The force of attraction between two particles depends on the mass of each particle. But does the force of attraction of a particle actually depend on the mass energy of the particle? If yes many things will change in physics!
There certainly is a relation, since the elementary particles are the only carriers of mass and charge in the universe.
For example the rest mass and the charge of the electron were confirmed in 1913 to be both invariant.
Consequently, the mass of any stabilized assembly of charged and massive elementary particles can only be the sum of the masses of the elementary charged and massive elementary particles of which they are made, starting with the atoms, then with the larger masses made of these atoms.
Now, let's imagine that we can vary the mass energy, is it possible for the gravitational force to vary?
Einstein said that the mass of a body becomes infinitely large if its speed increases to about the speed of light. Does the Lorentz factor become meaningless here? What about the mass energy? Does a body mooving at about speed of light could its mass energy vary?
particles can be described as built by a confined quantized field as I have shown (my first book). Gravity acts on the energy content just as it does on photons (bending of light).
I have constructed a relativistic version of newton gravity based on this picure. Predictions come out just right I could mention (bending of light, perihelium shift).
If you convert the photon into an equivalent mass the bending comes out wrong with Newton gravity.