On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following
With the success of special relativity it became apparent that the Newtonian theory of gravity, which had been so successfully applied to the mechanics of the solar system for almost 300 years, could no longer be exactly correct. The Newtonian gravitational interaction is instantaneous. The gravitational force $\vec{F}_{12}$ on a mass $m_1$ at a time $t$ due to a second mass $m_2$ is given in magnitude by \begin{equation} F_{12} = \frac{Gm_1m_2}{|\vec{r}_1(t) -\vec{r}_2(t)|^2} \end{equation} where $\vec{r}_1(t)$ and $\vec{r}_2(t)$ are the positions of the masses at the same instant of time. But in special relativity the notion of simultaneity is different in different inertial frames. The Newtonian law of gravity could be true only in one frame, and it would then single out that frame frome all others. The Newtonian law of gravity is thus inconsistent with the principle of relativity.
Two Questions:
- Did physicists immediately realize Newtonian mechanics was incorrect after special relativity was published? Was this like a "nail in the coffin" so to speak or was Newtonian gravity already suspect to begin with? I remember reading that perihelion precession of Mercury was known well before SR was theorized. So is Hartle's account the way it developed historically or is this an example of after-the-fact distortion of what happened because that's how we think of it now?
- Did physicists draw the same conclusion about Coulomb's law? If so, what did they replace it with? Maxwell's equations and the Lorentz force law? Is this part of why Maxwell's equations are so coveted?