# Gravitational Waves and Speed of Light

Can you explain for me what part of general relativity says that gravity must go outward from the body at the speed of light, rather than instantly?

I realize that Einstein believed nothing could go faster than the speed of light, but is there evidence that this must be so in the case of gravity? I wonder, if there is no graviton, that there may be no reason to think that massive bodies don't curve space-time around them continuously. Consider, for example, how Einstein refuted entanglement, but was found to be incorrect.

(In this, I know there is one case of indirect evidence of gravitational waves, but one example does not give strong evidence, and there could be unforeseen problems in explaining the observational results.)

Again, to sum, what exactly is it in general relativity that requires gravity to perpetuate at the speed of light. ("Because nothing can travel faster than the speed of light." is not an acceptable answer.)

Can you explain for me what part of general relativity says that gravity must go outward from the body at the speed of light, rather than instantly?

Without reproducing Einstein's equations here, let's just say that Einstein developed wave equations whose solutions predict gravitational waves traveling at the same speed as light. He did not arbitrarily insert the speed of gravitational waves out of belief that they should travel at light speed. Just like Maxwell did not arbitrarily insert c into his wave equations that predicted light should travel at the speed, c.

Staff Emeritus
Again, to sum, what exactly is it in general relativity that requires gravity to perpetuate at the speed of light. ("Because nothing can travel faster than the speed of light." is not an acceptable answer.)

I'm afraid that is the answer. General Relativity is a generalization of Special Relativity (hence the name). It was designed so that it would reproduce SR at sufficiently small scales, and sufficiently weak fields, so those predictions - like nothing can travel faster than light - come along with it.

Without reproducing Einstein's equations here, let's just say that Einstein developed wave equations whose solutions predict gravitational waves traveling at the same speed as light. He did not arbitrarily insert the speed of gravitational waves out of belief that they should travel at light speed. Just like Maxwell did not arbitrarily insert c into his wave equations that predicted light should travel at the speed, c.

With reference to: http://en.wikipedia.org/wiki/Gravitational_waves#Mathematics

I see that c does appear in Einstein's equation. However, from what I see, Einstein never wrote his equation out to be a "wave equation" himself. Other people have manipulated his equations for this. Correct?

Also, c can be in the equation for a number of reasons. For example, it is the only value that contains a distance value with which to find the strength of the field at a distance. This would not necessarily mean that gravity travels at c, or that the curvature of space somehow travels at c. Is c not a natural unit that can be used for the purpose as I have described?

JesseM
I'm afraid that is the answer. General Relativity is a generalization of Special Relativity (hence the name). It was designed so that it would reproduce SR at sufficiently small scales, and sufficiently weak fields, so those predictions - like nothing can travel faster than light - come along with it.
Is there a proof that even in non weak field situations, the curvature at a given point P in spacetime can be determined with complete certainty from any spacelike cross-section of the past light cone of P? That nothing outside the past light cone is relevant to determining the curvature at P, in other words?

phyzguy
With reference to: http://en.wikipedia.org/wiki/Gravitational_waves#Mathematics
However, from what I see, Einstein never wrote his equation out to be a "wave equation" himself. Other people have manipulated his equations for this. Correct?

This is simply false. Einstein was the first to derive gravitational waves from his field equations and to show that they propagate at the speed of light in this paper:

Einstein, A.: Über Gravitationswellen. In: Sitzungsberichte der Königlich Preussischen Akademie der Wis-
senschaften Berlin (1918), 154–167.

He also calculated his "quadrupole formula" which calculated the energy carried by gravitational waves, and which was spectacularly confirmed by the Hulse-Taylor binary pulsar.

This is simply false. Einstein was the first to derive gravitational waves from his field equations and to show that they propagate at the speed of light in this paper:

Einstein, A.: Über Gravitationswellen. In: Sitzungsberichte der Königlich Preussischen Akademie der Wis-
senschaften Berlin (1918), 154–167.

He also calculated his "quadrupole formula" which calculated the energy carried by gravitational waves, and which was spectacularly confirmed by the Hulse-Taylor binary pulsar.

However, Einstein himself was convinced that gravitational waves do not exist in 1936 http://arxiv.org/PS_cache/gr-qc/pdf/9704/9704002v1.pdf If he thought for a second that gravitational waves do not exist, it must not be and integral part to his theory of general relativity. Further we still have no direct evidence of gravitational waves, which we had predicted would be detectable by the current detectors we have built.

