Walter Maxwell wrote:
On Sat, 07 Apr 2007 16:10:03 GMT, Gene Fuller wrote:

[snipped]

Walt,

Your observation is "correct" only in the case that most people consider
for practical reasons. The calculation showing the null behavior is
almost invariably performed at infinite distant from the sources, i.e.,
far field condition. The path from each source to the observation point
is considered to be exactly parallel.

As you know, there are usually three or more linear dimensions that
enter into radiation calculations. In the case of two sources there are
four:

Wavelength
Size of each source
Distance between sources
Distance to the observation point

In the typical "null" presentation, such as that shown in the ARRL
publications, the distance to the observation point in always large.

Lets take another case, however. Suppose the distance between the
sources is some what larger than the wavelength. Make it large enough so
there is a region between the sources that would be considered far field
from each of the sources. Now calculate the phase differences along some
direction from the center point between the sources that eventually
points to a null region in the infinite distance. Don't pick an
obviously symmetric direction, such as broadside or end-fire, as that
would be a special case.

What you will find is that when looking at the phase difference along
the ultimate null direction is that there is no such null much closer to
the sources. The paths from the individual sources are not parallel in
this case. The null "line" is actually a curve. The waves pass right
through each other in the closer region. The "passing waves" then go on
to form nulls in the infinite distance. The nulls in the closer region
are not in the same directions as the nulls in the far field.

Again, the ground rules:

Totally coherent, monochromatic sources
Fixed phase difference
Far field conditions for each source

There are no "tricks" here; this is just a matter of simple geometry.
However, it shows that the null you believe demonstrates some permanent
interaction and annihilation of EM waves is simply a special case.

In classical, non-cosmic, non-relativistic conditions EM waves do not
interact in free space. This condition is so widely understood in the
scientific world that it becomes a prime candidate for argument on RRAA.

8-)

73,
Gene
W4SZ

Gene, at this point I can't disagree with you. However, in your next to the last paragraph in your post above,
if I interpret you correctly, you are saying that all directional arrays, such as are used in AM broadcasting,
are considered 'special' cases. Is that what you mean't to infer?

Walt, W2DU

Hi Walt,

Yes, those are special cases, but those special cases are the only ones
that most people care about.

What I was trying to say might be better illustrated by the following:

Two coherent laser beams from the same source can be arranged by
suitable mirrors to intersect at some angle. There will most definitely
be interference in the region of intersection, but the beams will
continue through unchanged. If one measured a beam somewhere downstream
from the intersection region it would not be possible to determine that
it had crossed another beam earlier.

The beams "interfere" but they do not "interact". I know this sounds
goofy, and it is critical to keep the definitions straight. When I say
the beams do not interact I mean that they do not cause any changes in
the other beam. The fact that the beams interfere means that the sum of
the fields shows the characteristic constructive and destructive
behavior. It does not mean that the waves are henceforth changed.

OK, so how does this square with the observation that there are nulls in
patterns from two or more RF sources? It is actually very
straightforward. In the far field the waves from the separate sources
are virtually parallel. Just like Timex, they interfere and they keep on
interfering. They never really pass beyond the intersection region.

I know it seems like a subtle, or even meaningless, distinction. Do the
waves interfere forever or do they actually annihilate each other? For
many purposes it does not matter. However, the non-interaction of waves
in free space is pretty basic to all of EM analysis.

73,
Gene
W4SZ