How Can We Understand Wave-Particle Duality in Water Waves?

[Ahmad Kishki]

Ahmad, would you be satisfied with a justification for the use of wave equations that took the approach, "water wave A consists of X molecules with average velocity v_A1 and mass density p_A1 at position dx_A1dy_A1dz_A1 (and other velocities for all the other infinitesimal volumes of the wave) while wave B contains Y molecules with average velocity v_B1 at position dx_B1dy_B1dz_B1 etc. and whose maximum peak will intersect wave A's maximum peak at time t etc., and since no two molecules can occupy the same space they must displace each other (superpose), but since we do not have the capacity to know each and every pair of interacting molecules' exact positions and collision angles, orientations, strength of van der Waals' forces and ionic interactions (for the dipolar water molecules) etc. that impart some elasticity and variable density to the water, we shall treat the liquid medium as an incompressible, continuous medium etc., and this has been found empirically to provide an accurate description of the macroscopic behavior of intersecting waves"?

I don't mean to imply that this is exactly what a particle description would look like, but just sort of what you had in mind.

Yes, precisely. Thank you.