One of the great advantages of a strict particle model of physics is that it requires discrete rather than continuous math to work out formulas at the limits. Instead of an infinite number of possible wavelengths, we have particles filling the void of space. The electric force, the magnetic force and gravity are all limited by a finite number of particles.
This means that we cannot end up with any infinities when calculating forces related to real objects. We cannot end up with black hole singularities of infinite density for the simple reason that there are no infinities we can draw upon in the realm of particle physics. Nor do we end up with infinite energy at the zero-point level. A strict particle model of physics has space full of particles, not wavelengths. If we add up all the energies of all the particles, we get a finite number, not the infinity that we get when adding up an infinite number of wavelengths.
When we have forces communicated by particles, we get the very interesting result that there cannot be any forces acting between objects that are so close to each other that no particle can find its way in between them. A proton attracts an electron, only when the electron is at a distance from it. An electron that is physically resting on top of a proton experiences no force. The only attraction at such an intimate distance is the Velcro-effect. This is a far cry from the infinite attraction that we end up with if we model the electric force as a continuous field.
Instead of infinities and singularities, we get zero. Coulomb’s Law breaks down. The probability of collisions in the aether between two charged objects goes to zero rather than infinity when they get extremely close to each other. Similarly, gravity will stop behaving in a continuous manner the moment we move towards extreme conditions. With no aether between the particles involved, the gravitational force goes to zero, not infinity.