The strict particle model proposed in my book has energy stored as size of subatomic particles. All energies, regardless of type, are stored as size.
When lifting a wood block from the floor up to a shelf, the size of subatomic particles in the block increase by a tiny bit. The same is true when throwing the block through the air. However, dropping the block results in no change in size, because the sum of potential and kinetic energy remains unchanged during the fall. There is no change in the total energy of the block before it hits the ground.
An alternative to this model is to have potential energy stored in the field between the block and the ground, and kinetic energy stored as motion. Lifting the block from the floor will in this model put potential energy into the field. Dropping the block will result in a transfer of potential energy stored in the field to kinetic energy in the block, with gravity facilitating this transfer.
The problem with such a field theory is that it is all pure math, with no simple mechanism to explain it.
However, the advantage with a field theory is that once we accept the idea of energy stored in a field, we have a ready supply of energy to draw on whenever needed.
This comes in handy when we are confronted with such phenomena as gravitational red-shift.
When light travels away from a massive body, it looses energy. When it travels towards a massive body, it gains energy. This is experimentally confirmed, and requires an explanation.
Photons passing by, moving towards and moving away from a massive body
Using a field theory, we can simply say that photons give up energy to the field when they travel away from massive bodies, and that they absorb energy from the field when they travel towards such bodies.
However, a strict particle model cannot use such an explanation, because no energy is stored outside of particles. When particles gain energy, other particles must loose energy. There has to be interaction between particles.
The way to solve this problem, using a strict particle model, is to invoke the aether.
When we combine the aether with the idea that a pilot wave accompanies every photon, we can imagine a mechanism for energy transfer between the aether and visible light.
Zero-point photons, abundantly available in the aether, readily soak up any excess energy of an outgoing visible photon. The red-shift of outgoing photons are facilitated by a corresponding blue-shift of incoming zero-point photons.
Conversely, blue-shift of incoming visible light is facilitated by the red-shift of outgoing zero-point photons.
Note that there is no need for any direct contact between the photons for the energy transfers to happen. As long as the pilot waves associated with each photon brush against each other, energy can be transferred.
Note also that this explanation has as a consequence that the aether is somewhat “hotter” close to massive bodies than farther away. The stronger the gravitational field, the more blue-shifted is the aether close to the surface of the body in question.