Misunderstood of wave-particle dualism?

Question

Reading about dual nature of light, and atomic transitions, it seems to me, maybe wrongly, that the dual nature depends on the way we look at the phenomena.

Suppose a water wave travels and reach another water source. Why can't we talk about a condition like:

$$\Delta E=h\nu$$

where $\nu$ is the frequency of water molecules impacts? Another point of view should be the interference of waves.

Isn't talking about light dualism quite the same? When a photon interacts with an electron, is must have an exact frequency, but also it might be understood as a wave interference (if I'm not mistaken).

Answer 1

A classical wave emerges in a medium of a huge number of molecules , we cannot identify individual molecules with the frequency of the wave, the molecules are the "coordinates" on which the energy and momentum of the wave motion can be mathematically modeled, by their small motions up or down (transverse wave), left or right (longitudinal wave) as the wave passes. It is like a wave in a stadium, the frequency has a very wide spectrum, depending on how fast the people can respond.

A photon and an electron are point particles, i e. have a definite position $(x,y,z,t)$ in the model that describes their interactions. When a photon interacts with an electron, its wave nature is not in energy, but in probability of interaction. It is the probability of interaction that is modeled as a wave, for the point particles which are the electron and the photon.

The classical wave in water, and does not behave as a particle, i.e. it is not defined by an $(x,y,z,t)$ point isolated in space, which is the definition of a point particle. One could extend the definition by allowing a $Δ(χ)$ ... In this extended case yes, there can be wave packets called solitons in water, which do behave as a particle carrying energy and momentum , in this case a one dimensional one. This is also interesting.

Answer 2

One might think that a particle such as a phonon, unable to form structures with other such particles, might not be considered a particle; but several elementary particles also do not form "structures," existing only as "force mediation" and also never themselves at rest. The term "particle" is not used consistently in different areas of physics, so phonons and solitons may reasonably be called particles, but I prefer to be more clear when I speak, and just call them phonons.