  In this paper, I argue that light is a continuous classical electromagnetic
wave, while the observed so-called quantum nature of the interaction of light
with matter is connected to the discrete (atomic) structure of matter and to
the specific nature of the light-atom interaction. From this point of view, the
Born rule for light is derived, and the double-slit experiment is analysed in
detail. I show that the double-slit experiment can be explained without using
the concept of a "photon", solely on the basis of classical electrodynamics. I
show that within this framework, the Heisenberg uncertainty principle for a
"photon" has a simple physical meaning not related to the fundamental
limitations in accuracy of the simultaneous measurement of position and
momentum or time and energy. I argue also that we can avoid the paradoxes
connected with the wave-particle duality of the electron if we consider some
classical wave field - an "electron wave" - instead of electrons as the
particles and consider the wave equations (Dirac, Klein-Gordon, Pauli and
Schrodinger) as the field equations similar to Maxwell equations for the
electromagnetic field. It is shown that such an electron field must have an
electric charge, an intrinsic angular momentum and an intrinsic magnetic moment
continuously distributed in the space. It is shown that from this perspective,
the double-slit experiment for "electrons", the Born rule, the Heisenberg
uncertainty principle and the Compton effect all have a simple explanation
within classical field theory. The proposed perspective allows consideration of
quantum mechanics not as a theory of particles but as a classical field theory
similar to Maxwell electrodynamics.
