This association, however, cannot be explained in terms of classical theory, and is entirely novel. As opposed to the behavior of particles and waves in classical mechanics, this association can only be interpreted statistically, with the wave function providing us the information necessary to make only probabilistic statements about where the photon may be located after measurement.
Prior to the advent of quantum mechanics, people were aware of the statistical nature of the connexion between waves of light and photons, however, they were not aware of was that the wave function represents the probability of one photon being in a particular place, as opposed to the number of photons in said space.
If the two beam components are made to interfere, the constituent photons will do so as well, meaning sometimes these photons would have to annihilate one another, and other times they would have to produce four photons.
The behavior of these photons represents the constructive and destructive interference resulting from the wave behavior of matter, where crests and troughs cancel out, and crests meeting crests combine.
The issue here is that this would violate the law of conservation of energy.
The new theory avoids this violation by connecting wave functions with probability for a single photon, where each photon is partially within the beam components, and thus only interferes with itself.