Can the Particle nature of light be explained by wave interactions?
When emitted from an atom, does a photon propagate through space-time as a sphere, in all directions, as a wave or as a directed point particle?
There is confusion here in the concepts "photon", and "light".
The photon is a quantum mechanical entity, i.e. its existence in space obeys quantum mechanical rules and a wave equation defines its wavefunction, a solution of a quantized form of Maxwell's equations. The Psi*Psi of the solutions of this equation for given boundarry conditions give the probability density of finding a "photon" hit at an (x,y,z,t).It is the probability density for the photon that has sinusoidal/wave properties.
therefore I think the particle nature of light is simply a by-product of wave interactions, they only exist as a way to show interactions of wave functions or put in another way, light is simply the interactions of wave functions.
Light is an emergent quantity from an enormous confluence of photons with energy h*nu. To see how this happens one needs quantum field theory. It is not surprising that the classical electromagnetic wave will have as a frequency in its amplitude the nu of the photon energy, because both are solutions of maxwell's equations.
The photons in a light beam do not interact, (very small probability) they are superimposed as wavefunctions and when complex squared the electric and magnetic fields which define the wave properties of light appear. It is the quantum nature that is the underlying framework. The same is true for classical waves emerging from the underlying quantum mechanical level of atoms and molecules