# The speed of gravity?

Sorry for the layman question, but it's not my field.

Suppose this thought experiment is performed. Light takes 8 minutes to go from the surface of the Sun to Earth. Imagine the Sun is suddenly removed. Clearly, for the remaining 8 minutes, we won't see any difference.

However, I am wondering about the gravitational effect of the Sun. If the propagation of the gravitational force travels with the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent.

What is the state of the art of research for this thought experiment? I am pretty sure this is knowledge that can be inferred from observation.

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I thought this had been asked before, but I did some searching and the closest I found was physics.stackexchange.com/q/703. Since that question is so vague, I'm fine leaving this one open. – David Zaslavsky Feb 18 '11 at 23:30
Gravity is due to a distortion in spacetime, and, perturbations of the gravitational field do travel at the speed of light. There is no contradiction between these two aspects as your 3rd para seems to suggest. – user346 Feb 19 '11 at 15:55

## 6 Answers

Since general relativity is a local theory just like any good classical field theory, the Earth will respond to the local curvature which can change only once the information about the disappearance of the Sun has been communicated to the Earth's position (through the propagation of gravitational waves).

So yes, the Earth would continue to orbit what should've been the position of the Sun for 8 minutes before flying off tangentially. But I should add that such a disappearance of mass is unphysical anyway since you can't have mass-energy just poofing away or even disappearing and instantaneously appearing somewhere else. (In the second case, mass-energy would be conserved only in the frame of reference in which the disappearance and appearance are simultaneous - this is all a consequence of GR being a classical field theory).

A more realistic situation would be some mass configuration shifting its shape non-spherically in which case the orbits of satellites would be perturbed but only once there has been enough time for gravitational waves to reach the satellite.

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Gravitational influences do propagate at the speed of light, not instantaneously.

The question of what would happen if the Sun instantly disappeared is actually a funny one in general relativity. The equations of general relativity imply as a mathematical consequence that energy must be locally conserved. Therefore, there is no valid solution to the equations that describes the Sun suddenly disappearing (since that scenario violates local energy conservation).

(A similar statement holds in electromagnetism, by the way: charge conservation is a logical consequence of Maxwell's equations, so if someone asks you what the electric field does when a charge suddenly disappears, there is no correct answer.)

But you can sensibly ask what would happen if the Sun suddenly changed its mass distribution -- if it exploded, say, sending its mass in different directions at high speeds. The answer is that the Earth's orbit wouldn't change for 8 minutes.

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Beat you to it with the same answer :) – dbrane Feb 18 '11 at 22:18
Uh, I don't like this discussion of energy conservation. There is no such implication made by GR. And there is also no problem in using discontinuous stress-energy tensor which would in turn imply discontinuity in curvature (in the very same way as happens at characteristic surfaces of gravitational waves). And the very same stuff can be said about EM. – Marek Feb 18 '11 at 22:29
I'm talking about local energy conservation, $T^{\mu\nu}_{;\nu}=0$. It follows from the Einstein equation as an identity. There's no solution corresponding to the Sun disappearing, because the Sun's disappearance would violate it. – Ted Bunn Feb 18 '11 at 23:09
Oh, and @Marek, if you really think there's no problem finding solutions to the field equations with sources that don't satisfy the conservation laws, then tell me this: what is a solution to Maxwell's equations corresponding to a point charge $q$ at the origin, which abruptly disappears at $t=0$ -- that is, $\rho({\bf r},t)=q\delta({\bf r})θ(−t)$, ${\bf J}=0$? – Ted Bunn Feb 19 '11 at 16:24
A followup: I agree that it would be better to insert "locally" before "conserved" in my answer. I'm aware of the problems with global energy conservation in GR. I'm making that edit now. – Ted Bunn Feb 19 '11 at 17:23
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All observations are consistent with standard GR so far, but I don't think the speed of gravity, in particular, has ever been measured.

