the photon
s that light waves consist of, and the theoretical graviton
s which make up the associated field particles of gravity (a theory of the graviton requires a theory of quantum gravity
, however).
The speed of physical changes in a gravitational or electromagnetic field should not be confused for "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field, because of relativistic considerations, are 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 direct 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.
's formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Urbain Le Verrier determined in 1859 that the elliptical orbit of Mercury precesses at a significantly different rate than is predicted by Newtonian theory.
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. 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 Lorentz invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity (this retardation actually does happen with the optical position of the Sun, and is called annual solar aberration
). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. The pull of gravity (if it behaved like a wave, such as light) would then be always displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount v/c compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence, it is instantaneous at distance, when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is almost infinite.
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.
, 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. So those hypotheses were rejected.
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 305 000 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.
tried to explain gravity on the basis of his ether theory
and the Maxwell equations. After proposing (and rejecting) a Le Sage type model
, he assumed like Ottaviano Fabrizio Mossotti and Johann Karl Friedrich Zöllner
that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton, in which it was shown by Pierre Simon Laplace that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order v2/c2 arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote:
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.
(based on synchronization by light signals) and the principle of relativity
. He wrote:
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:
Similar models were also proposed by Hermann Minkowski
(1907) and Arnold Sommerfeld
(1910). However, those attempts were quickly superseded by Einstein's theory of general relativity.
, the gravitational potential is identified with the metric tensor
and the gravitational force field with the Christoffel symbols
of the spacetime
manifold
. Tidal gravitational field is associated with the curvature of spacetime. General relativity predicts that gravitational radiation should exist and propagate as a wave at the speed of light. A slowly evolving and weak gravitational field will produce, according to general relativity
, similar effects to those we might expect from Newtonian gravitation. In particular, the gravitoelectric
(static and continuous) component of a gravitational field should not be confused with a possible additional gravitomagnetic
component (gravitational radiation); see Petrov classification
. Since the gravitoelectric field
is a static field, like the static electric field, it cannot be used for superluminal transmission of quantized (discrete) information, i.e., it could not constitute a well-ordered series of impulses carrying a well-defined meaning (this is the same for gravity and electromagnetism). If one of two gravitoelectrically
interacting particles were to suddenly be displaced (accelerated) from its position, the other particle would not feel the change due to the acceleration, until a delay corresponding with the speed of light. Such accelerations resulting from the change in quadrupole moment of star systems, like the Hulse-Taylor binary have been observed to carry off a great deal of energy (almost 2% of the energy of our own Sun's output) as gravitational waves. However, such waves would theoretically travel at the speed of light.
However, in the case of two gravitoelectrically
interacting particle ensembles, such as two planets or stars moving at constant velocity with respect to each other, each body feels a force which is directed at the instantaneous position of the other body, without a speed-of-light delay. The principle of Lorentz invariance demands symmetry between what is seen by body moving in static field, and what is seen by a moving body that is the source of such a static field. Thus, since a moving body does not see aberration
in a static field emanating from a "motionless body" (at rest), Lorentz invariance requires that in the reference frame
of the previously moving body, the (now moving) body that is the source of the static field must still show no retardation or aberration of its field lines, at distance. Thus, moving charged bodies (including bodies that are sources of static gravitational fields) exhibit static field lines which do not bend with distance, and do not show any speed of light delay effects, as seen from bodies moving with regard to them.
