Are there any well-known theories successfully unifying the inertial and gravitational mass?

Question

From what little I know of general relativity, the equality of inertial and gravitational mass is an axiom of the theory. I suspect that this precludes GR from unifying them in the same sense as electric, magnetic and weak interactions are unified as the electroweak force.

But since the two appear to be equal under staggeringly precise measurements, there must be some interest in constructing a theory of mass and motion which fundamentally unifies the two, that is, makes the separation nonsensical / impossible.

Are there any particularly outstanding attempts in this regard, even if the resulting theories are known to fail to correspond to our universe in some other important way?

Answer 1

The equivalence of gravitational and inertial mass is one of the ideas that inspired general relativity, but it's not an axiom of the theory. Instead, it's a consequence of the interpretation of gravity as spacetime curvature. You could say that GR was designed from the ground up such that the equivalence principle would come out of it.

Given the success of general relativity, there hasn't been much of any effort devoted to finding an alternate explanation for the equivalence principle.

Answer 2

You have to consider that both inertial and gravitational mass are the same because you are assuming that the body or the particle is going to behave under the accelerating process in the exact same way!

So the particle will not be able to change it´s velocity or state diffently in both situations. Despite of what is causing the acceleration, you have to remember that the particle is going to perceive that something is trying to give it cinetic energy and the rate of this flux is exactly the same in both situations.

In one hand you have a force, providing work that is immediately converted to cinetic energy and in the other hand you have a curved spacetime that is converting potential to cinetic energy and also changing it´s own potential energy during the process(that´s why General Relativity is so complex, it´s a non-linear field).

Math can be very tricky when dealing with physics, since we can begin to treat concepts "as it is" and stick with it.

So there is a lot of effort experimentally but theoretically it´s an assumption, a postulate. So it costed tons of dollars in experiments trying to disprove it(surelly it´s a nobel prize situation) but theoretically it´s just speculation trying to construct general relativity changing the weak and strong equivalent principle.

You will have to consider a different scheme to couple coordinates (Christoffel Symbols) and consider that the Riemann curvature tensor is not equal to zero, something that will imply a new type of structure for space-time in local frame. Considering that the whole theory will throw you to divergences, probably everywhere, from ultraviolet spectrum to strange space-time dilatations and etc...