When I read many academic books on antenna theory, most of them appear to
say that the radials reflect the radio wave emitted by the vertical. I do
not think that I am reading the books out of context. The replies from two
professors of antenna theory indicate that they believe that the radials
reflect the radio wave and form a mirror image.

Looking at the vertical monopole with four radials, I suspect that Douglas
Miron is correct in his book. He says that the radials radiate but have
horizontal cancelling fields.

I would expect the radials to radiate because current is forced through them
by the RF generator. The current splits between the radials, thus causing
the fields to cancel in the horizontal direction. The fields probably have
an effect in the vertical direction, causing a change in radiation pattern
and affecting angle of radiation.

I am not sure whether the return current through the radials causes any form
of mirror image. On a PCB track above a ground plane, the current returns
through the ground plane via the path of least impedance which is often
directly underneath the PCB track. The PCB track is the positive voltage
side. The ground plane current is the 0V side. It is said that the current
in the ground plane mirrors that flowing through the PCB track.