We will detect the interference pattern by replacing the screen with a photographic film, and we will make the light sources so weak that the total light energy in the apparatus at any time is no greater than the energy of a single photon. If we could examine the film minute by minute, we would see a pattern of dots that at first seems to be randomly distributed, but as more and more dots appear, the pattern of constructive and destructive interference fringes gradually takes shape.
An individual grain of the film is darkened by an interaction with a single photon. If we regard our light source as so weak that it emits individual photons one at a time, then a photon leaves the light source and later arrives at the film. Based on our experience with classical physics, we might then be tempted to ask how a photon gets from the source to the film. What is its trajectory? More specifically, through which slit did it pass?
If we try to answer such a question, we are clearly talking about the particle nature of light. Particles nature of have trajectories; waves do not. If we regard light as individual concentrated bundles of energy, clearly they must each pass through one slit or the other. The double-slit experiment depends on light behaving as a wave, so that we can divide the wave front into two pieces and then recombine the two pieces. These two descriptions, one based on particles and the other on waves, are clearly inconsistent with one another. Is light a particle or a wave?
This puzzling question has two equally puzzling answers
a) light is neither a particle nor a wave, and b)light is both particle and a wave. By the first answer, we mean that light does not satisfy the exclusive classical notions of strictly particle-like or strictly wave-light behavior. By the second answer, we mean that the particle and wave natures are both contained in what we call light, which can reveal one type of behavior or the other depending on the kind of experiment we do. Light has a more mysterious and complex behavior than is suggested by our simple ideas of “wave” or “particle.”