# Is gravity an instant-force?

1. Sep 17, 2010

### jumpjack

Has it been demonstrated that gravity effects propagate at light speed? I read somwehere that gravity is instead "instant force", i.e. if Sun suddenly disappeared, Earth would immediately leave the orbit, rather than after 8 minutes.

2. Sep 17, 2010

### Chronos

No, gravity propogates at the speed of light.

3. Sep 17, 2010

### twofish-quant

Also what confuses people is the fact that if you simulate gravity by having a force point to where the other object was x minutes ago, you end up with something unstable.

If you use Newtonian forces to model gravity it does turn out that you have to have the force point to where the object is now. It turns out that what does get transmitted is not forces but potentials.

4. Sep 17, 2010

### George Jones

Staff Emeritus
5. Sep 17, 2010

### D H

Staff Emeritus
Assuming Newtonian gravity, that is.

Crackpots (including some degreed physicists) pounce upon this instability as 'proof' that general relativity is incorrect. The problem is that speed of light propagation is but one part of general relativity. Taking away those other aspects in which GR differs from Newtonian gravity, leaving only the finite transmission speed, is making a straw man out of GR. That straw man is easily disproved. Disproving this straw man version of GR does not mean that GR is false. It just means that the straw man is false.

There's no telling what would happen to the Earth if the Sun suddenly disappeared. Who knows? The Earth might stand up straight and dance a little jig on the back of the giant world-supporting tortoise. The Sun suddenly disappearance would violate all kinds of laws of physics. So talking about what would take place if this happened puts us in the realm of non-science.

6. Sep 17, 2010

### twofish-quant

Also you can come up with Newtonian theories of gravity which can illustrate the basics of what is going on in GR.

Imagine gravity as ripples in a pool and the direction of gravity happens to be direction where the ripples come from. Now if you move an object, it will take a few minutes you to notice that the ripples are coming from a different direction and for the direction of gravity to change.

But what will work is to ask what happens if the Sun moves.

7. Sep 17, 2010

### D H

Staff Emeritus
E.g., a post-Newtonian expansion, which is what the better solar system ephemerides models use to model the behavior of the solar system.

8. Sep 18, 2010

### Medium9

So if I wanted to program a simulator application for large bodies in space (say solar systems), I'd have to account for that, and moving objects' gravity potentials would drag out behind them? (Of course, only notably if they move quite fast.)

Example: I have some big sun, and some smaller body. Assuming the sun would move amazingly fast, the smaller body would feel a force into a direction, where the cause of it has long gone? Or talking in discrete moments in time (which are commonplace in such simulations), that smaller body would be pulled into a direction that is the average of the past influences by that turbo-sun, weighed by the squared distances of it, which would be somewhere behind it. Right?

9. Sep 18, 2010

### bcrowell

Staff Emeritus
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.[Rindler 1979] 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.

Rindler - Essential Relativity: Special, General, and Cosmological, 1979, p. 51

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 [Broken]

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

Last edited by a moderator: May 4, 2017
10. Sep 19, 2010

### Chronos

All sorts of logical paradoxes arise when mass 'magically' disappears from the universe. No big surprise this is a constant source of confusion. If you settle for propelling the sun away from its current position at sublight speed, the problem is more easily fathomed.

11. Sep 19, 2010

### D H

Staff Emeritus
I assume that this is in reference to [post=2885746]this post[/post],
You only have to account for relativistic effects if you want extreme accuracy over a long period of time. If that is your goal, you will also need to account for lots of other effects as well. Just a few of these other effects: (1) The planets are attracted to one another as well as the Sun, (2) there are lots of small bodies in the solar system in addition to the Sun and the planets. (3) the Sun has a slightly non-spherical mass distribution, and (4) that planets have a non-spherical mass distribution affects the orbit of those planets' moons.

Finally, if you want extreme accuracy you will need an extremely accurate and extremely stable numerical integrator. Don't use RK4; it is not symplectic. Don't use Euler-Cromer either; it is an extremely inaccurate integrator. The errors induced from failing to use a very, very good numerical integrator will swamp the errors induced by ignoring relativistic effects.

Bottom line: Accounting for relativistic effects without going into a lot of other details is a bit silly because those relativistic effects are tiny. The effect is greatest on Mercury, and even there it is quite small. Mercury's orbit exhibits a relativistic perihelion precession of 43 arcseconds per century.