I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space:
When you actually see an electron trapped in a little electron trap, what's really going on, is that the cloud of amplitude distribution that includes you and your observed universe, can at least roughly factorize into a subspace that corresponds to that little electron, and a subspace that corresponds to everything else in the universe. So that the physically real amplitude distribution is roughly the product of a little blob of amplitude-factor in the subspace for that electron, and the amplitude-factor for everything else in the universe.
...which looks sensible enough, but I cannot figure out what is actually meant by this configuration space; specifically, what is the identity of an individual point in that space?
A simplified picture - mentioned in the above article - tells us that an individual point corresponds to something like "a photon here, a photon there (etc., for every photon), an electron here, an electron there, etc. for every species of elementary particles". But this can't be quite right: if an electron corresponds to a blob of amplitude in the configuration space, a single point in that space can't correspond to a position of this blob... and besides, what would a dimension of that space even be, since the number of particles in the universe isn't fixed.
An "explanation" offered in the article is as follows:
A single point in quantum configuration space, is the product of multiple point positions per quantum field; multiple point positions in the electron field, in the photon field, in the quark field, etc.
But what does this actually mean?
As I'm given to understand, in quantum field theory one has a wavefunction(al) defined over all configurations of a specific field, so if one jumps over to the real world where space-time is filled with many fields, is it possible to speak of the quantum configuration space over which the universal wavefunction is defined as a space where every point corresponds to some configuration of every quantum field, and if so, can this picture still be used to see an electron as a roughly independent part/blob of this giant amplitude distribution or not?
I've been gnawing at this for two days now and I'd really appreciate some help here...