Imagine firing tennis balls, one at a time, at a wall with two narrow gaps in it, toward a screen behind. You would expect two piles of marks, one behind each gap. Now replace the tennis balls with electrons. The marks arrive one at a time, as tiny dots, just like balls. But as thousands pile up, they form a pattern of bright and dark stripes that only waves should make. The physicist Richard Feynman called this experiment the heart of quantum mechanics, and it is worth taking slowly.

How waves make stripes

In the early 1800s the English scientist Thomas Young shone light through two narrow slits and saw a pattern of light and dark bands on a screen. Water waves do the same. Where crests from the two slits meet crests, they add up and make a bright band. Where a crest meets a trough, they cancel and leave darkness. This adding and canceling is called interference, the signature of waves adding and canceling one another. Particles, such as thrown stones, do not cancel each other out.

One at a time

The puzzle deepens when the source is made so weak that only one particle is in the apparatus at a time. In 1909 the British physicist Geoffrey Ingram Taylor photographed interference fringes using light so faint that one exposure lasted months. In 1989 Akira Tonomura and colleagues at Hitachi in Japan sent electrons one by one through a similar two path setup and filmed the screen. Each electron landed as a single dot at one spot. At first the dots looked random. After tens of thousands, the stripes appeared.

This rules out an easy explanation. The stripes cannot come from electrons bumping into one another, because they pass through one at a time. Each single electron must somehow be affected by both slits, since closing either slit destroys the stripes. Yet each one is detected at just one point. The electron travels like a wave and arrives like a particle.

Looking destroys the pattern

Suppose we add a detector to find out which slit each electron goes through. The detector works: every electron is found at one slit or the other, never both. But once the path is recorded, the interference stripes disappear, and the screen shows just two plain piles, as if the electrons were tennis balls. Remove the detector and the stripes return. Careful experiments suggest that what matters is not simply a clumsy push from the detector, but whether information about the path exists anywhere at all.

Niels Bohr called this complementarity: wave behavior and particle behavior are both real, but no single experiment shows both fully at once. An experiment can reveal the path or the interference, not both. The sharper the path information, the fainter the stripes.

Waves of matter

Louis de Broglie proposed that every particle has a wavelength, and that the greater its momentum, the shorter its wavelength. Momentum is mass times speed, so heavy or fast objects have very short waves. For electrons at modest speeds, the wavelength can be about the size of an atom, which is why electrons interfere so readily. This also means that beams of fast electrons, with their very short wavelengths, can reveal details far smaller than light can, a fact put to work in the example below.

Remarkably, the effect is not limited to tiny particles. In 1999 a team in Vienna led by Anton Zeilinger and Markus Arndt sent buckyballs, soccer ball shaped molecules, through a grating and showed that molecules of 60 carbon atoms can interfere just as electrons do. Later experiments have shown it with molecules of nearly 2,000 atoms. No known law sets a size limit; the difficulty of going bigger is practical, a point that returns in the final level.

Worked example: the electron microscope

Short wavelengths are useful. An ordinary microscope cannot show details much smaller than about half the wavelength of the light it uses, roughly a quarter of a micrometer for visible light. That limit hides most viruses and the fine machinery of cells. In 1931 the German engineers Max Knoll and Ernst Ruska built the first electron microscope, which replaces light with a beam of electrons and glass lenses with magnetic coils. Because fast electrons have wavelengths many thousands of times shorter than visible light, the microscope can resolve far finer detail. Modern instruments can image individual atoms.

The design rests on the electron's double nature. Its wave side sets the finest detail it can show, just as the wavelength of light does for an ordinary microscope, and engineers raise the electrons' speed to shrink that wavelength. Its particle side shows up at the detector, where each electron leaves a single spark and the image is built dot by dot, exactly as the stripes were in Tonomura's film. Ruska shared the 1986 Nobel Prize in Physics, more than half a century after his invention. Today, in a form called cryo electron microscopy, the same idea lets biologists see the shapes of proteins and viruses, including ones studied in designing vaccines. A puzzle about stripes on a screen has become one of medicine's sharpest eyes.