The physicist Richard Feynman once said, approximately, that all of quantum physics could be understood if you understood the double-slit experiment and thought through its consequences carefully. (This is obviously in spirit, if not in reality, something of a follow-up to the LHC visit article Part III which has yet to be written.) The double slit experiment is important because it is the experimental evidence of something often talked about but poorly understood: so-called wave-particle duality.
It was thought by Newton that light was "corpuscular" in nature; he thought it must be made up of particles. Later it was found that if you take a beam of light, and shine it through two tall, narrow, adjacent slits, you get an interference pattern --this can only happen if light is a wave of some sort. Even later, the photoelectric effect seemed to show the contrary: that light was indeed corpuscular in nature.
The funny thing is this: take a beam of light or some other suitably quantum-sized particle, like an electron. Fire it through one slit: you will see a simple blurred outline, roughly in the shape of the slit: a diffraction pattern, due to the scattering of the light waves. Fire it through two slits, and you will see an interference pattern: alternating light and dark bands, which can be interpreted as reinforcing and cancelling wave-fronts. It would seem the case is closed: light is wave-like in nature --but the case is more complicated.
As it happens, if you are using a beam of light and you have good equipment, you can turn the intensity of the beam down until only one photon is being emitted at a time. You will see, on your detector, only one "hit" at a time, at a specific location. Yet, if you let the "hits" build up over time, they will eventually form an interference pattern --as if, somehow, the particle had passed through both slits at once and was somehow interfering with itself. And this is a very funny thing. (Here we clearly intend, "funny" to mean "intensely intuitively frustrating; Einstein, and Schrödinger and quite a lot of other physicists, philosophers, and simple well-intentioned layman have found it anything but funny. It led to one of the best quotes in the history science, which was Schrödinger's remark about the famous equation that bears his name, and describes the wave-function of a quantum system: "I don't like it, and I'm sorry I ever had anything to do with it.")
Now all this is already trying enough: we are unable to understand intuitively what this means, because at the physical scales our five senses can operate within we are not familiar with any such behavior. The problem, naturally, has gotten even worse as quantum mechanics has evolved. Einstein postulated that if you put a detector at each of the two slits, this would reveal which of the slits through which the particle had passed. If this is the case, then the particle should, so to speak, no longer be able to pass through both slits at once --in technical terms you may say the superposition of states (slot A and slot B) has collapsed into a single discrete value. It was not technically possible to do such experiments until the 1970s but it indeed proved true.
Now, suppose you were to somehow mark the particle so you could tell after it had passed through the slit, which one it had passed through.
As it turns out, when you do this, what you expect would happen, does. If you know through which slit the particle passes, then the interference pattern disappears. But suppose you could somehow erase the mark, so to speak, after the particle passed through the slit? If we follow through the logic of the experiment, then "erasing" this quantum information should cause the interference pattern to re-appear.
The manner in which the notion has been put to the test experimentally is extremely interesting.
Take a photon source: a laser will do nicely. Let the photons pass through two slits. Then let the photons pass through a special prism that splits each photon into two photons. As each pair came from a single parent they are said to be entangled --as with most common-sensible sounding terms in quantum mechanics this has a precise mathematical formulation which need not concern us here. It broad terms, it means that the two "child" photons cannot be thought of as completely separate quantum systems: they must be described as parts of a larger quantum system. In practical terms this means that if you measure some aspect of one "child" you will know the complementary aspect of the other without having to take a measurement of it directly.
Having started with one stream of photons, you passed them through the two slits, yielding two sets of photons. Having passed each stream subsequently through a producer of entangled pairs, you now have four "children." One of each set of twins is referred to technically as the "signal" photon, and the other is referred to as the "idler."
Now if you know through which slit the signal photons have passed, you should not see any interference pattern with the signal photons. If you do not, they should create an interference pattern. Here is the important part. You arrange the pathways of the "idler" photons so that they arrive at one of four detectors.
At two of these detectors, you can tell through which slit the parent of the idler photon passed. If you compare the idler photons from these detectors with the signal photons, then an interference pattern emerges.
Oddly enough, however, if you compare the signal photons with the other two detectors --at which you cannot tell through which slit the parent of the idler photon passed --then the interference pattern disappears. You have "erased" that information.
The truly peculiar thing about this, is that you can set up your idler photon pathway so that it takes longer for the idler photons to get to the detectors than it does for the signal photons --the usual interval is 8 nanoseconds but in principle it could be as long as you like --billions of years, even. The results would still be the same --which seems to imply that the idler photons are sending information backwards in time. This worried a lot of people.
As it turns out, however, there is a catch: you can only observe an interference pattern for the subset of photons which you compare to the idler particles that have arrived at the detectors that erase their origin. If you look at the whole set of signal photon detections, they do not form an interference pattern taken alone. This does something very happy: it saves causality.