I don't think it's incorrect. But for constant velocities it is canceled out because the relative motion causes things to also appear in a different direction. This happens with ordinary light, also. Stars appear in a different place to us because of our relative motion (they appear to be located more "forward" in our direction of motion).
As as example, assume there is a star directly perpendicular to our motion (and that the Earth moves in a straight line). Due to the vector addition of our motion and the light travel direction, it appears to us that the star is located slightly forward of perpendicular (typically by about 1/100 of a degree) Now assume the star were to disappear. During the light travel time the star would have time to move backwards as seen by us (due to our forward motion) so that at the moment it disappears, it appears to be located perpendicular to us.
In the context of gravity, this effect (it's called aberration) exactly cancels and the net effect is that the gravitational attraction is in a direction different from the actual location of the attractor such that it appears that gravity is instantaneous.
This only works for constant velocities, once you have accelerations it becomes more complicated. And it's not a relativistic effect at all, it's present for all waves with finite propagation speeds. You can do this experiment with boats making waves and get the same result.
Edit: And your charge example is not so good. For Galilean invariant theories it's only relative motions that matter. There is no effect if the two are moving with the same velocity. (Plus, once there are relative motions between the charges, there will be induced magnetic fields which affect the dynamics.)
> And your charge example is not so good. For Galilean invariant theories it's only relative motions that matter.
E&M is Lorentz invariant though, not Galilean.
This causes an issue with your starlight aberration example as well. Velocities do not add linearly (though that is a reasonable approximation for low velocities).
As as example, assume there is a star directly perpendicular to our motion (and that the Earth moves in a straight line). Due to the vector addition of our motion and the light travel direction, it appears to us that the star is located slightly forward of perpendicular (typically by about 1/100 of a degree) Now assume the star were to disappear. During the light travel time the star would have time to move backwards as seen by us (due to our forward motion) so that at the moment it disappears, it appears to be located perpendicular to us.
In the context of gravity, this effect (it's called aberration) exactly cancels and the net effect is that the gravitational attraction is in a direction different from the actual location of the attractor such that it appears that gravity is instantaneous.
This only works for constant velocities, once you have accelerations it becomes more complicated. And it's not a relativistic effect at all, it's present for all waves with finite propagation speeds. You can do this experiment with boats making waves and get the same result.
Edit: And your charge example is not so good. For Galilean invariant theories it's only relative motions that matter. There is no effect if the two are moving with the same velocity. (Plus, once there are relative motions between the charges, there will be induced magnetic fields which affect the dynamics.)