What happens to a single photon in the double-slit experiment?
A single photon is not measurable in my interpretation, there is no associated observable variable. Photons are indistinguishable, so one cannot say where a particular photon is. What exists is the photon density. This extrudes itself, as it were, like an oil through the double slit, and forms an interference pattern according to the rules of quantum mechanics. (This is a picture and should not be taken too literally!)
On impact with the screen, the non-local dynamics ensure that from time to time, at a rate proportional to the photon density, an electron is put into an excited state, a chemical reaction takes place, or some such thing relevant to the detection mechanism. That this occurs in a stochastic fashion is a result of the fact that the experiment is highly sensitive to the rest of the universe.
How one can justify this stochastic behaviour at the formal level is discussed in this FAQ in the section 'How can we explain randomness?'. This is, however, more technical, and requires advanced techniques from statistical mechanics.
V.B. Braginsky and F.Ya. Khalili,
Cambridge Univ. Press, Cambridge 1992
is an outstanding book about real quantum measurement processes, which are tightly bound up with modern experiments in quantum optics, and have nothing to do with the von Neumann caricature of a quantum measurement. At the bottom of P.3 they write:
''Experiments on the interference and diffraction of light, when performed with very low intensities, revealed further that an interference pattern (a classical, pure wave effect) shows up on a photographic plate only when the number of photons falling on the plate is very large. Each photon in such an experiment is _completely_destroyed_ [original italic] (ceases to exist) by interacting with the plate's silver chloride molecules. When the photon is destoyed there appears somewhere on the photographic plate an atom of free silver, which acts as an embryo from which, by photographic developing, a small seed of silver will grow. The silver embryo is much smaller than an electromagnetic wavelength. This is remarkable. In the interference process (e.g. in the two-slit experiment of Fig. 1.1), [standard picture] the photon must have been influenced by the locations of both slits, since the interference pattern depends on the distance between them. This means that the photon must have occupied a volume larger than the slit separation. On the other hand, when it fell on the photographic plate, the photon must have been localized into the tiny volume of the silver embryo. Later the terms 'collapse of the wave function' and 'reduction of the wave packet' were used to describe such localization.''
In agreement with the thermal interpretation they ascribe to the photon in a double-slit experiment a volume that is bigger than the separation of the two slits.
Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