How can it be proven that a magnetic field is not an emission of a magnet using physics terminology and concepts? I need to prove that a magnetic field is not an "emission" by unpacking the word emission to legitimize a solution. I've had people answer this by saying a magnetic field is not an emission because the magnet is not losing mass (or matter?), but I was hoping someone could further elaborate on this concept or offer another explanation.
 A: lets start with definitions:
I choose 2a from webster for emissions:
2a : something sent forth by emitting: such as
(1) : electromagnetic radiation from an antenna or a celestial body
(2) usually emissions : substances discharged into the air (as by a smokestack or an automobile engine) 
The definition of a field in physics:
In physics a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time
Let us take the electric field:

Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge, by an infinitesimal test charge at that point.

So the field is a mathematical mapping describing the behavior a charge would induce on an infinitesimal test charge.  Missing the test charge, the field is just real numbers organized in vector form mapping the charge under study onto real numbers as a function of (x, y, z). 
By construction the electric field is a mathematical map because nothing is emitted, and nothing happens unless a test charge is introduced.
The magnetic field is in the same manner a mathematical map of a magnet, which will predict the interaction of the behavior of an infinitesimal test magnet.  Without the test magnet, it is just real numbers organized in vector form.
These electric and magnetic maps can be fitted with the equations of classical electrodynamics, but that is another story.
A: A radiation field would be an emission. My guess is that the question aims for a proof that no energy is transported by the field so the Poynting vector is zero everywhere.
