Atoms behave in particle accelerators like incompressible objects (roughly). When you combine atoms, you get matter which is always compressible yet the physics community treats the results from particle accelerators as though it is diagnostic of the behavior of elastic matter i.e. F=ma but is it really F=ma or is it F=ma + change in internal energy. Change in internal energy may be significant. A case in point would be to take a cylinder 10 miles long and 100 ft across filled with helium and sealed at both ends with massive plugs weighing several hundred million tons. The gravitational attraction of the two ends exactly balances the pressure of the helium gas. Now the body is accelerated at one g. What happens? At first, the helium simply compresses as the first plug is accelerated iff the orientation of the plug is suitable. In other words, if the tube is on its side, the gas is not compressed. With the correct orientatation i.e. parallel to the long dimension of the the tube, then gas pressure builds up and the temperature increases according to the formula PV=nrT. At some point in the compression, the pressure exceeds the static pressure and the second plug is briefly displaced forward faster than g. Oscillations occur, and then subside to a stasis situation. All matter is elastic so this oscillatory phase should be common to all matter. It should not occur with incompressible objects i.e. discrete particles in a particle accelerator. It should not occur in response to gravity. In other words, if this cylinder of helium drifts into the earths gravity, will it exhibit the same properties as inertia? The answer is no because the tube in a gravitation setting is insensitive to orientation. In other words gravity will pull the exact same amount just as long as the center of mass is fixed. In fact, the tube can rotate about the center of mass in any manner and the gravitational attraction will be the same. It is clearly evident that this is not the case with inertia.
Oscillatory behavior may be an analog to earlier phases of the universe. During the expansion phase, the elastic properties of the universe caused it to give the illusion of antigravity, when, instead, it was the behavior of an elastic aether.