Einstein also never predicted "gravitons" or that such things would travel at the speed of light. I still do not believe that gravity has to travel at the speed of light. because it is a gradient that is there in spacetime around a body of mass, not a particle traveling out from the body of mass to influence other bodies of mass. Gravitation is spacetimes' influence on objects, not gravitons influence on objects.

I do not find this to be in discrepancy with the fact that information cannot travel faster than light, because the curvature at any point in spacetime does not tell you about the bodies involved with that curvature. It is not as if gravitons are coming at an atom from all directions, arriving at the speed of light from all the differing bodies.

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bcrowell
Staff Emeritus
Gold Member
Is there a proof that even in non weak field situations, the curvature at a given point P in spacetime can be determined with complete certainty from any spacelike cross-section of the past light cone of P? That nothing outside the past light cone is relevant to determining the curvature at P, in other words?

When there are strong fields, you actually get speeds that can be less than c. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c. See MTW, p. 957. The effect is weak when the amplitude is small or the wavelength is short compared to the scale of the background curvature.

It might be a little tricky to define what is meant by the speed of propagation in complete generality. I think the results MTW talks about are probably for a strong wave propagating on a (probably static?) background of weak fields. In the general case where the backround is not static and contains strong fields, and the wave itself is strong, it's not obvious to me how you would even define the speed of propagation.

However, Einstein himself was convinced that gravitational waves do not exist in 1936 http://arxiv.org/PS_cache/gr-qc/pdf/9704/9704002v1.pdf If he thought for a second that gravitational waves do not exist, it must not be and integral part to his theory of general relativity. Further we still have no direct evidence of gravitational waves, which we had predicted would be detectable by the current detectors we have built.

But the Weyl Tensor, which is part of the Riemann curvature tensor, is the bit that carries gravitational waves and Einstein certainly knew that.

Einstein also never predicted "gravitons" or that such things would travel at the speed of light. I still do not believe that gravity has to travel at the speed of light. because it is a gradient that is there in spacetime around a body of mass, not a particle traveling out from the body of mass to influence other bodies of mass. Gravitation is spacetimes' influence on objects, not gravitons influence on objects.

No he didn't predict gravitons because a quantum theory of gravity is need for this concept, but gravitons are not needed in GR it is a classical theory. Anyway is it the changes in curvature which propagate at c. You seem to be mixing a whole bunch of disconnected ideas together.

This is fairly easy to understand without going into any mathematical detail.

1. Impose a gravity wave on a background of otherwise flat spacetime. This wave curves spacetime. Call the velocity b. It really doesn't matter if it is c, or not.

2. We know that the natural velocity, c, and all others, are not constant but depend upon curvature.

3. So we now superimpose a higher frequency upon the curved space generated by the first wave. These wave will therefore tavel as different velocities according to a nonlocal observer.

Therefore, there are two velocities for these waves. Only one, at most, can be c.

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I understand the theory of gravitational waves.

My problem with it is that there is nothing to travel, i.e. no gravitons. So why can't the curvature be directly continuous (as Newton saw it). Like I said, I don't feel it would be in violation of information traveling faster than the speed of light, because the state of spacetime curvature anywhere does not really tell you anything about the objects which made the curvature. Could it not be that curvature is automatic, not traveling outward from the body of mass, but just the spacetime accommodating the body continuously?

Is it required that because there is an equation that predicts it, that it must be existent in reality?

PAllen
I understand the theory of gravitational waves.

My problem with it is that there is nothing to travel, i.e. no gravitons. So why can't the curvature be directly continuous (as Newton saw it). Like I said, I don't feel it would be in violation of information traveling faster than the speed of light, because the state of spacetime curvature anywhere does not really tell you anything about the objects which made the curvature. Could it not be that curvature is automatic, not traveling outward from the body of mass, but just the spacetime accommodating the body continuously?

Is it required that because there is an equation that predicts it, that it must be existent in reality?

If a change in position of A propagated instantly to B, you could send signals FTL by wiggling A.

I don't understand what you are saying about 'continuous'. All quantities in GR are assumed to be continuous. A wave is just function that is periodic. That is, if you follow a worldline, you find that change in metric encountered is at least partly periodic.

What Newton proposed was instant action at a distance, and this was required for stable orbits. (In GR, in principle, no orbits are stable because there is no action at a distance; however, the instability is completely insignificant in the solar system).

