Proof for velocity of gravity

[hstarbuck]

It is my understanding that gravity moves at the speed of light (c = 3E8 m/s²). That means, as an object like the Earth is journeying around the sun, at an instantaneous position it sends out a force that is received by another object --like the Moon-- at time t = c/d later. The Moon then responds to the direction of the force, which corresponds to the previous location of Earth because at that time the Earth would have stepped into a new position. Of course this happens continuously and for most cases I am aware of is of no consequence. I was wondering what the "proof" for the velocity of gravity is. Do measurements or theory provide the evidence? It can't be instantaneous because it is information of a sort...right? I am only barely familiar with theory of General Relativity, but understand Special Relativity well enough (I don't think it applies directly here).

[neufer]

Orbiting bodies radiate away energy inversely with the fifth power of
the speed at which gravitation propagates (i.e., power radiated ~ c^-5).

<<Gravitational waves carry energy away from orbiting bodies. For the Sun and Earth the gravitational wave power radiated is about 200 Watts and leads to a decay in the orbit by about the diameter of a proton per day. However, there are other orbiting bodies for which the gravitational radiation is substantial...e.g., the Hulse-Taylor binary — a pair of stars, one of which is a pulsar:


Orbital decay of PSR B1913+16.The data points indicate the observed change
in the epoch of periastron with date while the parabola illustrates the
theoretically expected change in epoch according to general relativity
[assuming explicitly that gravitation propagates at the speed of light].

[Chris Peterson]

It is my understanding that gravity moves at the speed of light (c = 3E8 m/s²). That means, as an object like the Earth is journeying around the sun, at an instantaneous position it sends out a force that is received by another object --like the Moon-- at time t = c/d later. The Moon then responds to the direction of the force, which corresponds to the previous location of Earth because at that time the Earth would have stepped into a new position. Of course this happens continuously and for most cases I am aware of is of no consequence.

What you're referring to here is analogous to the aberration of light, an observed phenomenon where objects appear in a different location than their actual position due to the finite speed of light. While it seems intuitive that you should see this effect for gravity as well, in fact you don't. The reason why not is well understood and completely consistent with GR, but surprisingly difficult to compute or explain in a simple way. Take my word for it <g>.

I was wondering what the "proof" for the velocity of gravity is. Do measurements or theory provide the evidence? It can't be instantaneous because it is information of a sort...right? I am only barely familiar with theory of General Relativity, but understand Special Relativity well enough (I don't think it applies directly here).

There is no proof. The speed of gravity is difficult to measure, and it hasn't been done with high accuracy. The best evidence is seen in looking at the rate that the orbits of massive bodies decay due to their losing energy to the production of gravity waves. These measurements strongly suggest that the speed of gravity is within a few percent of c (c being the actual value predicted by GR).

[hstarbuck]

Thanks guys. Good for now.

[RJN]

This is a very interesting but (another) deceptively deep topic. One reason I find it so interesting is because ordinary dust particles orbiting the Sun see, through the finiteness of the speed of light leading to aberration, the Sun slightly ahead of them, so that light pressure actually slows them down. So why doesn't this work for gravity as well? It indeed does not, and a good overview of limits on the speed of gravity is given in Wikipedia here: http://en.wikipedia.org/wiki/Speed_of_gravity . The researcher Steve Carlip has done a lot of good work on this one, and a readable write-up of some of it is here: http://math.ucr.edu/home/baez/physics/R ... speed.html.

However, one concern I have about this I still have (not that anyone cares what I think) is that it is usually assumed inherently that real energetic gravitons would move at that same "speed of gravity", and I haven't closed that mental loop yet in my mind's eye.

[Chris Peterson]

However, one concern I have about this I still have (not that anyone cares what I think) is that it is usually assumed inherently that real energetic gravitons would move at that same "speed of gravity", and I haven't closed that mental loop yet in my mind's eye.

I don't understand. Are you concerned that gravitons are predicted to move at c, or that by looking at gravity as particle mediated we should see the same sort of aberration seen with light?

[neufer]

This is a very interesting but (another) deceptively deep topic. One reason I find it so interesting is because ordinary dust particles orbiting the Sun see, through the finiteness of the speed of light leading to aberration, the Sun slightly ahead of them, so that light pressure actually slows them down. So why doesn't this work for gravity as well? It indeed does not,...

One shouldn't confuse the aberration of light with the direction of horizontal field lines.
Special relativity affects the strength of horizontal field lines but NOT their direction.

http://en.wikipedia.org/wiki/Relativist ... omagnetism

A view of the electric field of a point charge moving at different velocities

Only accelerations change the direction of horizontal field lines.

[RJN]

Chris: My worry that just because real gravitons are experimentally constrained to move near c, that it necessarily follows that gravity -- virtual gravitons in a QM formulation -- must also move near c. So I don't see a binding connection between the real and virtual. One might exist, but I can't make the logical connection in my mind just now.

Art: I'm still working on that one. Offhand, it seems to me that special relativity necessarily causes vectors in one frame to appear at a slant in a frame moving with respect to that frame.

[neufer]

Art: I'm still working on that one.

Offhand, it seems to me that special relativity necessarily causes vectors in one frame to appear at a slant in a frame moving with respect to that frame.

That's why I explicitly stated "horizontal" field lines such those that might affect a circular orbit.

There seemed to be impression left that "horizontal" field lines might somehow
be relativistically slanted in the fashion of incoming photon trajectories.
This is NOT the case for either gravitational or electrical forces.

(Note: even accelerations between two orbiting bodies would all be along the radial direction
and, hence, could not affect the "horizontal" field line direction.)

[RJN]

I don't really understand what you mean by "horizontal". Take the Earth moving around the Sun (but give it back later). Is the direction the Earth is moving at any one time "horizontal", or is the direction toward the Sun "horizontal"?

[neufer]

I don't really understand what you mean by "horizontal". Take the Earth moving around the Sun (but give it back later). Is the direction the Earth is moving at any one time "horizontal", or is the direction toward the Sun "horizontal"?

Assuming the Earth moves in a circular orbit the relative earth/sun motion is "tangential"
whereas the radial direction between the earth/sun is "horizontal" to this motion.

Electromagnetic photons from the sun onto the earth appear (from the earth)
to propagate from the forward direction thereby slowing down the earth's orbital motion.

However, gravitational forces undergo no sort of aberrational effects and are always purely radial.

Chris should probably not have even brought up the concept of aberration in this regard.
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P.S.: I'm going to keep the Earth moving around the Sun.