In the double-slit experiment, we shine a light wave through two closely-spaced parallel slits at a screen, and observe an interference pattern on the screen. We then reduce the intensity of the light source until we can observe single energy quanta, like Geiger counter clicks, which we call photons, and we observe the same interference pattern in the distribution of where the quanta arrive. We infer that light behaves in some ways like a wave, because it creates an interference pattern, and in some ways like a particle, because we can count the individual photons. It seems like a single photon can interfere with itself. Weird!
Question: How do we know the light travels in quanta? Could it not be the case that the light has a continuous wave nature, and only the interaction between the light wave and the source, and the light wave and the detector, is quantized? Separately from each other, of course, because of causality.
If this hypothesis was true, we should see that quanta would be deposited on the detector at the same average rate they were removed from the source, but there would be no correlation between the precise timing of each. In the usual experimental setup, there is no way to know this because the energy quanta taken from the source are not counted. Has this been experimentally tested?