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.
of gravity that Newton was originally concerned with, because there is no aberration in static field effects. Because the acceleration of the Earth with regard to the Sun is small (meaning, to a good approximation, the two bodies can be regarded as traveling in straight lines past each other with unchanging velocity), the orbital results calculated by general relativity are the same as those of Newtonian gravity with instantaneous action at a distance, because they are modelled by the behavior of a static field with constant-velocity relative motion, and no aberration for the forces involved. Although the calculations are considerably more complicated, one can show that a static field in general relativity does not suffer from aberration problems as seen by an unaccelerated observer (or a weakly accelerated observer, such as the Earth). Analogously, the "static term" in the electromagnetic Liénard–Wiechert potential theory of the fields from a moving charge, does not suffer from either aberration or positional-retardation. (Only the term corresponding to acceleration and electromagnetic emission in the Liénard–Wiechert potential shows a direction toward the time-retarded position of the emitter). 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.
s) can be calculated from observations of the orbital decay rate of binary pulsar
s PSR 1913+16
(the Hulse-Taylor binary system noted above) and PSR B1534+12. The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%. However, according to PPN formalism setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed cannot be infinite.
In September 2002, Sergei Kopeikin
and Edward Fomalont
announced 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 the 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 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 However, Kopeikin and Fomalont continue to vigorously argue their case and the means of presenting their result at the press-conference of AAS that was offered after the peer review of the results of the Jovian experiment had been done by the experts of the AAS scientific organizing committee. In later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time null cone in two – one for gravity and another one for light, the authors claimed that Asada's claim was theoretically unsound. The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors but was never properly employed by Asada and/or the other critics.
Stuart Samuel also suggested that the experiment did not actually measure the speed of gravity but the speed of light . A response by Kopeikin and others challenges this opinion. .
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. The most comprehensive review of the definition of the speed of gravity and the way of its measurement with high-precision astrometric and other techniques has been provided in the textbook .
Classical theories of gravitation
The current Gold Standard Theory of Gravitation is the general theory of relativity. This is a classical, relativistic field theory of gravitation...
, the speed of gravity is the speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
at which changes in a gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
propagate. This is the speed at which a change in the distribution of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
and momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In a more physically correct sense, the "speed of gravity" refers to the speed of a gravitational wave
Gravitational wave
In physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...
.
The speed of gravitational waves in the general theory of relativity is equal to the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum, c. Within the theory of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any massless particle. Such particles include the gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
(carrier of the strong force), the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s that light waves consist of, and the theoretical graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
s which make up the associated field particles of gravity (a theory of the graviton requires a theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
, however).
The speed of physical changes in a gravitational or electromagnetic field should not be confused for "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field, because of relativistic considerations, are 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 direct 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
Isaac NewtonIsaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
's formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Urbain Le Verrier determined in 1859 that the elliptical orbit of Mercury precesses at a significantly different rate than is predicted by Newtonian theory.
Laplace
The first attempt to combine a finite gravitational speed with Newton's theory was made by LaplacePierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
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. 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
Mechanical explanations of gravitation
Mechanical explanations of gravitation are attempts to explain the action of gravity by aid of basic mechanical processes, such as pressure forces caused by pushes, and without the use of any action at a distance. These theories were developed from the 16th until the 19th century in connection...
.
From a modern point of view, Laplace's analysis is incorrect. Not knowing about Lorentz invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity (this retardation actually does happen with the optical position of the Sun, and is called annual solar aberration
Aberration
An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system...
). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. The pull of gravity (if it behaved like a wave, such as light) would then be always displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount v/c compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence, it is instantaneous at distance, when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is almost infinite.
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.
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 WeberWilhelm Eduard Weber
Wilhelm Eduard Weber was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.-Early years:...
, Carl Friedrich Gauß, Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
and James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
. 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
Maurice Lévy
Maurice Lévy was a French engineer and member of the Institut de France.Lévy was born in Ribeauvillé in Alsace. Educated at the École Polytechnique, where he was a student of Adhémar Jean Claude Barré de Saint-Venant, and the École des Ponts et Chaussées, he became an engineer in 1863...
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. So those hypotheses were rejected.
However, a more important variation of those attempts was the theory of Paul Gerber
Paul Gerber
Paul Gerber was a German physicist. He studied in Berlin from 1872-1875. In 1877 he became a teacher at the Realgymnasium in Stargard in Pommern...
, 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 305 000 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.
