According to A. Einstein, gravity and inertia are two different words for the same phenomenon. Great scientists intuitively feel objective truth, but sometimes they cannot reveal its content. This is only really quantitatively true with opposite signs.
Even the most ardent opponent of the theory of relativity and, in essence, its author, A. Einstein, is forced to admit, listening to the radio or watching TV, that moving electrons in the transmitter antenna still emit something. It would be better not. Then it would be possible to speak more persistently about ether, a special vacuum, unknown fields, strings, etc. But antennas emit electromagnetic waves, the carrier frequency of which is quanta . That is, a moving electron emits quanta that make up photons . Photon is part electron .
The mass of the electron has long been known. Although a quantum is a very small part of an electron, it is still mass. And we are not yet able to catch this mass. Moreover, it was transformed, or rather, turned around, into another phase - electromagnetic radiation. Try to measure the mass of a droplet of evaporated water, without using a closed volume during evaporation. It's complicated. It is also difficult to measure the mass of an unfolded quantum or even a photon, which can be much larger than a quantum.
The emitted photon, thanks to this mass, has an impulse. This momentum is transmitted to the emitting photon electron. A reactive force is formed due to a decrease in the mass of an electron. The electron resists the force that is trying to set it in motion. This is inertia .
"Well ..." - scientists and non-pundits will say - "Some kind of photon, yes, resists the force ... This cannot be." Please note, we do not know for certain how an electron generates a photon. It is possible that a photon acquires a light speed even when it is detached from an electron, and at such a speed even a small mass can have a large momentum.
And indirect signs, how a small mass generates large forces? The explosion of one kilogram of uranium moves mountains, and only about 5% of this uranium is split there. And all this work is done to a greater extent by photons, and not by alpha and beta particles. And the rods at nuclear power plants? Each rod with its internal energy can transport millions of the same rods for thousands of kilometers.
Each visible mass contains, God knows, how many electrons. The sum of the emitted photons and creates inert resistance.
Thus, an obvious situation arises. By applying force to the body, that is, by accelerating it, we make it emit photons. Picture 1.
If bodies A and B are represented by electrons, then the forces F and F1 will be equal only if the impulse of the pushing force is the impulse of the emitted photon. And this is not always possible. It may be that the pushing force is not enough to excite an electron to emit a photon, and then there is no inert mass. There is mass as an equivalent of energy, but it does not provide inertial resistance. You can read about this in the article "Impact of force on an electron"
It just so happened in nature that a photon of the same energy creates the same reactive force both in the mode of decreasing mass, and in the mode of increasing mass. For this reason, the inert and gravitational masses are the same. That is, in the ratio Fg=mg , the amount of absorbed photon energy in this action is equal to the amount of emitted photon energy in the ratio F a = ma .
But this is an ideal case when F g = F a . But in fact, these forces may differ slightly, at least by one photon. Naturally, we will not be able to catch this difference.