I've only just got around to reading the OP of this topic and it's very interesting. I wish I'd read it earlier. The part about Gaede's rope theory seems to be what has most exercised the contributors after the initial post. But the original quote from Eddington, pointing out that the finite speed of the propagation of the gravitational force would result in a couple, or torque, in the interaction of two gravitating bodies is interesting and, I think, deserves thinking about. I may have missed it, but I don't see anywhere where anyone in the subsequent posts has done so.
A "couple", of course, means two forces acting on different points in a physical system and pointing in different directions, resulting in angular acceleration. So, in a classical Newtonian consideration of gravity it's correct to say that, in order for conservation of momentum to work, gravity has to be assumed to propagate instantly. Of course the same is true in electromagnetism because the electromagnetic force doesn't propagate instantly. But, in the case of gravity, the equations of General Relativity ensure that the gravitational force of the Sun on Jupiter points towards the point where the sun
will be.
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Going back to the subjects onto which the posts drifted after the OP. I think this, from, Xris is interesting to examine:
It's like dropping a thousand pebbles in pond and expecting to get a clear image of each stone from the resulting complex wave formation. This is not even asking how a wave can be transmited without a medium or if a medium exists why we have not found it.
If you wanted to, you could in fact, with a bit of trouble, do that experiment and demonstrate that you can indeed get a clear "image" of each stone. Your best bet would be to make a water-wave equivalent of a pinhole camera.
As you said, there are so many waves travelling around in so many directions at the same time that if you simply consider those waves as they are, you won't get any image at all. That's why when you hold up a white sheet of paper to your window you don't get an image of the world outside on the paper. You get uniform whiteness - lots of light from all over the scene outside simultaneously hitting every point on the paper. To get an image, you need to filter out almost all of those light waves. That's what a pinhole camera does. Place the piece of paper in a light-proof box with a small hole in the end and you
do get an image. Because you create a single one-to-one path between each point in the scene and each point on the paper.
Do a similar thing in your pond, ensuring that the size of the hole is comfortably bigger than the wavelength, and you'd get clear "water wave rays" corresponding to each pebble.