Richard,

As often happens, I don't think we're fully communicating.

Richard Clark wrote:

I presume by your response that it affirms my description. Moving on
to your comments, it stands to reason that the reduction of the
argument proves you cannot build an antenna with directivity within a
very specific constraint - the null space. As there is zero dimension
on the axis that connects the two sources, then no directivity can be
had from a zero length boom as one example. Other examples would
demand some dimension other than zero along this axis is where I see
the counter-argument developing.

In the two antenna example, the null space is a plane. Since the plane
is infinite in extent, you can create in that plane an antenna with a
boom of any length, and therefore with arbitrarily high directivity.
However, if you restrict that antenna to lie entirely in the null plane,
that directivity won't be in a direction such that the antenna will
favor one radiator over the other. Therefore it can't tell if the null
plane is simply an area in space with no field, or whether it's the
result of two superposing fields. And I believe this is true for any
antenna, of any size, orientation, or design that you can construct
which lies completely in that plane.

This then suggests that there is something special about null space
that is observed no where else. That is specifically true, but not
generally. What is implied by null is zero, and in a perfect world we
can say they are equivalent. Even a dipole inhabiting that null space
would bear it out, whereas an antenna with greater directivity along
that axis would not.

But I'm claiming you can't get directivity such that you can favor one
radiator over the other, by any antenna lying entirely in the null
space. In other words, any antenna you build in that null space will
detect zero field. The special thing about null space is simply that
it's a limit, and it makes a good vehicle for illustration because we
can more easily distinguish between nothing and something than between
two different levels.

However, if we open up the meaning of null to mean a point, or region,
within which we find a minimum due to the combination of all wave
contributions, then I would say a directive antenna is back in the
game, and that it exhibits Owens proposition (if I understand it - but
I still need to see Owen's elaboration).

I'll extend my hypothesis to include all such regions. Create a null
space or region of any size or shape by superposing any number of waves.
I claim that any antenna, regardless of size or design, lying entirely
in that space or region will detect zero signal. In fact, no detector of
any type which you can devise, lying entirely within that null space or
region, will be able to detect anything or otherwise tell the difference
between the superposition and a simple region of zero field. It will
take only a single contrary example to prove me wrong.

Roy Lewallen, W7EL