How to Falsify Dipole Gravity?

Some readers of the dipole gravity article objected to the notion that there is a relativistic center of mass shift for a rotating hemispherical rotor by invoking Ehrenfest's paradox, which states that due to the length contraction effect of special relativity, the circumference of a rotating ring will be shorter than given by 2piR(the length of the radius will still be the same).

So the mass of the rotating ring should be the same regardless of the speed of the rotation according to their objection.

However, if we assume that the ring is made up of N number of atoms connected in series, each atoms will experience the special relativistic mass increase effect, and since the number of the atoms can not change due to the rotational motion, the relativistic mass increase effect for the whole ring(as well as for the whole hemisphere) should still be effective.

The next objection is from the simple comparison with the electromagnetic phenomenon. The electricity and magnetism has electric and magnetic dipole moment because there are two different charges in the theory of electromagnetism, ie, positive and negative charges of electricity and north and south poles of magnetism, but there is no negative mass in gravity so how can you have gravitational dipole moment?

While gravity and electromagnetism are both long range forces, they are fundamentally different forces of nature. In fact, the fact that there is no observed negative mass in the universe has contributed greatly to the notion that there should be no gravitational dipole moment in the physical world. However, general relativity in the linearized form only requires a physically meaningful shift(not the kind that can be eliminated by a coordinate translation) of the center of mass, not the presence of a negative mass for the existence of a gravitational dipole moment.

The question on why this shift implicated in the linearized theory of general relativity should be identified with the relativistic shift of the center of mass of a rotating longitudinally asymmetric object may be entirely a matter of faith. There is no reason it should be identified as such. But then there is also no reason it should not. At least it confirmed the result calculated by a different method of analytic integration performed by Lens-Thirring.

As in the Dirac's equation of the relativistic theory of positrons, a mathematical equation can be interpreted by predicting a certain new physical reality.
The entire justification of such an interpretation totally remains in its predictive power of the physical nature.

So the last resort to falsify dipole gravity remains in the test of its fundamental predictions since all the features of the dipole gravity potential have been consistent with the observed cosmological data.

Newtonian gravity started from the conceptual extension of the force that was observed from a falling apple(the real story behind will be much more complicated and deeper than can be described by such a simple story), the same force is exerted in the planetary system as well as in our daily lives. It seems clear that the massive cosmological phenomena like the jets and the dark matter problems should have a similar counter part in our daily lives so that we can observe it. Since dipole gravity is the second order effect from general relativity, its strength should be much weaker than Newtonian gravity and as such its effect will be much harder to detect in the terrestrial environment. But it is certainly within our current technological reach to test it as shown in the previous pages.

What if the test disproves the prediction?

I think it is possible, but it will ultimately mean the disproof of general relativity.