Why does F=ma in Newton's Equation of Motion? How does a gravitational field produce a force? Why are inertial mass and gravitational mass the same?

It appears that all three of these seemingly axiomatic foundational questions have an answer involving an identical physical process: interaction between the electromagnetic quantum vacuum and the fundamental charged particles (quarks and electrons) constituting matter. All three of these effects and equalities can be traced back to the appearance of a specific asymmetry in the otherwise uniform and isotropic electromagnetic quantum vacuum. The key insight is that the asymmetry in an accelerating reference frame in flat spacetime is identical to that in a stationary reference frame in curved spacetime.

It was shown by Unruh and by Davies that an accelerating detector will experience a Planckian-like heat bath whose apparent ``temperature'' is a result of quantum vacuum radiation. A tiny fraction of the (enormous) electromagnetic quantum vacuum energy can emerge as real radiation under the appropriate conditions. The existence of Unruh-Davies radiation is now generally accepted and SLAC physicist Pisin Chen has recently proposed an experiment to measure it. Rueda and Haisch analyzed a related process and found that as perceived by an accelerating object, an energy and momentum flux of radiation emerges from the electromagnetic quantum vacuum and that the strength of this momentum flux proves to be proportional to acceleration. If this momentum flux is allowed to interact with matter, presumably at the level of quarks and electrons, a reaction force is produced that can be interpreted as the origin of Newton's F=ma. In this view, which we call the quantum vacuum inertia hypothesis, matter resists acceleration not because of some innate property of inertia, but rather because the electromagnetic quantum vacuum provides an acceleration-dependent drag force.

GR declares that gravity can be interpreted as spacetime curvature. Wheeler coined the term geometrodynamics to describe this: the dynamics of objects subject to gravity is determined by the geometry of four-dimensional spacetime. What geometrodynamics actually specifies is the family of geodesics -- the shortest four-dimensional distances between two points in spacetime -- in the presence of a gravitating body. Freely-falling objects and light rays follow geodesics. However when an object is prevented from following a geodetic trajectory, a force is experienced: the well-known force called weight. Where does this force come from? Or put another way, how does a gravitational field exert a force on a non freely-falling, fixed, object, such as an observer standing on a scale on the Earth's surface? This proves to be the identical process as described in the quantum vacuum inertia hypothesis.

In the SED approximation, the electromagnetic quantum vacuum is represented as propagating electromagnetic waves. These should follow geodesics. It can be shown that propagation along curved geodesics creates the identical electromagnetic momentum flux with respect to a stationary fixed object as is the case for an accelerating object. This is perfectly consistent with Einstein's fundamental assumption of the equivalence of gravitation and acceleration. An object fixed above a gravitating body will perceive the electromagnetic quantum vacuum to be accelerating past it, which is of course the same as the perception of the object when it is doing the accelerating through the quantum vacuum. Another useful intuitive picture is to imagine the downward deviation of tangential light rays near a gravitating body resulting in a net downward force, somewhat analogous to radiation pressure, on a fixed object.

Thus in the case of gravity, it would be the electromagnetic momentum flux acting upon a fixed object that creates the force known as weight, thereby answering the second question. The answer to the third question then immediately follows. Since the same electromagnetic momentum flux would be seen by either a fixed object in a gravitational field or an accelerating object in free space, the force that is felt would be the same, hence the parameters we traditionally call inertial and gravitational mass must be the same. This would explain the physical origin of the weak principle of equivalence.

All of this is consistent with the mathematics of GR. What this view adds to physics is insight into a specific physical process creating identical inertial and gravitational forces. What this view hints at in terms of advanced propulsion technology is the possibility that by locally modifying either the electromagnetic quantum vacuum and/or its interaction with matter, inertial and gravitational forces could be modified or even nullified.

See the two papers
Gravity and the Quantum Vacuum Inertia Hypothesis. I. Formalized Groundwork for Extension to Gravity
Geometrodynamics, Inertia and the Quantum Vacuum