I am very new to quantum field theory, so forgive me if this question is a bit silly. The Casimir force is usually explained by the zero point energy of the field. You assume that the frequencies of the field are quantized between the two plates, perform some regularization, and out pops, for the electromagnetic field, $$F=-\frac{\pi^2\hbar c}{240a^4}A$$ where $a$ is the separation and $A$ is the area of the plates. However, what if we have multiple fields? For an ordinary scalar field, I believe the Casimir force for that only differs by a factor of $2$ (due to the polarizations of light), so we have $$F=-\frac{\pi^2\hbar c}{480a^4}A$$ In a world with both of these fields, I'd assume the total Casimir force would be their sum of each contribution. In the real world, we have a bunch more fields than just the electromagnetic one (including a scalar Higgs field)! I would assume that each of these would produce a Casimir force in the same manner as the scalar field and the electromagnetic field, and that the total Casimir force is their sum. However, we only measure the Casimir force due to the electromagnetic field. Why is this? Is there a flaw in my reasoning?