On Apr 19, 5:52 pm, Owen Duffy wrote:

....

I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond that
point, each unchanged, mustn't they? If that is so, the waves must be
independent, but the resultant at a point is something separate to each
of the components and doesn't of itself alter the propagation of either
wave.

Owen

Hi Owen,

I've seen it written, by a well-respected expert on antennas, that
electromagnetic fields may be viewed in either of two different ways.
Are there more than two, other than minor variations on the theme?
I'm not sure. The two I know from that author are that (1) fields are
real physical entities, and (2) that fields are merely mathematical
abstractions to help explain our observations: in the case of
electromagnetic fields, that acceleration of a electron results in
sympathetic motion of free electrons throughout the universe. It
seems to me that in either of those cases, the result of fields from
multiple sources, in a linear medium, is always the sum of the fields
from each of the sources independently. That is practically the
definition of linearity, is it not? It does not depend on us putting
something there to detect the field, or to test if the mathematical
model is correct. Certainly if we were watching waves in water, we
could see lines along which there was cancellation, where the water
would not be moving. But even if the fields are merely a mathematical
abstraction, then I still know where they sum to zero. The utility of
a mathematical abstraction to practical folk, of course, is that it
can accurately predict the behaviour in the physical world. So if
fields are just an abstraction, I can still use them to predict where
I can place a wire that's in the sphere of influence of two or more
radiating sources, and have the electrons in that wire unaffected by
the sources (because those theoretical fields canceled there). On the
other hand, if my field theory is describing something physical, if
fields are entities apart from (but inexorably linked to) the motion
of electrons, then it seems that whether we are able to observe those
fields directly or not, their cancellation is real. That does assume
that we've correctly deduced the nature of those fields, I suppose, so
that our model does say what's going on in that physical medium we can
only probe with our free electrons.


Cheers,
Tom