# Speed of gravity?

I like the animated gif on the previous page... but it is missing something important too.
Remember, for an object to "suddenly accelerate", something else must also do the same in the other direction. And that something else also has its own mass and creates its own gravity, and the combined changes in gravity can actually cancel out in some cases. Remember that the center of mass of a set of objects will never change its motion from forces acting only between those objects.

Especially when that "sudden" acceleration is caused by gravity, I would assume the other objects do take it into account when "predicting" the location of the gravity sources.

(I do not actually know the math for any of that, take me with a grain of salt)

PeterDonis
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2019 Award
Well i never mentioned force at all and don't see why it makes a difference. Of course the end result in the world is an acceleration vector whether you attribute it to force or geometry isn't really germane.
Yes, it is, because if you attribute it to geometry then there doesn't have to be any "acceleration vector"; the Earth moves on a geodesic, i.e., an unaccelerated world line, and on the geometric view this is perfectly natural since "gravity" is just curvature of the geometry. If you view gravity as a "force" then that at least strongly suggests that there *is* an actual acceleration, i.e., that the object's motion is *not* geodesic; that's the reason why in GR we no longer view things like gravity that don't induce proper acceleration as "forces".

You could look at it as information. If displacement of a charge or mass effects a local field fluctuation, then this information has to get from there to all other parts of the field. This seems to imply a mediator wither a wave or a virtual particle.
If by "a wave" you just mean "a disturbance in an underlying medium", then yes, a displacement of a mass produces gravitational waves that carry the information about the change outward.

SO if we rule out any non-local quantum instantaneous field responce then the question is specifically how does the motion of the mass/charge affect the wave or particle in a way that is equivalent to instantaneous responce when it arrives at the distant locations in the field. Yes?
It's not exactly equivalent, just approximately equivalent. See below.

The term extrapolation as I understand it means either projecting into the future based on the past or projecting from a series of values to determine a value outside the range of known values. Both being purely abstract mathematical procedures which I find difficult attaching to any possible physical interaction.
Don't get hung up on the word "extrapolation". The important point is that the information carried by the field disturbance caused by a displacement of a source (the gravitational waves, in the case of displacement of a mass), as it is modeled in GR, is not just information about the source's position; it's information about the source's position *and* velocity, to a degree of accuracy which is enough to compensate for the light-speed time delay to a certain order of approximation. (For gravity it's second order, i.e., quadratic; for electromagnetism it's first order, i.e., linear.) So the disturbance, when it reaches a distant object (say, the disturbance caused by the Sun reaching the Earth), affects the motion of that object in a way that happens to be the same, to the given order of approximation, as an "instantaneous force" would affect it.

So I still would like to know what the velocity dependent factors could be. Vectors? tensors? They are certainly not any kind of "conceptual crutch" as there is no concept whatsoever to be attached to the term "velocity dependent factors" per se.
They're a conceptual crutch because they only appear if you insist on viewing the effect of one body on another (say the Sun on the Earth) as a "force" and expanding it out order by order in the relative velocity. The "velocity dependent factors" are just terms in the expansion. But the fact that we humans need to do the expansion to form a conceptual picture of what's happening does not imply that nature has to "do the expansion".

Does this mean that I was not sufficiently clear in my description and you are unsure of my meaning or do you understand it but are digesting it to find the flaws in my interpretation or inference???
It means I didn't have time to read it carefully enough to form a response. I'll respond to it separately.

PeterDonis
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Regarding a photon , the observed directional vector points to the retarded position due to aberration.
There is a key point here that you may be missing. The observed direction of an incoming photon--say from the Sun, being observed on Earth, to be concrete--does show aberration, but that aberration is *not*, strictly speaking, the "aberration" that Carlip is talking about in his paper. He is talking (in the EM case) about the observed direction of the Coulomb force exerted by a charged source, which also shows "aberration" in the case of an accelerating source. The radiation emitted by the accelerating source is what carries the information about the acceleration, but that information causes a *change* in the observed direction of the Coulomb force. So there's a key distinction between the direction the information about the change in the Coulomb force appears to come from, and the direction that the Coulomb force itself appears to come from.

I won't comment on the rest of what you say about photons and wave fronts because I think you should reconsider it in the light of the above.

I'll post separately about the case of a gravitational binary system since you give more details about that in your response to Bill_K's post.

PeterDonis
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2019 Award
During the recessional phase, the retarded postion of the point of emission is a distance Dr ,less than the actual instantaneous position distance Di relative to the point of reception. Dr < Di SO the negative acceleration arising from this is greater than the force should be from the actual position by the inverse square difference in distance
No, it isn't, because of the velocity-dependent factors I mentioned. You are assuming that the change in relative distance is the only thing that contributes to a change in "acceleration" (I put that in quotes because, as I mentioned before, both objects are traveling on geodesics, so they have zero proper acceleration; you are talking about coordinate acceleration in the frame in which the common center of mass of the two objects is at rest). It isn't. A given increase in distance during the recessional phase translates into a significantly *larger* change in "acceleration" than your calculation indicates, because of those velocity-dependent factors. Similar remarks apply to the closing phase.

All of the rest of your reasoning appears to depend on the above mistake, so I'm not sure it's worth my making specific comments on it. The only thing I would say is that the above reasoning applies to the EM case as well.

[Edit: Realized that some of the wording in the first paragraph was kind of garbled, so I re-worded it to hopefully make more sense.]

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