Thank you. This explanation helps. I am not so sure why I wanted to go along with Newton. Perhaps it was because I do not believe there are gravitons. So, would you say that gravitational waves do not require gravitons?

Finally, if the Sun were to suddenly disappear out of the solar system, the Earth would not leave it's orbit immediately, while photons would get there a moment later? But rather the Earth's path in spacetime would not change until the last light from the Sun arrived?

PAllen
Thank you. This explanation helps. I am not so sure why I wanted to go along with Newton. Perhaps it was because I do not believe there are gravitons. So, would you say that gravitational waves do not require gravitons?

Finally, if the Sun were to suddenly disappear out of the solar system, the Earth would not leave it's orbit immediately, while photons would get there a moment later? But rather the Earth's path in spacetime would not change until the last light from the Sun arrived?

In GR, gravitational waves have nothing to do with gravitons. Gravitons arise from quantizing gravity.

The sun disappearing is impossible in a solution of the GR equations. You could envision a process by which the sun explodes into a few fragments moving near the speed of light. Then, indeed, the earth's orbit would first be affected shortly after the arrival of the first light from the explosion.

In GR, gravitational waves have nothing to do with gravitons. Gravitons arise from quantizing gravity.

I'm not sure I agree with this. The gravitational interaction between two bodies is Coulombic. In quantum field theory it would be mediated by a virtual particle field. Off shell, they are not locally constrained by the velocity c. The quantized, real field would have an associated wavelength and frequency. Any changes in the Coulombic field would necessarily be associated with real particle fields locally constrained to c.

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PAllen
I'm not sure I agree with this. The gravitational interaction between two bodies is Coulombic. In quantum field theory it would be mediated by a virtual particle field. Off shell, they are not locally constrained by the velocity c. The quantized, real field would have an associated wavelength and frequency. Any changes in the Coulombic field would necessarily be associated with real particle fields locally constrained to c.

If on is looking at GR, there is no such thing as QFT - GR, as I view it, is strictly classical. A successor theory that reproduces GR in the classical limit would have gravitons.

If on is looking at GR, there is no such thing as QFT - GR, as I view it, is strictly classical. A successor theory that reproduces GR in the classical limit would have gravitons.

I see. I missed you qualifying phrase the first time, as the question was specifically about gravitons.

I do not find this to be in discrepancy with the fact that information cannot travel faster than light, because the curvature at any point in spacetime does not tell you about the bodies involved with that curvature. It is not as if gravitons are coming at an atom from all directions, arriving at the speed of light from all the differing bodies.

Hello, I can say you are wrong, very wrong. Einstein's equations are local, that means valid on one point of the manifold that describes the spacetime, and this is very important in physics as almost everything is local. This equation tells you that matter acts on the curvature because matter is energy, not really that curvature creates matter, not so literrally. "Pure curvature" can be seen as a form of energy, but it is also defined locally. So, once you move your source, it acts on the curvature, but not instantly, and information about the location of the sources take a time to travel. There is no necessary need to carry real energy for that (and thus gravitons or photons), for example the electromagnetic wave signals the late position (and other dynamic variables) of a charge, that is a source of electromagnetic field, but if you look at the coulombian information, that concern only the position, (for example the electric field along the line in the direction of a linear acceleration), it also take a while to reach the observer, but doesn't carry energy (and decrease in r^-2).

Thank you. This explanation helps. I am not so sure why I wanted to go along with Newton. Perhaps it was because I do not believe there are gravitons. So, would you say that gravitational waves do not require gravitons?

Finally, if the Sun were to suddenly disappear out of the solar system, the Earth would not leave it's orbit immediately, while photons would get there a moment later? But rather the Earth's path in spacetime would not change until the last light from the Sun arrived?

Yes.

This is visually explained by Brian Greene on his show "The Elegant Universe".

If on is looking at GR, there is no such thing as QFT - GR, as I view it, is strictly classical. A successor theory that reproduces GR in the classical limit would have gravitons.

You mean the quantification of GR requires the invocation of a boson in the classical limit? That is to say that when trying to turn GR into a quantum theory, gravitons would be required..

Or are you getting at something else here?

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Y'all. There are no little teeny-weenie little billiard balls called gravitons or photons or electrons, or any other x-ons. The best we can say is that measurements obtain irreducable quanta in terms of energy, angular momenta and a few other things that often times finds a convenient model in terms of little teeny-weenie billiard balls.

The word 'graviton' should be read as 'graviton field' where the count is one.