Lorentz, in the work quoted, found it necessary to complete his hypothesis by assuming that all forces, whatever their origin, are affected by translation in the same way as electromagnetic forces and, consequently, the effect produced on their components by the Lorentz transformation is still defined by equations (4).Newton proved that an inverse square law of gravity gives elliptical orbits, assumed instantaneous transmission of the force. Laplace proved that if the propagation speed were at the speed of light or slower, then Newton's proof would be wrong, and planetary orbits would not be like what we observe.
It was important to examine this hypothesis more closely and in particular to examine what changes it would require us to make on the law of gravitation. That is what I sought to determine; I was first led to suppose that the propagation of gravitation is not instantaneous, but happens with the speed of light. This seems at odds with results obtained by Laplace, who announced that this propagation is, if not instantaneous, at least much faster than that of light. But in reality, the question posed by Laplace differs considerably from that which occupies us here. The introduction of a finite velocity of propagation was the only change Laplace introduced to Newton's law. Here, on the contrary, this change is accompanied by several others; it is possible, and that is indeed what happens, that a partial compensation occurs between them.
When we therefore speak of the position or velocity of the attracting body, it will be the position or the velocity at the time when the gravitational wave leaves the body; when we talk about the position or velocity of the attracted body, it will be the position or the velocity at the moment when this body was reached and attracted by the gravitational wave emanating from the other body; it is clear that the first instant precedes the second.
Poincare proved that in a relativistic theory of gravity, the forces can propagate as gravitational waves at the speed of light, and we would still have nearly elliptical orbits matching astronomical observations.
Poincare was completely correct. He was a decade ahead of everyone else.
To the relativity pioneers, Maxwell, Lorentz, and Poincare, local causality is at the core of the theory. Finding a way to resolve Laplace's paradox was crucial to establishing a causal and relativistic view of nature.
I am not sure that Einstein ever had good understanding of relativistic causality. He kept flip-flopping on gravitational waves, and on causality in quantum mechanics.
A couple of weeks after Einstein's library received this paper, Einstein submitted his own relativity paper, which was primarily a recapitulation of Lorentz's electromagnetic theory.
Einstein historian Galina Weinstein just posted:
Around 1936, Einstein wrote to his close friend Max Born telling him that, together with Nathan Rosen, he had arrived at the interesting result that gravitational waves did not exist, though they had been assumed a certainty to the first approximation. He finally had found a mistake in his 1936 paper with Rosen and believed that gravitational waves do exist. However, in 1938, Einstein again obtained the result that there could be no gravitational waves!Einstein did not find the mistake himself. He submitted it to a journal and a referee explained the error, as Lumo explains.