The double slit

In 1801 Thomas Young let sunlight fall on a card with two narrow slits and looked at the wall behind. He saw bands — alternating light and dark stripes, evenly spaced, across a region where common sense predicts two bright patches and nothing else. Newton had held that light was a stream of corpuscles. Newton had been dead for seventy-four years and was not lightly contradicted, particularly in England. Young was attacked in the Edinburgh Review with a viciousness that is startling to read now — his work was described as destitute of every species of merit — and he largely withdrew from optics afterwards. He turned his attention elsewhere, and among other things did much of the early work on deciphering the Rosetta Stone.

Thomas Young’s 1807 engraving: two point sources emitting overlapping circular wavefronts, with lines marking where they cancel. — Young’s own plate, from his *Lectures* of 1807. Two sources, overlapping circular waves, and the lettered points along the bottom marking where they arrive out of step and cancel. He drew this to argue that light is a wave — and every word of that argument survives intact when you replace the light with single electrons, which is the problem.

Note the envelope — the broad curve the fringes sit inside, set by the width of each individual slit.

Loading the slits…

Evenly spaced fringes inside a single-slit envelope. The envelope is why the central fringes are brightest, and why certain orders vanish entirely when the slit width divides into the separation. Most textbook diagrams omit it and show a uniform picket fence, which is not what you see.

Someone committed to particles has an obvious reply, and it deserves a serious hearing. Each particle goes through one slit or the other. Some go left, some go right. What builds up on the screen is simply the pile from the left slit added to the pile from the right slit. There is no mystery; there are just two sources. That is a reasonable hypothesis. It is also, and this is the point, a quantitative one. "One slit's pattern plus the other's" is a specific curve. You can draw it, and you can compare it against what happens.

Three curves, one scale. Look at the marked positions, where the red curve is high and the blue is on the floor.

Loading the slits…

One slit alone (yellow), the particle prediction of one plus the other (red), and what actually happens (blue) — all on the same scale, with one slit peaking at 1. The particle prediction peaks at 2 and has no fringes. Reality peaks at 4, because amplitudes add before they are squared. The integrated totals are equal to within 0.04%: the light is redistributed, not created or destroyed.

Opening a second hole makes places darker

Two things are wrong with the particle prediction, and the second is fatal. The centre is too bright. Reality peaks at four times one slit, not twice. Amplitudes add, and intensity is amplitude squared: (2A)² = 4A². Adding intensities gives 2A². The factor of two discrepancy is a direct signature that what combines is amplitude, not brightness. And some places go dark. At the marked positions, light arrives when one slit is open — and stops arriving when you open a second one. Sit with that. You have light falling on a screen. You give it an additional route through the barrier, and a spot that was illuminated goes black. No account in which each particle travels through one slit or the other can produce this. If a particle went through the left slit, it cannot matter to that particle whether the right slit is open — it was never near the right slit. Yet it demonstrably does matter. (No light is destroyed. The integrated totals match: it piles up into the bright fringes instead.)

For light, in 1801, none of this is troubling. Light is a wave. Waves do exactly this. A water wave arriving at two gaps in a harbour wall passes through both, and the two spreading wavefronts interfere behind it in precisely this pattern. Nobody finds that mysterious, because a wave is a spread-out thing and going through both gaps is simply what a spread-out thing does. The question "which gap did the wave go through?" has an obvious answer: both, because it is not the sort of thing that goes through one place. So Young's experiment is a demonstration, not a paradox. It settled that light is a wave, and for a century that was the end of it.

Now do it with electrons. De Broglie says an electron has a wavelength λ = h/p. If that is right, a beam of electrons through two slits must produce fringes. The obstacle is arithmetic. A 50 keV electron has a wavelength of about 5 picometres — roughly a hundredth of an atom. With slits 2 micrometres apart, the fringes come out about 1 micrometre apart at the detector. You cannot see fringes that fine, and you cannot simply move the detector further away, because the beam intensity falls off and the whole thing is inside a vacuum system. The answer is to magnify the pattern — by a factor of about ten thousand, with electron lenses, which brings a 1 μm fringe spacing up to a visible centimetre, without disturbing what you are trying to look at.