Lorentz
In 1900 Hendrik LorentzHendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
tried to explain gravity on the basis of his ether theory
Lorentz ether theory
What is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
and the Maxwell equations. After proposing (and rejecting) a Le Sage type model
Le Sage's theory of gravitation
Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles impacting...
, he assumed like Ottaviano Fabrizio Mossotti and Johann Karl Friedrich Zöllner
Johann Karl Friedrich Zöllner
Johann Karl Friedrich Zöllner was a German astrophysicist who studied optical illusions. He invented the Zöllner illusion where lines that are parallel appear diagonal. The lunar Zöllner crater is named in his honor...
that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton, in which it was shown by Pierre Simon Laplace that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order v2/c2 arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote:
In 1908 Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
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.
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 timeRelativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...
(based on synchronization by light signals) and the principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
. He wrote:
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
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
. He wrote:
Similar models were also proposed by Hermann Minkowski
Hermann Minkowski
Hermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
(1907) and Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
(1910). However, those attempts were quickly superseded by Einstein's theory of general relativity.
Background
In general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the gravitational potential is identified with the metric tensor
Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...
and the gravitational force field with the Christoffel symbols
Christoffel symbols
In mathematics and physics, the Christoffel symbols, named for Elwin Bruno Christoffel , are numerical arrays of real numbers that describe, in coordinates, the effects of parallel transport in curved surfaces and, more generally, manifolds. As such, they are coordinate-space expressions for the...
of the spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
. Tidal gravitational field is associated with the curvature of spacetime. General relativity predicts that gravitational radiation should exist and propagate as a wave at the speed of light. A slowly evolving and weak gravitational field will produce, according to general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, similar effects to those we might expect from Newtonian gravitation. In particular, the gravitoelectric
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
(static and continuous) component of a gravitational field should not be confused with a possible additional gravitomagnetic
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
component (gravitational radiation); see Petrov classification
Petrov classification
In differential geometry and theoretical physics, the Petrov classification describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold....
. Since the gravitoelectric field
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
is a static field, like the static electric field, it cannot be used for superluminal transmission of quantized (discrete) information, i.e., it could not constitute a well-ordered series of impulses carrying a well-defined meaning (this is the same for gravity and electromagnetism). If one of two gravitoelectrically
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
interacting particles were to suddenly be displaced (accelerated) from its position, the other particle would not feel the change due to the acceleration, until a delay corresponding with the speed of light. Such accelerations resulting from the change in quadrupole moment of star systems, like the Hulse-Taylor binary have been observed to carry off a great deal of energy (almost 2% of the energy of our own Sun's output) as gravitational waves. However, such waves would theoretically travel at the speed of light.
However, in the case of two gravitoelectrically
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
interacting particle ensembles, such as two planets or stars moving at constant velocity with respect to each other, each body feels a force which is directed at the instantaneous position of the other body, without a speed-of-light delay. The principle of Lorentz invariance demands symmetry between what is seen by body moving in static field, and what is seen by a moving body that is the source of such a static field. Thus, since a moving body does not see aberration
Aberration
An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system...
in a static field emanating from a "motionless body" (at rest), Lorentz invariance requires that in the reference frame
Reference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
of the previously moving body, the (now moving) body that is the source of the static field must still show no retardation or aberration of its field lines, at distance. Thus, moving charged bodies (including bodies that are sources of static gravitational fields) exhibit static field lines which do not bend with distance, and do not show any speed of light delay effects, as seen from bodies moving with regard to them.
In other words, since the gravitoelectric field
Gravitomagnetism
Gravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
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
Reference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
in which the distant charged body is now at rest.
