When a physicist studies Qunatum Mechanics, he knows that on the macroscopic scale, QM will behave like classical electromagnetism.
Why do you say this? Quantum Mechanics in the classical limit does not become classical electrodynamics. How could it? QM is non-relativistic. Classical electrodynamics is relativistic. QM in the classical limit becomes classical (Newtonian) mechanics.
I admit I haven't studied QM, but I believe that it's relativistic. Maybe you have confused General Relativity with Special Relativity? QM is incompatible with GR, but I think it's based on SR.
Well, it isn't, and no, I haven't confused General with Special Relativity, trust me on that :) Maybe you confused Quantum Mechanics with Quantum Field Theory?
Why do you say this? Quantum Mechanics in the classical limit does not become classical electrodynamics. How could it? QM is non-relativistic. Classical electrodynamics is relativistic. QM in the classical limit becomes classical (Newtonian) mechanics.