The experiment

Two slits, with electrons

Claus Jönsson, as a doctoral student under Gottfried Möllenstedt · 1961 · University of Tübingen

The question: Do electrons produce a genuine two-slit interference pattern — not crystal diffraction, but the actual Young geometry, with the fringe spacing de Broglie’s relation demands?
The apparatus: Slits made by a method Jönsson devised himself: he wrote the slit pattern in oil onto a glass slide with a fine electron beam, evaporated copper over the whole surface, then dissolved the oil away, leaving copper slits about 0.5 μm wide and 2 μm apart in a 0.5 μm film. Electrons at 50 keV were passed through and the resulting pattern magnified about 10⁴ times by electrostatic electron lenses before reaching a photographic plate. The whole apparatus ran under high vacuum.

Theory predicted

If λ = h/p holds, 50 keV electrons (λ ≈ 5 pm) through slits 2 μm apart give fringes about 1 μm apart before magnification, at positions fixed entirely by the geometry and the de Broglie wavelength.

They measured

Clear interference fringes at the predicted spacing. Jönsson then repeated the experiment with three, four and five slits, and in every case the pattern matched the prediction for that number of slits — including the sharpening of the maxima that additional slits produce.

How sure could they be? Fringe positions matched theory well within the resolution of the plates. Extending to three, four and five slits is what makes the result hard to dismiss: a spurious effect might mimic two-slit fringes, but reproducing the distinct signatures of five different geometries is another matter.

Why it mattered

The first true double-slit experiment with matter. Davisson–Germer and G.P. Thomson had shown electron diffraction from crystals in 1927, which is compelling but is a many-scatterer effect; this is Young’s own geometry, with two holes. The paper was published in German in 1961 and not translated into English until 1974, which is part of why Feynman could write in the early 1960s that the experiment had never been performed.

We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.
Richard FeynmanThe Feynman Lectures on Physics, Volume III, 1965

You might think

Feynman said the single-electron double slit was a thought experiment that could never actually be done.

Actually

He did say that — and he was wrong, in a way worth knowing about. In the Lectures he presents the electron two-slit experiment as a "thought experiment", remarking that it had never been done in this way and that the apparatus would have to be impossibly scaled down. In fact Jönsson had performed the two-slit version with electron beams in 1961, four years before the Lectures were published; the paper was in German and not translated until 1974. And the single-electron version — one electron in the apparatus at a time — was achieved by Merli, Missiroli and Pozzi in 1976 and definitively by Tonomura in 1989. Feynman’s physics was exactly right and his experimental claim was out of date. It is a reminder that even the best physicists rely on what has reached them.

1801Young demonstrates two-slit interference with light and measures its wavelength.
1803He is savaged in the Edinburgh Review and largely leaves optics.
1818Fresnel’s wave theory wins the Académie prize; Poisson’s spot is found where he predicted it as a reductio.
1927Davisson–Germer and G.P. Thomson diffract electrons from crystals.
1961Jönsson performs the true two-slit experiment with electrons — and with three, four and five slits.
1965Feynman calls it the only mystery, believing it has never been done.
1974Jönsson’s paper is translated into English.

Where this leaves us

For a wave, "which slit did it go through?" is not a good question — a wave is spread out, and it went through both. That is a complete and comfortable answer. But an electron is not comfortable in that role. It has a definite mass and a definite charge. It arrives at a detector at one place, making one click, leaving one spot. Nobody has ever detected half an electron. So the uncomfortable question is unavoidable: what happens if you send them through one at a time? Turn the beam down until there is only ever a single electron in the apparatus — so that for the several milliseconds it is in flight, there is nothing else in there for it to interfere with. Each one arrives at a single point, like a particle. And the pattern that assembles itself out of those points, over hours, is the interference pattern. That experiment has been done, and readers of Physics World once voted it the most beautiful in all of physics.