The two-slit experiment demonstrates better than any other experiment that a quantum wave function is a probability amplitude that can interfere with itself, producing places where the probability (the square of the absolute value of the complex probability amplitude) of finding a quantum particle is actually zero.

There is nothing like this in the motion of classical particles, although something like it is well known in the cancellation of crests and troughs in the motion of water and other waves.

The two-slit experiment demonstrates the famous "collapse" of the wave function or "reduction" of the wave packet, which show an inherent probabilistic element in quantum mechanics that is irreducibly ontological and nothing like the epistemological indeterminacy (human ignorance) in classical statistical physics.

Note that probability, like information, is neither matter nor energy. When a wave function "collapses" or "goes through both slits" in this dazzling experiment, nothing physical is traveling faster than the speed of light or going through the slits. This is similar to the Einstein-Podolsky-Rosen experiments, where measurement of one particle transmits nothing physical (matter or energy) to the other "entangled" particle but only the instantaneous information that has come into the universe. That information, together with conservation of momentum, makes the state of the coherently entangled second particle certain, however far away it might be.

In the two-slit experiment, as in the Dirac Three Polarizers experiment, the critical case to consider is just one photon at a time in the experiment.

With one photon at a time, we can show the fact that a quantum particle can interfere with itself. Indeed, even in the one-slit case, interference fringes are visible, although this is rarely described in the context of quantum mysteries.

It is the two-slit case that raises the "local reality" question raised by Albert Einstein, Erwin Schrödinger, and others. How, they ask, can the photon go through both slits? We will see that the thing that goes through both slits is only immaterial information - the probability amplitude wave function.

Let's look first at the one-slit case. We prepare a slit that is about the same size as the wavelength of the light in order to see the Fraunhofer diffraction effect most clearly. Parallel waves from a distant source fall on the slit from below. The diagram shows that the wave from the left edge of the slit interferes with the one from the right edge. If the slit width is d and the photon wavelength is λ, at an angle α ≈ λ/2d there will be destructive interference. At an angle α ≈ λ/d, there is constructive interference (which shows up as the lightening in the interfering waves in the illustration).

The height of the function or curve on the top of the diagram is proportional to the number of photons falling along the screen. At first they are individual pixels in a CCD or grains in a photographic plate, but over time and very large numbers of photons they appear as the continuous gradients of light in the band below (we represent this intensity as the height of the function).

Now what happens if we add a second slit? Perhaps we should start by showing what happens if we run the experiment with the first slit open for a time, and then with the second slit open for an equal time. In this case, the height of the intensity curve is the sum of the curves for the individual slits.

But that is not the intensity curve we get when the two slits are open at the same time! Instead, we see many new interference fringes with much narrower width angles α ≈ λ/D, where D is the distance between the two slits. Note that the overall envelope of the curve is similar to that of one big slit of width D. And also note many more lightening rays in the overlapping waves.

Remembering that the double-slit interference appears even if only one photon at a time is incident on the two slits, we have established that the photon interferes with itself.

But how do we see the "collapse" of the wave function? At the moments just before a photon is detected at the CCD or photographic plate, there is a finite non-zero probability that the photon could be detected anywhere that the modulus (complex conjugate squared) of the probability amplitude wave function has a non-zero value.

If our experiment were physically very large (and it is indeed large compared to the atomic scale), we can say that the finite probability of detecting (potentially measuring) the photon at position x₁ on the screen "collapses" (goes to zero) and reappears as part of the unit probability (certainty) that the photon is at x₂, where it is actually measured.

Since the collapse to zero of the probability at x₁ is instantaneous with the measurement at x₂, critics of quantum theory like to say that something traveled faster than the speed of light. This is most clear in the nonlocality and entanglement aspects of the Einstein-Podolsky-Rosen experiment. But the sum of all the probabilities of measuring anywhere on the screen is not a physical quantity, it is only immaterial information that "collapses" to a point.

Here is what happens to the probability amplitude wave function (the blue waves) when the photon is detected at the screen (either a photographic plate or CCD) in the second interference fringe to the right (red spot). The probability simply disappears instantly.