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With regard to E&M fields . . . in the static case the field concept
certainly makes little difference. One can work directly with Coulomb's
law and get the same answers. So I suppose in the static case you claim
the field is just an mental construct that aids in problem-solving.
It _sometimes_ aids in problem solving
But
when we consider charged particles in relative motion, we must treat the
field as real property of the space surrounding the charges in order to
account for the forces that act on the charges.
We may _choose_ to treat the field as a "real property" and follow the
likes of Bill Nye, but look! If it is a "property" of the system it
follows that it is not "real." The system may have the property of "blue"
but "blue" isn't "real" -- You can not get a bucket of blue. Blue paint
yes, but not the property of blue. We often have this discussion re the
property of "energy" -- Show me a bucket of "energy."
If E&M fields are not
real-- just as real as the charged particles they affect-- how do we
account for the finite propagation speed of the information of each
particle's location as seen by all the other particles?
We discover how things really are -- perhaps strings, perhaps other
discoveries -- but we don't wave our arms and claim we understand e/m
propagation by invoking an invention and claim we have discovered a bucket
of "field".
And how do we account for the propagation of light in empty space if the
fields are not real things? Isn't light a real thing?
Ah yes, you tell me what "light" is and then maybe someone can answer this
question.
Jim