Aberration of field direction in general relativity, for a weakly accelerated observer
The finite speed of gravitational interaction in general relativity does not to lead the sorts of problems with the aberrationAberration
An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system...
of gravity that Newton was originally concerned with, because there is no aberration in static field effects. Because the acceleration of the Earth with regard to the Sun is small (meaning, to a good approximation, the two bodies can be regarded as traveling in straight lines past each other with unchanging velocity), the orbital results calculated by general relativity are the same as those of Newtonian gravity with instantaneous action at a distance, because they are modelled by the behavior of a static field with constant-velocity relative motion, and no aberration for the forces involved. Although the calculations are considerably more complicated, one can show that a static field in general relativity does not suffer from aberration problems as seen by an unaccelerated observer (or a weakly accelerated observer, such as the Earth). Analogously, the "static term" in the electromagnetic Liénard–Wiechert potential theory of the fields from a moving charge, does not suffer from either aberration or positional-retardation. (Only the term corresponding to acceleration and electromagnetic emission in the Liénard–Wiechert potential shows a direction toward the time-retarded position of the emitter). 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.
Possible experimental measurements
The speed of gravity (more correctly, the speed of gravitational waveGravitational wave
In physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...
s) can be calculated from observations of the orbital decay rate of binary pulsar
Binary pulsar
A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. Binary pulsars are one of the few objects which allow physicists to test general relativity in the case of a strong gravitational field...
s PSR 1913+16
PSR 1913+16
PSR B1913+16 is a pulsar which together with another neutron star is in orbit around a common center of mass, thus forming a binary star system. In 1974 it was discovered by Russell Alan Hulse and Joseph Hooton Taylor, Jr., of Princeton University...
(the Hulse-Taylor binary system noted above) and PSR B1534+12. The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%. However, according to PPN formalism setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed cannot be infinite.
In September 2002, Sergei Kopeikin
Sergei Kopeikin
Sergei Kopeikin is a USSR-born theoretical physicist presently living and working in the United States, where he holds the position of Professor of Physics at the University of Missouri in Columbia, Missouri. He specializes in the theoretical and experimental study of gravity and general relativity...
and Edward Fomalont
Edward Fomalont
Edward Fomalont is an American scientist working at the National Radio Astronomy Observatory. He specializes in radio galaxies, X-ray binary systems, astrometry, and general relativity...
announced that they had made an indirect measurement of the speed of gravity, using their data from VLBI measurement of the retarded position
Retarded position
Einstein's equations admit gravity wave-like solutions. In the case of a moving point-like mass and in the linearized limit of a weak-gravity approximation these solutions of the Einstein equations are known as the Lienard-Wiechert gravitational potentials...
of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
on its orbit during Jupiter's transit
Astronomical transit
The term transit or astronomical transit has three meanings in astronomy:* A transit is the astronomical event that occurs when one celestial body appears to move across the face of another celestial body, hiding a small part of it, as seen by an observer at some particular vantage point...
across the line-of-sight of the bright radio source quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
QSO J0842+1835
QSO J0842+1835
QSO J0842+1835 is a quasar that was used to measure the speed of gravity in VLBI experiment conducted by Edward Fomalont and Sergei Kopeikin in September 2002....
. 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
Clifford Martin Will
Clifford Martin Will is a Canadian born mathematical physicist who is well known for his contributions to the theory of general relativity....
and Steve Carlip
Steve Carlip
Steve Carlip is an American professor of physics at the University of California, Davis. He is known for his work on -dimensional quantum gravity, the quantum gravitational basis of black hole thermodynamics, and causal dynamical triangulations. Carlip graduated from Harvard University with a...
, 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 However, Kopeikin and Fomalont continue to vigorously argue their case and the means of presenting their result at the press-conference of AAS that was offered after the peer review of the results of the Jovian experiment had been done by the experts of the AAS scientific organizing committee. In later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time null cone in two – one for gravity and another one for light, the authors claimed that Asada's claim was theoretically unsound. The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors but was never properly employed by Asada and/or the other critics.
Stuart Samuel also suggested that the experiment did not actually measure the speed of gravity but the speed of light . A response by Kopeikin and others challenges this opinion. .
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. The most comprehensive review of the definition of the speed of gravity and the way of its measurement with high-precision astrometric and other techniques has been provided in the textbook .
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?.