The present theories about the behaviour of light can be expressed either as wave equations or as streams of particles (photons) - both theories work in the sense that they model observed behaviour pretty well. But it would be a help to know which was the more realistic. Why? For two main reasons - one, it is the nature of scientific curiosity that we feel more comfortable with one winner - one explanation which is superior to the others; second, it might help if we could be sure which light was in trying to find the Grand Unified Theory (GUT) - the one which integrates gravity with electromagnetism and the nuclear forces hoding the protons and neutrons of atoms together and explaining their behaviours. The search for the GUT (or Theory of Everything - ToE) is currently the holy grail of the theoretical physics world - it would tie together Einstein's theory of relativity (concerning gravity amongst other things) with the theory of electro-chromo-dynamics which concerns sub-atomic structures and behaviours. If we could do this, then we could more honestly and defensibly claim that we understood how the physical world works - a triumph for the scientific method.
The essential nature of the curious result of the double slit experiments can be explained as follows (see Gribbin, op cit., pages 163ff)
What if we shut one of the holes? Then we get the pattern we would expect from a stream of particles - the deflected (left hand side pattern, whose shape depends on the width of the slit). But what does that prove? Nothing. That is the pattern we would get with a wave as well.
OK, go back to the twin slit apparatus, and slow down the rate at which we release the stream of photons (this experiment is actually done with electrons - are they particles or are they waves?). OK - so this is pretty clever stuff, and needs seriously sophisticated equipment, but it can be done reliably - that is, it can be replicated time and again. Suppose we slow the stream from the electron gun down enough that we just let one single electron go at a time. Then what do we get on our screen, our electron detector?
The answer is seriously perplexing. We get a diffracted pattern. In other words, as we let our electrons go one at a time, waiting till we have caught the first one on the screen before letting the next one go, we get the diffracted pattern and not the deflected pattern of particles. Each single electron can only have passed through one of the holes, not both. Indeed as Gribbin says (p 170 -1) "if we took a thousand experiments in a thousand different laboratories, and let one particle pass through each experiment, we could add up the thousand different results and still get an overall distribution in line with diffraction, just as if we let a thousand electrons through one of those experiments together. ... We can even try cheating - shutting or opening one of the holes quickly while the electron is in transit through the apparatus. It doesn't work - the pattern on the screen is always the "right" one for the state of the holes at the instant the electron was passing through." (that is, deflected if only one hole is open, and diffracted if both are open). "We can try peeking, to "see" which hole the electron goes through. .. The result is even more bizarre ... The electrons not only know whether or not both holes are open, they know whether or not we are watching them, and adjust their behaviour accordingly."
Gribbin concludes: "A single electron, or a single photon, on its way through one hole in the wall, obeys the statistical laws which are only appropriate if it "knows" whether or not the other hole is open. This is the central mystery of the quantum world". These electrons behave as particles when we set up our experiments to see them as particles, but not otherwise. Furthermore, they know how to behave after we have looked at them but before we have seen them! And this is the stuff of which we suppose we are all made! The Aspect experiment, which concerns the behaviour of photons - the particles of which light and all electromagnetism are supposed to consist - reveals exactly the same fundamental dilemma.