Various books claim that a ground plane reflects the radio wave emitted by
the vertical, and then claim that a ground plane is formed or simulated by
four elevated radials.
I emailed two Professors of antenna theory about this.

Reply from Professor Constantine Balanis:
"The radials should act more as a ground plane. Four of them are usually the
minimum. The more of them, the better the ground plane. The objective of the
ground plane is to reflect the energy from the main element; the vertical
wire".

Reply from Professor Vincent Fusco:
"My view would be that the radials form an image plane, the radials
themselves do not radiate".

The following link on Navy Training Series show the radials as reflecting
the radio wave and forming an image antenna:
http://www.tpub.com/content/neets/14.../14182_219.htm

Quotations from books below.

Antenna Theory third edition by C.A. Balanis page 205 "Improvements in the
efficiency can be
obtained by placing radial wires or metallic disks on the ground. [New
paragragh] The analytical procedures that are introduced to examine the
ground effects are based on the geometrical optics models of the previous
sections. The image (virtual) source is again placed a distance h below the
interface to account for the reflection."

Antenna Theory third edition by C.A. Balanis page 511 "To reduce the wind
resistance, to simplify the design, and to minimise the costs, a ground
plane is often simulated, especially at low frequencies, by crossed wires as
shown in Figure 9.11(b). Usually only two crossed wires (four radials) are
employed. A larger number of radials results in a better simulation of the
ground plane."

Antenna Theory and Design by Stutzman and Thiele page 198: "A ground plane
can take many forms, such as radial wires around a monopole, the roof of a
car, or the real earth....The pattern of an antenna over a real earth is
different from the pattern when the antenna is operated over a perfect
ground plane. Approximate patterns can be obtained by using image theory.
The same principles discussed in Sec 2.3.1 for images in perfect ground
planes apply, except that the strength of the image in a real ground will be
reduced from that of the perfect ground plane case".

Antenna Theory and Design by Stutzman and Thiele pages 66 & 67: "The
principles of image theory are illustrated in this section with several
forms of the monopole antenna. ... Figure 2-12(c) Practical monopole
antenna with radial wires to simulate a ground plane".

Antennas for all applications third edition by J.D. Kraus page 719: "In Fig
21-9d the solid-sheet ground plane is replaced by 4 radial conductors. Fig
21-9(d) stub antenna with 4 radial conductors to simulate a ground plane".

Antenna Engineering Handbook by R.C. Johnson page 110: "The geometrical
shape of a sleeve antenna, or a sleeve monopole, is sketched in Fig. 4-22a.
If the image of the structure is included, then we have a sleeve dipole as
shown in Fig. 4-22b". Figure 4-22a shows a coax cable with the centre wire
going upwards forming a vertical element, and the braid being connected to a
ground plane. Fig 4-22b appears to show a dipole being formed from a
monopole and its image antenna.

Foundations of Antenna Theory and Techniqes by Professor Vincent Fusco pages
190 and 191. Claims that image theory i.e. image cancellation applies to the
horizontal section of an inverted L antenna. The vertical part of inverted L
antenna is a short monopole i.e. less than a quarterwave long.

However references against this are below.
Antenna Engineering Handbook by R.C. Johnson page 118: "When the ground
plane is of finite size, the image theorem does not apply."

Professor Douglas Miron in his book Small Antenna Design says that the
vertical element is driven against some horizontal elements. The horizontal
elements have canceling fields. He says that the radials are an artificial
ground called a counterpoise that also radiates.

Various books also say about using image theory to analyse corner reflector
antennas.

RF experts appear to disagree with each other over the vertical monopole
with quarterwave radials - Roy Lewallen and Professor Douglas Miron versus
Professor Constantine Balanis and Professor Vincent Fusco.