Understanding the Speed of Gravity: GR vs. SR and the Impact on Orbital Dynamics

[sjw40364]

According to GR (General Relativity) space-time curvature causes gravity. Updates to this curvature occur at the speed of c, yet aberration is set to 0, effectively making the propagation speed of gravity instantaneous. In SR (Special Relativity) nothing can exceed c. We know that light takes 8.3 minutes to reach the Earth from the Sun. If gravity or space-time curvature changes took the same amount of time to update, aberration would be induced, effectively doubling the Earth's orbital distance around the Sun in 1200 years. From observation over the last few thousand years we know this has not happened, supporting faster than light propagation speeds for gravity or space-time curvature updates. So if aberration is set to 0 then space-time curvature updates must propagate at faster than c speeds. If space-time curvature updates occur at c or less then aberration must be factored in not set to 0 to make the theories work.

 

[bcrowell]

Sounds like you've swallowed van Flandern's incorrect analysis.

Updates to this curvature occur at the speed of c, yet aberration is set to 0, effectively making the propagation speed of gravity instantaneous.

For an explanation of why van Flandern is wrong, see the Carlip reference below.

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

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

 

[sjw40364]

Yes, But GR uses the propagation speed of c with aberration set to 0, which in effect makes the propagation speed of gravity infinite. You cannot ignore the effects of aberration. If the space-time curvature updates at the speed of c aberration would effectively cause the Earth to double its orbitational distance in approximately 1200 years. Even the small 8.3 minute delay it would take to update the space-time curvature out to the Earth would induce aberration, a fact ignored in both GR and Newtonian gravity theories. Perhaps this lack of aberration is acceptable to you, but it is not acceptable to me and any theories which ignore aberration need to explain why they do so. If you ignore aberration you are actually adopting an infinite propagation speed for gravity.

 

[bcrowell]

Yes, But GR uses the propagation speed of c with aberration set to 0, which in effect makes the propagation speed of gravity infinite. You cannot ignore the effects of aberration. If the space-time curvature updates at the speed of c aberration would effectively cause the Earth to double its orbitational distance in approximately 1200 years. Even the small 8.3 minute delay it would take to update the space-time curvature out to the Earth would induce aberration, a fact ignored in both GR and Newtonian gravity theories. Perhaps this lack of aberration is acceptable to you, but it is not acceptable to me and any theories which ignore aberration need to explain why they do so. If you ignore aberration you are actually adopting an infinite propagation speed for gravity.

You seem to be repeating material from your original post. Have you read the Carlip paper, which explains the errors in this analysis?

 

[FtlIsAwesome]

But GR uses the propagation speed of c with aberration set to 0, which in effect makes the propagation speed of gravity infinite.

Ok, first you said it travels at c, then you said it travels at infinite speed. Could you clarify?


Can someone tell me what exactly is aberration?


From my understanding, gravity travels at the same speed that light does, no slower, no faster. If it traveled faster paradoxes would result. We could logically say that the universal speed limit is the speed of gravity.

http://en.wikipedia.org/wiki/Speed_of_gravity

 

[Dale]

aberration is set to 0, effectively making the propagation speed of gravity instantaneous.

This is a non-sequiter. Read the materials bcrowell provided.

 

[Calrid]

There's only one thing that transmits a force instantaneously and that's love. Ahh let's all sing songs and hold hands.

Kum buy yah me lord*

Seriously though who in the what where why would ever claim something that is totally impossible in a theory?

Can someone tell me what exactly is aberration?

In this case its an aberration.

Error in the calculation.

Originally it was just nonsense though as far as I can tell, the aberration, if I'm getting the context right, should be the speed of light which is not 0 obviously.

 

[sjw40364]

No, GR says it travels at c, yet I say if you set aberration to 0 then gravity must propagate at faster than light speeds. As for gravitational radiation entering the equation in our solar system, the only bodies we have seen that emit this are massive binary pulsars, black holes, and extremely large bodies moving at extreme speeds, and last I looked we had no dual pulsars or other such in our solar system.

http://en.wikipedia.org/wiki/Gravitational_wave"

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html"

All other gravitational radiation emitted from smaller bodies has already been shown to be virtually undetectable. So this may indeed apply to light passing binary pulsars, but no such explanation can be used for objects within our solar system.

So perhaps you should read more before relying on useless information that has only to do with light passing massive binary pulsars. Pretty neat how they try to use one situation to fit all others when small bodies, if they do emit gravitational radiation remain virtually undetectable, so its interactions would also be negligible.

 

[Calrid]

No, GR says it travels at c, yet I say if you set aberration to 0 then gravity must propagate at faster than light speeds. As for gravitational radiation entering the equation in our solar system, the only bodies we have seen that emit this are massive binary pulsars, black holes, and extremely large bodies moving at extreme speeds, and last I looked we had no dual pulsars or other such in our solar system.

http://en.wikipedia.org/wiki/Gravitational_wave"

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html"

All other gravitational radiation emitted from smaller bodies has already been shown to be virtually undetectable. So this may indeed apply to light passing binary pulsars, but no such explanation can be used for objects within our solar system.

