David wrote:
The text below applies to vertical quarterwave antenna in free space with
four quarterwave radials.

In transmit mode, the field from the radials cancel out.

When the antenna is receiving, the incoming wave interacts with the radials
and is reflected into the vertical element.

No. The wave strikes the radials. This induces currents in the radials.
Those currents cause radiation, and also the currents are conducted to
the feedpoint. When the signal is coming from directions in which the
radial radiation was zero, the induced currents will add to zero at the
feedpoint, and the re-radiation will be zero in those directions.

How does this fit in with the antenna reciprocity theorem? The antenna field
arrangement is working in different ways between transmit and receive. . .

No, your concept of how it works when receiving is incorrect. That's the
cause of the apparent contradiction.

. .
In transmit mode, the radials have a standing wave on them and provide the
RF ground side by 'converting' the high voltage at open circuit end to a low
voltage (RF ground with high current) at base of antenna.

Unfortunately, your concept of how the antenna works when transmitting
is also incorrect. The radials are just as much a part of the antenna
system as the "antenna". Their symmetry results in their total radiated
field being much smaller than that from the "antenna". The notion of an
"RF ground" in space is simply a matter of your imagination; no such
thing exists.

Do the radials have a standing wave on them in receive mode?

Yes. So does the vertical. And both do in transmit mode also.

Does antenna
reciprocity theorem agree that the antenna can form same feedpoint impedance
and field pattern in both transmit mode and receive mode, even though the
electromagnetic field works differently?

The impedance is the same for transmitting and receiving. The
electromagnetic field does not work differently.

Are the electromagnetic field
patterns noticeably different according to whether antenna is receiving or
transmitting?

No. They are the same. This is part of what is known as reciprocity.

The vertical element is always known as the radiating element.

The antenna doesn't know or care what you call the parts. If the radials
lie in the same plane, they radiate very little. If bent down, say, as
is often done with a ground plane, they radiate a very substantial
amount. What you call or "know" the various parts of an antenna as
doesn't make any difference in how they operate. All conductors behave
the same with respect to currents and fields, regardless of how you've
positioned them or what you call them.

Roy Lewallen, W7EL