Are gravitational effects instantaneous?

[jacksonb62]

My friend tried to tell me that the effects of gravity are instantaneous and I assured him that he was wrong because nothing can move faster than the speed of light. Can someone verify that statement because the discussion got me thinking

 

[Dickfore]

What test would you propose to measure the speed of propagation of gravitational influence?

 

[jacksonb62]

There are many topics in modern physics that cannot be tested per say. I'm talking theoretically. If tomorrow, our sun were to explode, would we notice the gravitational effects of no longer having a sun prior to seeing the light from the supernova? And actually come to think of it there are devices for detecting gravitational waves. I am merely wondering if gravitational effects are instantaneous

 

[Dickfore]

The predicted speed of propagation of gravitational waves by General Relativity is equal to the speed of light in vacuum. However, this is not what you ask in your posts.

 

[jacksonb62]

That was my intended question. thank you for verifying

 

[edpell]

Jackson, the effect of gravity propagates at the speed of light, c.

It is hard to move large masses around at near the speed of light. I do not know of any experimental results that measure the speed of propagation of gravity.

 

[D H]

My friend tried to tell me that the effects of gravity are instantaneous and I assured him that he was wrong because nothing can move faster than the speed of light. Can someone verify that statement because the discussion got me thinking

The answer is a bit complicated.

Gravitation is indeed instantaneous in Newtonian mechanics. On the other hand, relativity theory says nothing (including gravitation) can go faster than the speed of light. This suggests adding a light-time correction to Newton's law of gravitation. Here's the problem: This would result in something far worse than pretending that gravitation is instantaneous. So how does Newtonian mechanics work so well for predicting the behavior of the solar system?

One way to look at it is "mass-energy tells spacetime how to curve; the curvature of spacetime tells mass-energy how to move." When some small object moves in a region subject to the gravitational influence of a larger mass, the curvature of spacetime from the larger mass is already present in the region into which the object moves. Gravitation appears to be instantaneous. Well, almost instantaneous. Instantaneous gravity cannot explain the precession of Mercury, for example.

Another way to look at it is that general relativity says a finite transmission speed is only one of many subtle effects of gravitation. Some of these other effects nearly cancel the effects of a finite transmission speed. The end result is that gravitation appears to be (almost) instantaneous, at least for objects moving at relative speeds that are much slower than the speed of light. Instead of a light-time correction, you get a 1/r⁴ correction to Newtonian gravity (for "slow" moving objects).

 

[bcrowell]

FAQ: How fast do changes in the gravitational field propagate?

General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel at the speed of light. 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.

Why does it make sense that low-amplitude waves propagate at c? In Newtonian gravity, gravitational effects are assumed to propagate at infinite speed, so that for example the lunar tides correspond at any time to the position of the moon at the same instant. This clearly can't be true in relativity, since simultaneity isn't something that different observers even agree on. Not only should the "speed of gravity" be finite, but it seems implausible that that it would be greater than c; based on symmetry properties of spacetime, one can prove that there must be a maximum speed of cause and effect.[Ignatowsky, Pal] Although the argument is only applicable to special relativity, i.e., to a flat spacetime, it seems likely to apply to general relativity as well, at least for low-amplitude waves on a flat background. As early as 1913, before Einstein had even developed the full theory of general relativity, he had carried out calculations in the weak-field limit that showed that gravitational effects should propagate at c. This seems eminently reasonable, since (a) it is likely to be consistent with causality, and (b) G and c are the only constants with units that appear in the field equations, and the only velocity-scale that can be constructed from these two constants is c itself.

High-amplitude gravitational waves need *not* propagate at 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.[MTW, p. 957] This effect is weak when the amplitude is small or the wavelength is short compared to the scale of the background curvature.

