Does one need to invoke quantum mechanics to explain Casimir or van der Waals forces? I see that textbooks show derivations of van der Waal forces with no QM but the Casimir force is typically described within QM.
Additional questions I have are: Is there a difference between van der Waals and Casimir forces? Are there distinct examples of these two forces in real life? Is there a way to prove a given force is van der Waal and not Casimir or vice versa?
The Casimir effect and the Van der Waals force between two conducting plates are one and the same thing.
To see this, consider the boundary conditions postulated for the Casimir effect. The electric field has to be exactly zero at the plates. Because of this, it is said, the zero point energy of the vacuum is lower in between the plates than outside, which causes the interaction. But these references to the vacuum and virtual particles are mere heuristics. What does it mean for the electric field to be zero at the plates? The charges in the plate will have to redistribute and polarize the plate to generate a corresponding field.
But the interactions between fluctuating polarizations are precisely the dispersion forces that are responsible for the Van der Waals interaction.
Thus they are two explanation of the same phenomenon.
I think people tend to equate both and present them as "alternative explanations of the same phenomenon" simply because both forces tend to have the same order of magnitude and dimensional dependency.
I haven't heard a proper argument why this should be so. Casimir is related to missing modes lowering the inter-layer vacuum pressure, while Van Der Waals are dipole-dipole interactions. So it seems to me they are different effects, which very similar behaviours in the same orders of magnitude, so probably the experimental measurements are actually subtle contributions from both.
I don't know of any practical way of discerning between both macroscopically, i would be glad to hear what others have to say on this
Here is an argument that Casimir force is really van der Waals force, and not a force that originates from vacuum energy: http://www.arxiv.org/abs/1605.04143
In short, vacuum energy originates from the pure electromagnetic term in the Hamiltonian, which does not have any explicit dependence on matter degrees of freedom and hence cannot generate any forces on matter. It does have an implicit dependence on matter degrees (the distance between the Casimir plates) originating from the solution of equations of motion, but the general principles of classical and quantum mechanics tell us that it is not legitimate to use such an implicit dependence to calculate the force.
