kostik

I found some Internet discussion of this topic under "gravity magnetism". Apparently the fact that charge comes in two types, + and -, is indeed what causes the theories to split. If you bring three charges together, at least two of them must repel each other, unlike gravity. One web site expounded that if you try to carry out the formulation for Maxwell's equations based on gravity you would end up with a formula for gravitational radiation that carries away negative energy, which is impossible.

My question is more straightforward and really just about the mathematical development of the theory, not philosophical. If the magnetic field and Maxwell's equations are derived SOLELY from Coulomb's law plus special relativity, then why don't we end up in exactly the same place with respect to gravity? Why doesn't a test-mass experience a velocity-dependent perpendicular force near a "current" of mass, analogous to the Lorentz force law? The only difference between Coulomb's and Newton's laws is that the force can be attractive or repulsive, whereas in gravity the force is always attractive. I suspect that must be the factor that somewhere causes the theories to diverge .... but it's not obvious exactly where it happens.

In the theory of electricity and magnetism, which follows from Coulomb's inverse square law, the magnetic field and force arises from moving charge due to considerations of special relativity and different moving frames of reference. Therefore, since Newton's and Coulomb's laws are identical in form (both inverse square), with the exception of the constants involved, and the fact that Coulomb's law allows for charge and force to have the same or opposite signs, why is there NO analog to magnetism in the theory of gravity? Why doesn't a moving mass (or "mass current") give rise to another velocity-dependent force on a nearby test-mass, as a moving charge does to a nearby test-charge? Why do Maxwell's equations have no analog for gravity, when the fundamental laws - Coulomb's Law and Newton's law - are identical in form?