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The double-slit self-interference property of electromagnetic radiation is best modeled as a wave phenomenon and persists down to single photon events

But if the photons arrive one at a time, no photon knows where its predecessors went.

Only when I sum up many photon and I analyze their distribution on screen I can reach a conclusion that the superimposed image of billions of photons looks like an interference pattern.

But the underlying question is why, if each event is independent and the result of a single particle travelling through one slit or another, the distribution has more than two peaks?

Is a single photon alone a wave or a particle?