So perhaps you should read more before relying on useless information that has only to do with light passing massive binary pulsars. Pretty neat how they try to use one situation to fit all others when small bodies, if they do emit gravitational radiation remain virtually undetectable, so its interactions would also be negligible.

Is aberration another way of saying if you set a variable to a range it can't take you get nonsense?

Because I agree setting aberration to 0 and hence the equations answer to warp factor infinity is nonsense.

 

[sjw40364]

I agree, if you set aberration to 0 it is nonsense, that must be why GR uses an aberration of 0 (perhaps because it is nonsense?)

Do you believe the Sun is stationary, that it does not move through space as the Milky-Way rotates? The space-time curvature must continually update as the Sun moves around the barycenter of our solar system and our solar system moves as our galaxy spins, and our galaxy moves through space. Everything is in constant motion so space-time must be continuously updated.

the Milky Way is moving at approximately 630 km per second relative to the local co-moving frame of reference that moves with the Hubble flow. If the galaxy is moving at 600 km/s, Earth travels 51.84 million km per day, or more than 18.9 billion km per year.

It turns out that our solar system is moving nearly 100,000 m.p.h. faster than previously thought — revolving around the center of the Milky Way at 568,000 m.p.h., announced Mark Reid of the Harvard-Smithsonian Center for Astrophysics at the American Astronomical Society's conference in Long Beach, Calif.

There is no choice but that it MUST continually update.

If this space-time did not update nearly instantaneously, by the time the update reached us at the speed of c, we would be following the old curvature and as it did update we would be deeper within the curvature, causing the Earth to accelerate , effectively increasing its orbital distance. the space-time curvature the Earth follows is caused by the Sun's mass, so as the Sun moves, so the curvature follows, the Sun does not follow its own curvature of space-time, it follows the Sun as it moves around the galaxy, which in turn follows the space-time curvature of the entire galaxy. So every moving star within our galaxy must be in continuous communication with every other space-time curvature caused be each star. If you induce any delay into the mathematics of such a complicated system the results are disastrous. This is why GR uses aberration of 0, effectively making the propagation of space-time curvature instantaneous, even though it states it updates at the speed of c. If it did indeed update at the speed of c then aberration must be >0.

 

[Calrid]

It might help if you told us what the hell aberration is finally you know. Can you show us the equation? :tongue:

I have never heard of that expression so it must be some odd phrase?

Whatever it is it is nonsense, you set the speed of gravity to c or you don't have an equation at all it's just nonsense.

The propagation of space time curvature is c.

If God Kicked the sun into Andromeda scoring a superb swerve shot into it's supermassive black hole, the rate at which we would notice this or more correctly Earth would be affected by the change, assuming even God's shot is only traveling < c is exactly the same time it takes light to reach earth.

$\simeq$8.32 minutes, sadly I had to google that as I can't remember the exact value of 1 au or c off the top of my head. hehe

We assume that God exists in this scenario, although so as not to offend anyone it could quite easily have been Thor or Chronos or Buddha or Superman or someone.

 

[sjw40364]

As for those who like to use Kopeikin's papers on the speed of gravity.
The man had to change his own theory and math to get the results he wanted and still didn't measure gravity, but the speed of light.

http://www.metaresearch.org/media%20and%20links/press/SOG-Kopeikin.asp

 

[sjw40364]

http://en.wikipedia.org/wiki/Aberration_of_light
The only definition of aberration you will get besides in Newtonian gravity as GR says it doesn't exist, yet GR says space-time propagates at the speed of c and yet light has aberration due to this delay, but gravity doesn't. go figure :)

 

[Calrid]

http://en.wikipedia.org/wiki/Aberration_of_light
The only definition of aberration you will get besides in Newtonian gravity as GR says it doesn't exist, yet GR says space-time propagates at the speed of c and yet light has aberration due to this delay, but gravity doesn't. go figure :)

I can't see where that causes any odds with the theory?

Where does GR say it doesn't exist as well?

I think the problem is we're talking about an observer here and hence special relativity, in GR it can be ignored because this is an observation issue. No idea but I don't see what the problem is I've got to admit.

 

[Jonathan Scott]

In GR, in addition to the Newtonian field, gravity has additional components due to motion (loosely analogous to the effects of magnetism in electromagnetism, but a bit more complicated). These effects mean that the effective direction of the overall gravitational force in GR is NOT towards the visible location of the source (as seen by light or other light-speed signals) but rather towards where it will be at the current time, taking into account its velocity when last seen and even to some extent its acceleration due to gravitational forces.

It is very difficult to create a "surprise" gravitationally. If you for example try to push something sideways suddenly, then you need enough energy and momentum to do it, which will itself act as a source, and the effective "center of mass" of the combined system will still be moving in a straight line at constant speed. The most rapid change that occurs in practice is when a pair of objects is orbiting rapidly around each other and change from being aligned parallel to the line to a nearby observer to being perpendicular to that line.

 

[George Jones]

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