It is difficult to design empirical tests that specifically check propagation at c, independently of the other features of general relativity. The trouble is that although there are other theories of gravity (e.g., Brans-Dicke gravity) that are consistent with all the currently available experimental data, none of them predict that gravitational disturbances propagate at any other speed than c. Without a test theory that predicts a different speed, it becomes essentially impossible to interpret observations so as to extract the speed. In 2003, Fomalont published the results of an exquisitely sensitive test of general relativity using radar astronomy, and these results were consistent with general relativity. Fomalont's co-author, the theorist Kopeikin, interpreted the results as verifying general relativity's prediction of propagation of gravitational disturbances at c. Samuel and Will published refutations showing that Kopeikin's interpretation was mistaken, and that what the experiment really verified was the speed of light, not the speed of gravity.

A kook paper by Van Flandern claiming propagation of gravitational effects at >c has been debunked by Carlip. Van Flandern's analysis also applies to propagation of electromagnetic disturbances, leading to the result that light propagates at >c --- a conclusion that Van Flandern apparently believed until his death in 2010.

W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972

Palash B. Pal, "Nothing but Relativity," Eur.J.Phys.24:315-319,2003, http://arxiv.org/abs/physics/0302045v1

MTW - Misner, Thorne, and Wheeler, Gravitation

Fomalont and Kopeikin - http://arxiv.org/abs/astro-ph/0302294

Samuel - http://arxiv.org/abs/astro-ph/0304006

Will - http://arxiv.org/abs/astro-ph/0301145

Van Flandern - http://www.metaresearch.org/cosmology/speed_of_gravity.asp

Carlip - Physics Letters A 267 (2000) 81, http://xxx.lanl.gov/abs/gr-qc/9909087v2

 

[TrickyDicky]

There are many topics in modern physics that cannot be tested per say. I'm talking theoretically. If tomorrow, our sun were to explode, would we notice the gravitational effects of no longer having a sun prior to seeing the light from the supernova? And actually come to think of it there are devices for detecting gravitational waves. I am merely wondering if gravitational effects are instantaneous

It is a tough question as DH said, and judging from DH and bcrowell's answers one there is no complete consensus about. I really have a hard time with it, being completely convinced at times that we would feel the effects inmediately without having to wait 8 minutes for the explosion flash, and equally convinced at other times that the gravitational effects and the visual perception must be simultaneous. Ouch, I don't like that.

 

[D H]

It is a tough question as DH said, and judging from DH and bcrowell's answers one there is no complete consensus about. I really have a hard time with it, being completely convinced at times that we would feel the effects inmediately without having to wait 8 minutes for the explosion flash, and equally convinced at other times that the gravitational effects and the visual perception must be simultaneous. Ouch, I don't like that.

There is no controversy here. I wrote about the weak field approximation, bcrowell about strong gravity.

 

[TrickyDicky]

There is no controversy here. I wrote about the weak field approximation, bcrowell about strong gravity.

Great then, what about the exploding sun scenario, what is your answer to that?

 

[George Jones]

Great then, what about the exploding sun scenario, what is your answer to that?

Read carefully, skipping the mathematical derviations,

Carlip - Physics Letters A 267 (2000) 81, http://xxx.lanl.gov/abs/gr-qc/9909087v2

 

[TrickyDicky]

Read carefully, skipping the mathematical derviations,

From that I assume you think both the orbital effects and the flash from the explosion are exactly simultaneous from the Earth's's POV, and for about 8 minutes the Earth orbits a star that is no longer there, right?

 

[Naty1]

George: thanks for the reference..a good read

From that I assume you think both the orbital effects and the flash from the explosion are exactly simultaneous from the Earth's's POV, and for about 8 minutes the Earth orbits a star that is no longer there, right?

That's what Carlip says...the electromagnetic and gravitational force effects behave the same:
my notes:

...as in Maxwell’s theory, if a graviatational source abruptly stops moving at a point z(s0), a test particle at position x will continue to accelerate toward the extrapolated position of the source until the time it takes for a signal to propagate from z(s0) to x at light speed..

