Applications of
Quantum Mechanics
Implications of
Quantum Mechanics

31. The Double-Slit Experiment.

Summary
The double-slit experiment shows both the wave-like and particle-like aspects of matter. But it can be explained using the properties of the wave function alone.

The double-slit experiment is of interest because it illustrates both the wave-like property of interference and the particle-like property of localization. But it does not provide evidence for the existence of particles; both the wave-like and particle-like properties can be explained by the properties of the wave function alone (principle [P15], No Evidence for Particles).

Interference. We start with interference. When you have a wave, something oscillates. In a water wave, the height of the water oscillates up and down about some average level. In a sound wave, the density of the air oscillates, in the same direction as the wave. In a (classical) light wave, the electric and magnetic fields oscillate (see Photons and Polarization). In each case, there is a peak in a wave followed by a trough. The ‘height’ of the wave, the maximum amount above or below average, is called the amplitude.

Suppose we now consider a light wave going through the two slits. After going through the slits, the two waves spread out (diffraction) and hit a screen covered with film grains. If we let x be the distance to the right from the midpoint of the screen, a small part of each wave will hit near point x. But the wave from the left slit has traveled farther than the wave from the right slit, so the two waves will be ‘out of phase.’ If the upper (left) wave has traveled half a wavelength farther, then when a peak from that wave hits near x, a trough from the lower wave will hit near x. But the trough (below average) will just cancel out the peak (above average) and so the net disturbance near x will be zero. This is destructive interference.

On the other hand, if the upper wave has traveled a full wavelength farther, peaks from both waves will simultaneously hit near point x, so the net disturbance will be a maximum—constructive interference. Thus the ‘disturbance’ at the screen as point x moves from the center towards the edge of the screen will go through maxima and minima. If the wave is a water wave, the waves from the two sources will produce a wave of maximum height at each constructive interference points but it will produce no wave at all at the destructive interference points.

If the wave is a light wave and the screen is covered with grains of film, the density of exposed grains will be a maximum at the constructive interference points but there will be no grains exposed near the destructive interference points.

Quantum considerations. Suppose now, instead of considering a beam of light, which contains many photons (photon-like wave functions) we consider the wave function of just one photon. Then after the wave function goes through the two slits, it will produce a constructive-destructive interference pattern. But now, if we do a microscopic examination of all the film grains, we find that just one grain is exposed! That is, the interference pattern of the single-photon wave does not translate into an interference pattern on the screen. Instead, the interference pattern corresponds (roughly) to a probability wave (see The Probability Law); the one exposed grain is more likely to be found near the maxima, and will never be found at the minima.

The particle interpretation. If one assumes there are particles, then the interpretation of the above results is that the particle goes through one slit or the other, and is then ‘guided’ by the probability wave generally towards the maxima. When the particle hits a single grain, it is that grain which is exposed.

The no-particle interpretation. The no-particle interpretation exactly follows the localization analysis of the section on Localization (principle [P13]). The uncollapsed wave function contains many versions of reality, each with one exposed grain, but we perceive just one of those versions of reality. All versions continue to ‘exist’, but just one version—with just one grain exposed—enters our perception. Thus the wave-particle duality displayed in the double-slit experiment—a diffraction pattern (wave) plus only one grain exposed (‘particle’)—is properly accounted for by the wave function alone.  