K7ITM wrote:

For what it's worth...

I've often found it useful to consider alternate ways to think about
things. In this thread, there have been some comments about electric
fields, magnetic fields and electromagnetic fields. So, I ask: how
do we measure fields? As far as I know, it's by their interaction
with matter: we observe how an electromagnetic field accelerates
electrons, for example. Do we have any way other than by observing
how a (E, M, or EM) field interacts with matter to measure a field?
If not, does a field _necessarily_ have any physical reality, any
reality beyond a mathematical model to explain what we observe?

. . .

On the first day of the first class of Electromagnetic Fields, I asked
the professor (Carl T.A. Johnk, author of _Engineering Electromagnetic
Fields and Waves_), "What is an electromagnetic field?" His answer:
"It's a mathematical model we use to help us understand phenomena we can
observe and measure." And I see that in the second paragraph of his book
he writes "A field is taken to mean a mathematical function of space and
time." I've been satisfied with that definition.

Roy Lewallen, W7EL