..the gravitational interaction propagates at the speed of light, but velocity-dependent terms in the interaction nearly cancel the effect of aberration. Indeed, it can be rigorously proven that no gravitational influence in general relativity can travel faster than the speed of light…

As Poincar´e first observed, any Lorentz-invariant model of gravitation necessarily requires additional velocity-dependent interactions, which can provide “a more or less perfect compensation” for the effects of aberration…..

but actual experiments so far say very little about the speed of gravity.

 

[Dickfore]

There is one point about Einstein's equations that I've read in textbooks (see Landau Lifgarbagez vol.2) that makes them quite different from Maxwell's equations.

While in EM, you can solve for the fields if the motion of the charges is given (as long as the continuity equation is satisfied), or, conversely, solve for the motion of the charges if the "external fields" are given (as long as they obey the sourceless Maxwell's equation in the region where the charges are), this is generally quite impossible for Einstein's equations, even in principle. One must solve simultaneously for the metric as well as the geodesic motion of the particles.

I never quite understood why this is so. Perhaps because of the non-linearity of Einstein's equations. Maybe someone could illuminate this issue further.

 

[jtbell]

for about 8 minutes the Earth orbits a star that is no longer there, right?

The mass of the sun and the associated energy can't simply disappear. If the sun were to explode, you'd still have (at least approximately) a spherical distribution of mass and energy, expanding at a rate less than c.

 

[D H]

Great then, what about the exploding sun scenario, what is your answer to that?

What exploding sun scenario?

If you mean that all of mass of the sun instantaneous converts into energy (e.g., some hitherto undiscovered process in quantum mechanics), no problem. It is energy that gravitates. The intrinsic mass of all of those photons moving away from the sun at the speed of light is equal to the (former) sun's mass. That collection of photons will gravitate just as the sun did.

 

[TrickyDicky]

The mass of the sun and the associated energy can't simply disappear. If the sun were to explode, you'd still have (at least approximately) a spherical distribution of mass and energy, expanding at a rate less than c.

Sure, I'm aware of the fact that mass and energy can't simply disappear if only for conservation reasons, so this kind of set up is impossible and hardly helps solve anything about the propagation of gravitational effects in the first place. I got a little carried away in my effort to be graphic
I think wrt a empirical verification of what really happens we are stuck as Dickfore says in #2 with the impossibility or at least great difficulty to come up with a practical test given the limitations that c imposes to signal sending. So the only answer is purely theoretical.

 

[Dale]

Expanding on D_H's last comment, accordking to Birkhoff's theorem for any spherically symmetric distribution of matter the exterior solution is given by the Schwarzschild solution. So the Earth will continue to orbit the ball of photons until the ball of photons passes the earth, at which time Earth is no longer in the exterior and things change.

http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity )

 

[TrickyDicky]

What exploding sun scenario?

If you mean that all of mass of the sun instantaneous converts into energy (e.g., some hitherto undiscovered process in quantum mechanics), no problem. It is energy that gravitates. The intrinsic mass of all of those photons moving away from the sun at the speed of light is equal to the (former) sun's mass. That collection of photons will gravitate just as the sun did.

Yes, I addressed this in my previous post.

 

[TrickyDicky]

There is one point about Einstein's equations that I've read in textbooks (see Landau Lifgarbagez vol.2) that makes them quite different from Maxwell's equations.

While in EM, you can solve for the fields if the motion of the charges is given (as long as the continuity equation is satisfied), or, conversely, solve for the motion of the charges if the "external fields" are given (as long as they obey the sourceless Maxwell's equation in the region where the charges are), this is generally quite impossible for Einstein's equations, even in principle. One must solve simultaneously for the metric as well as the geodesic motion of the particles.

I never quite understood why this is so. Perhaps because of the non-linearity of Einstein's equations. Maybe someone could illuminate this issue further.

In EM the fields are independent of the background metric, but in GR this is not the case , the gravitational field effects (the motion of the particles) are understood as curvature (Riemann tensor) given by solving for the metric so you must solve at once for the metric and the motion of the particles (the Christoffel symbols are functions of the metric).