Dancing David
Penultimate Amazing
Hello.
I think Mr. Mozina might be a bit confused regarding the origin of the Casimir effect. The effect is not due to particles bouncing off the surface of plates.
In the quantum theory of electrodynamics, each mode of the electromagnetic field is treated as an independent quantum harmonic oscillator. Excitations from the ground state of each mode are, of course, photons: the carrier particles of the EM force. However, even in the absence of photons, the electric and magnetic fields associated with each mode aren't everywhere zero, and the energy of the mode is likewise not zero. So each mode of the EM field carries energy in the absence of photons.
The Casimir force is calculated from a rather simplistic approximation. Two neutrally charged conducting plates are placed parallel to each other in a vacuum. The plates are assumed to be perfectly conducting, so the EM field must be zero on the surface of the plates. The modes of the EM field are thus functions which are sinusoidal in the space between the plates or outside the plates, but zero on the plates. Configurations with different distances between the plates result in different possible modes, and thus different energies. In fact, closer plates result in lower EM field energies, so the plates experience an attractive force.
The Casimir force is due to what is happening between the plates, and not what is outside of them. They are being pulled towards each other, not pushed. That is why the pressure between them is considered to be negative, as opposed to a vacuum-sealed container which is held together by the positive pressure of the Earth's atmosphere.
The Casimir effect itself might be confusing, and it seems the reason it was brought up (sorry if I'm mistaken in this; I'm too lazy to read all 14 pages of the discussion) was because of difficulty in understanding the concept of negative pressure. A simpler example, I think, would involve a capacitor carrying charge. The two parallel capacitor plates carry opposite electric charges and are attracted to each other. This force is the Coulomb force (which can be attributed theoretically to the exchange of photons), and it is attractive: it results in the plates being pulled towards each other, and is not due to the plates being pushed together by particles on the outside. So the plates experience a negative pressure from the Coulomb force, which is usually counteracted by the positive pressure of a dielectric keeping the plates apart.
Hopefully this can clear at least a little bit up for Mr. Mozina.
Welcome. Great post.