# Does Gravity Warp Coulomb's force?

Does gravity effect the "sphericalness" of the Coulomb force?

For example, is the field 1 meter above a charge weaker than the field 1 meter below the charge?

Could a 0.014% difference in the field be detected?

Have there been any such experiments run?

Edit:

In answer to firtree's question below, I am working on the admittedly heretical idea that the "curvature of space" is actually the flow of space into a massive body and as such space is flowing into Earth at 11km/s at its surface (its escape velocity).

At the moment, I'm trying to develop a model for length contraction. Using the notions of perturbation theory and $r=ct$ one could perhaps reformulate Coulomb's Law: $$F(r)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi r^2}$$ as: $$F(t)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi c^2t^2}$$ Time moving against the flow: $$t_u=\frac{d}{c-v}$$ and with the flow: $$t_d=\frac{d}{c+v}$$ The 0.014% comes from comparing the force for the two times plugging in $d=1$ and $v\approx11,000$ m/s

However, as the calculation of length contraction illustrates, the actual effect is dependent on the two way speed of light. And aside from that, if things actually worked this way it would seem to violate Newton's 3rd law. But, I just wanted to get a sanity check and see if there were any experimental (or theoretical) results related to this.

• For clarification, are you looking for a super-precise answer involving general relativity, or are you just looking for an answer that assumes that Newtonian gravity is accurate enough? Aug 22 '14 at 3:50
• @RedAct I believe that if this were the case, it would violate Newton's 3rd law. I'm basically just looking for a sanity check to see if 1: such an effect would be detectable and 2: if such an attempt was made to detect it and 3: that such attempts always returned a null result. -- Also, I'm not looking for a super precise answer, but definitely I'm thinking in the context of GR. Aug 22 '14 at 4:37
• In GR it surely does. But where does the figure 0.014% come from? GR effect is orders of magnitude smaller. Aug 22 '14 at 9:41
• @firtree I edited the details into the question. Aug 22 '14 at 10:24
• I know of no such experiments, and I think 0.014% difference would be noticed very early, perhaps in 19th century. The precision of experimental check of Maxwell's equations is much higher. And this heretical idea (in no way new) is cut off by many other checks, much earlier than discussing Coulomb force. Are you familiar with GR? If so, Maxwell-Einstein equations in static grav field are the same as $\varepsilon/\varepsilon_0=\mu/\mu_0=1/\sqrt{g_{00}}$ where $g_{00}\approx 1+2\phi/c^2$, $\phi$ being Newtonian grav potential and $\phi/c^2\sim 10^{-9}$ near Earth. Aug 22 '14 at 11:31