Relating Quantum Mechanics to Classic Electromagnetism I've been directed to a few articles, and I am sure there is a related post, but can someone explain the procedure by which we can view classic electromagnetism through quantum mechanics? Indeed we need to be able to look at any field as an ensemble of particles (photons), but how can we develop classic field theory assuming quantum mechanics? 
 A: I think the fundamental problem that many people have with quantum mechanics is, that is seems to be about particles, when, in reality, it is about quanta. A quantum is not the same thing as a particle! 
A quantum is the exchanged amount of physical quantities between two parts of a physical system. That can be a quantum of energy, a quantum of momentum, a quantum of spin etc.. Quanta do NOT have to be discrete amounts (e.g. integer multiples of a unit). The numerical amount of the quantum of energy exchanged between an atom and a field can, for instance, be from the continuum of the atom's spectrum, in which case it is not discretized.
What is "discrete" about the exchange of quanta is the "before and after" picture. In case of quantum systems, one can't divide the events "before" and "after" into arbitrarily small fractions or time slices. It's an all or nothing kind of deal. Either the interaction has happened, or it has not, but one can't "watch" it happen halfway trough, as one can in classical mechanics. 
As a result, we are not looking at fields as an ensemble of particles. Even quantum fields are, as the name implies, "smooth" objects. What differentiates them from classical fields is, that they can only interact by exchanging their physical states in form of quanta and that we can only measure the differences between initial and final states in terms of quanta, which, in many important cases, can be interpreted as particles. What determines the physical dynamics, however, is not the individual particle that shows up in our measurement devices, but the totality of quanta that can be exchanged in the process of interest. 