Experimental measurements of the speed of gravity was quite a controversy a few years ago when a paper came out claiming that the speed of gravity was very close to $c$ as measured by the Shapiro delay. To see papers on the subject google shapiro+speed+gravity:
http://www.google.com/search?q=speed+of+gravity+site%3Aarxiv.org+shapiro

Clifford Will is an expert in the area and says that there was no measurement. He has a website on the subject that gives links to the various papers:
http://wugrav.wustl.edu/people/CMW/SpeedofGravity.html

My guess is that the Will side won. But academia means "never having to admit you were wrong". Here's a pair of dueling papers on the subject, published in the same journal at the same time (that date to after Clifford Will last updated his page above):

Class.Quant.Grav. 22 (2005) 5181-5186, Sergei M. Kopeikin, Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy'
http://arxiv.org/abs/gr-qc/0510048

Class.Quant.Grav.22 (2005) 5187-5190, S. Carlip, Reply to Comment on Model-dependence of Shapiro time delay and the`speed of gravity/speed of light' controversy''
http://arxiv.org/abs/gr-qc/0510056

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 This is a good answer, but may give the incorrect impression that nothing at all is known empirically about this, only theoretically. Gravitational waves have never been detected directly, but the loss of energy from the Hulse-Taylor binary pulsar has been checked to high precision against GR's predictions of the power emitted in the form of gravitational waves. Therefore it is extremely unlikely that there is anything seriously wrong with general relativity's description of gravitational waves. – Ben Crowell May 18 at 18:48

Your question was first asked by Laplace. The following is from the Wikipedia article on "The speed of gravity"

"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.[4] 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. In fact, as is now known, it may be considered to be infinite, since as a static influence, it is instantaneous at distance, when seen by observers at constant transverse velocity.

In a field equation consistent with special relativity (i.e., a Lortentz invariant equation), the attraction between static charges 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 at a steady speed, the effect on the orbit is order v2/c2, and the effect preserves energy and angular momentum, so that, and orbits do not decay. The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge."

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And they used to think that gravity was the longitudinal wave to go with the transverse wave of electromagnetism (i.e. as in the P and S waves of seismology). – Carl Brannen Feb 22 '11 at 3:53

the fact that distortion travels 'as soon' as a mass is removed or not is not implied in any way by gravity being due to a distortion of spacetime. In fact distortions of spacetime are as limited to travel to the speed of light as any other physical influence.

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I feel like this question is being asked wrong and/or it is being interpreted wrong for what you're actually asking. It is understood that the propagation of anything cannot exceed 'c', but I don't think propagation is necessary to answer the question, or to create a valid thought experiment. First off, gravity is not fully understood by any mainstream science and a lot of the paradoxial problems inherent within our current accepted understanding tend to leave many scratching their heads. I'm no physicist, or scientist for that matter, but this has been on my mind for a very long time and I decided to throw it out here and allow you all to tear it to pieces or at least lead me in a better direction lol.

The question, how would the sudden disappearance of the sun affect gravitation, and would it follow 'c' or happen instantaneously?

My answer is Both.

Lets look at gravity in a couple of different ways to explain why I believe this. I see a lot of references to gravity as a wave...I assume this is because of the apparent "propagation" that occurs within a gravitationally active region. I accept that any physical change made by object A that "could" effect object B must travel to object B no faster than 'c'. So yeah, sun goes poof, we wait the 8 minutes before gravity is released. Here's where I go left.....That "wave" isn't necessary to get information from A to B instantly. Look at it backwards, mass is the force (cause), gravity is the result of that force (effect). I don't view gravity as we observe it as a force but the released energy of another force.....displacement. The region that would see a net change if the sun went poof would be space-time. Look at it in a simplified way, I stand at one end of a field and you at the other with 2 cans and a string, pull it taunt and yell into it.....the vibrations travel down the string to my can at the speed of sound and I can hear it. For the sake of this example, lets assume the speed of sound represents 'c', and the sound wave represents gravity....the string would represent space-time. Everything works just as you would expect it. Now, i would ask you to make a constant humming noise into the can. Several milliseconds later, I begin to hear it. Suddenly, you pass out from humming instead of breathing and drop the can. Again, I must wait several milliseconds before I realize something has happened and you've stopped. What I failed to realize was that I already had that information. As the can left your hand (the pull of your gravity), the gravitational constant in local space-time was changed (the tension on the string went slack). Does this not happen instantly? Granted, I know of no device that can measure the gravitational constant in a specific region of space-time but is this not a method of reading the net effect of a massive and sudden gravitational change? What if I lay at the bottom of a pool with an air hose and blow bubbles? The bubbles travel to the surface at (hypothetical) 'c' but the bubbles themselves displace the water causing it to slightly rise in apparent volume. Does this increase in net volume not happen the instant the bubble displaces the water?

Bottom line, I agree that if the sun vanished, it would take 8 minutes for a change in its gravitational influence on the Earth to be observed, but I believe that the net effect on the region of space-time between the earth and sun could be observed instantly using the proper equipment to detect those changes.

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This looks more like a separate (though related) question than an answer. I suggest you make it into a question. – Wouter Mar 3 at 11:07