One particle at a time, and still the stripes

Send electrons at a wall with two slits, one at a time, so slowly that each has landed before the next leaves. The dots that pile up on the far side still form the striped pattern of a wave.

What the experiment is

A source fires particles at a barrier with two narrow openings. Behind it, a screen records where each particle lands. The rate is turned down until only one particle is in the apparatus at a time. Each arrival is a single dot. Given enough dots, they form bands: stripes where many land, separated by stripes where almost none do.

Why it is worth your attention

Bands like these are what waves make. Two overlapping waves add where crests meet and cancel where a crest meets a trough, giving light and dark stripes called an interference pattern. A single dot is what a particle makes. This experiment shows both at once: each arrival is a point, and the statistics of the points are a wave pattern. There is no lone particle you can point to that went through one slit or the other and still built up those bands. Richard Feynman described this as a thought experiment in 1965; Bach and colleagues carried it out with electrons in 2012, using a movable mask to open and close each slit, and recorded the pattern building up one detection at a time. Single-photon versions have since been filmed with a triggered camera, and one has been built as an undergraduate lab.

How the mechanism works

Quantum mechanics assigns each way of reaching a spot on the screen a number called an amplitude. It has a size and a phase: an arrow with a length and a direction. The probability of landing there is the square of the total arrow's length.

What matters is how arrows combine. If two ways of arriving cannot be told apart by anything in the experiment, add the arrows first and square the total. If they can be told apart, square each arrow separately and add the results.

With both slits open and nothing watching them, the paths through slit A and slit B are indistinguishable. Their arrows point in different directions at each point on the screen, because the two paths differ in length. Where the arrows point the same way, the total is long and the probability is high. Where they point opposite ways, the total is near zero and almost nothing lands. That alternation across the screen is the bands.

Close one slit and there is one arrow, so one broad hump of arrivals (with faint side bands far out, from single-slit diffraction). Open both slits but add a detector recording which slit was used, and the two paths are now distinguishable. The arrows are squared separately and added; the bands vanish, leaving one smooth spread of arrivals. The detector never registers half a particle; what changed is whether the experiment could, even in principle, distinguish the two routes.

None of this says where any single particle will land. It fixes only the odds for each spot. The dots arrive at random, and nothing in the experiment predicts where the next lands, but the odds behind them are exactly the wave pattern.

In short

One particle at a time still produces an interference pattern, because probabilities in quantum mechanics come from adding amplitudes for every route that cannot be told apart, then squaring. Each arrival is a single dot. The pattern is in the odds, and the odds are set by which routes were open and whether anything could distinguish them.