The Double-Slit Experiment

The double-slit experiment was first performed by Thomas Young in 1801 to demonstrate the wave behavior of visible light. In 1927, at the advent of quantum mechanics, the experiment was reproduced with electrons, and since then, with atoms and ever larger molecules. The observations are qualitatively the same.

A beam of particles is directed at a plate with two small, parallel slits. On a detector screen behind, one observes an interference pattern, alternating bands of high and low intensity. Crucially, this interference pattern is created by the statistical distribution of individual impact points. If one sends in a single particle at a time, each produces a small dot on the screen in a seemingly random position. A large number of particles build up the interference pattern: alternating regions where many particles are detected and regions where few or none are.

Interference is a typical wave phenomenon: when two waves overlap, their amplitudes combine, so that in some places, the waves reinforce each other (constructive interference), while in others, they reduce or cancel each other (destructive interference). On the other hand, the individual dots appearing on the screen suggest the impact of localized particles rather than extended waves.

The double-slit experiment is therefore a key demonstration of the so-called wave-particle duality. The microscopic constituents of light and matter, photons, electrons, atoms, etc., exhibit both wave-like and particle-like properties.

Bohmian mechanics resolves this apparent paradox in a straightforward way. Electrons (for example) are actual particles, but their motion is guided by the wave function. This is why Bohmian mechanics has also been called pilot wave theory. The guiding law is such that most particle trajectories follow the peaks of the wave function (where there is constructive interference) and avoid regions where the amplitude of the wave function is small. Each particle passes through only one of the slits, moving along a well-defined trajectory. Taken together, many such trajectories build up the statistical interference pattern on the detector screen.

While the founding fathers agonized over the question
'particle' or 'wave'
de Broglie in 1925 proposed the obvious answer
'particle' and 'wave'.

Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.

Note: The screen must interact with the particles in order to detect them. The simulation ignores the effect of this interaction on the particle‘s wave function and trajectories. In most cases, this effect is small, but in principle, it could alter the trajectories, especially in situations where the detector screen is placed very close to the slits.