Also, van der Waals forces are supposedly a result of the Casimir effect.

Here's what I don't understand. Supposedly, an accurate solution to the Schrödinger equation - without a quantized field, but rather with instantaneous coulomb forces, does give vdW forces as a long-range electron correlation effect. (This is a important problem in DFT, where most correlation functionals are local and do not reproduce vdW effects)

Would someone more versed in QED care to reconcile this for me?

My working assumption is that that vdW forces are reproduced, but only approximately, with 'c=infinity' then. In which case I'm wondering: How good is that approximation?