Figure 1:
The double-slit experiment. Narrow openings in the slits cause the wave to spread through diffraction, and because of the different distances traveled in the path from the two different slits to a given point on the far screen P, the waves will experience either constructive or destructive interference, resulting in the wavy bands of light and dark as shown. The quantum paradox here is that this pattern obtains even when a single particle is emitted at a time. The particle only ever goes through one slit or the other, but somehow the wave goes through both. Figure from wikimedia commons by Lacatosias.
Figure 2:
Results of a double-slit experiment using electrons, with increasing numbers of electrons recorded (11, 200, 6,000, 40,000, and 140,000). The interference pattern emerges over time, even though only single electrons are detected on each trial. Figure from by Dr. Tonomura via wikimedia commons.
The double-slit experiment (also known as Young’s experiment) (Figure 1), is said to illustrate the full mystery of quantum mechanics, and nicely demonstrates some puzzling aspects of wave-particle duality. Interestingly, the double slit experiment was around long before quantum mechanics, as a way of generating interference patterns with waves, but it “just got weird” when the intensity of the light, or beam of electrons or other particles, is reduced to the point where there is only a single particle passing through the apparatus at a time.
Surprisingly, one still observes the interference effect in this case (Figure 2). How can a single “hard little particle”, all by itself, produce this wave-like interference effect? There are many other results that all add up to the strong conclusion that, somehow, elementary particles like electrons have both wave and particle properties.
The pilot-wave framework of de Broglie and Bohm provides the most natural, intuitive explanation of these effects: the wave goes through both slits, and the particle goes through one, but it is influenced by the wave.
Figure 3:
Trajectories for particles in the double-slit experiment computed according to the de Broglie-Bohm pilot-wave model. The interference effects can be seen as relatively localized bumps in the trajectories, corresponding to steep gradients in the Schrodinger wave equation. Critically, the underlying trajectories are considered to exist at all points even if you don’t happen to observe them.
Figure 3 shows what the underlying trajectories of particles under the pilot-wave framework look like in a double-slit experiment, and Figure 4 shows some recent data from an experiment where weak measurements that minimally disturb the system allow one to infer particle trajectories, which look remarkably similar to those predicted by the pilot-wave model (Kocsis et al., 2011).
Figure 4:
Reconstructed trajectories of photons in a double-slit experiment using a weak measurement technique that allows aggregate trajectory information to be reconstructed over many repeated samples that are post-sorted according to a weak additional modulation of the system — these are not individual particle trajectories. There is a striking correspondence to the predictions of the de Broglie-Bohm model. Figure from Kocsis et al, 2011.