Andy Resnick said:
The question isn't really a scientific question. Magnetism is a well-defined phenomenon (materials either possesses a magnetic moment or are induced to develop a magnetic moment), but the concept 'magnetic field' is an artificial ('man-made', excuse the gender specificity) construct.
In my opinion, asking questions is naturally scientific. Claiming a question is "not scientific" sounds ignorant.
Andy Resnick said:
Farady introduced the concept of 'fields' as a way to explain action-at-a-distance, but it wasn't appreciated until later than using the idea of a field gives independent meaning to B (and E), independent of the sources.
Field is not a concept, it's a label, it's a name given to something to explain its effects and not itself. The "field" always depends on the source and can never be manipulated without manipulating the source because we don't know what it's made of.
Andy Resnick said:
Rather than asking "what is the magnetic field made of", a better question is to ask "what are the measurable properties of the magnetic field?". Some of the properties include energy, flux, and angular momentum. Based on this, a reasonable object used to represent the magnetic field is a vector field.
Things that you mentioned all are effects of a magnetic field. We also know the source creation of a magnetic field. But we don't know what it is exactly.
A good analogy would be, we know wind flow can turn a wind turbine, and we know wind is generated by thermal/pressure gradient in the air. We also know that wind is made out of a mixture of gas molecules exchanging thermal energy and kinetic energy between the source and the turbine.
But what can we say about the magnetic field. What are the carriers of the magnetic field?
Andy Resnick said:
Photons can also be described in terms of a vector field, and so the magnetic field can be described in terms of photons.
Can you cite a reference for your statement, that the magnetic field is made out of photons, or the magnetic field interaction with a charged particle is through photon interaction with the charged particle?
The thing is unlike matter, where we deeply focused on its constituents and we have formulated different theories down to quarks, we stopped thinking about the magnetic field or fields in general because the current theories work and we haven't had a need to study their nature further but rather focused on their effects on other things.