Matter Waves

Louis de Broglie’s idea sounds like a riddle. Light, which everyone thought was a wave, turned out to also be particles (Chapter 0). So de Broglie asked: what if the reverse is true too? What if particles – electrons, atoms, footballs – are also waves? Each moving thing would carry a wavelength: the faster and heavier it is, the shorter its wave. It sounded absurd. Within three years, experiments proved him right, and it earned him the Nobel Prize. This chapter is about what those matter waves are – and about the experiment Richard Feynman called “the only mystery” of quantum mechanics.

De Broglie’s rule, in plain words: every moving thing carries a wave, and the heavier or faster the thing, the smaller its wave. The waves of everyday objects are absurdly, unmeasurably small – a thrown baseball’s wave is a billion billion times smaller than an atomic nucleus. That’s why the world looks solid and un-wavy: not because quantum mechanics stops applying to big things, but because their waves are far too small to ever notice.

Shrink down to an electron, though – the lightest particle there is – and the wave becomes as big as an atom: impossible to ignore. Explore the scale below.

Fire electrons – one at a time, with long gaps between them – at a wall with two narrow slits, and record where each lands on a screen behind. Each electron arrives as a single dot: particle. But wait, and the dots organise into stripes – zones where electrons often land, separated by zones where they never do: an interference pattern, the unmistakable fingerprint of a wave passing through both slits at once. Each electron interferes with itself.

Stranger still: put a detector at the slits to see which one each electron went through, and the stripes vanish. Watching the wave forces it to pick a side. Run the experiment below – and try the detector toggle.

A pure wave goes on forever – but a particle is somewhere. The fix: add together many waves of slightly different wavelengths. They agree in one region (a lump) and cancel everywhere else. That lump – a wave packet – is the closest a wave gets to being a particle.

Watch two speeds in the animation: the little ripples inside the packet move at one speed, while the lump itself moves at another – twice as fast, in fact. The lump is what carries the particle. And notice the packet slowly spreading out: the price of building “somewhere” out of waves is that “somewhere” gets blurrier over time.

Now the payoff. Chapter 0 left a mystery: why is an electron allowed only on certain orbits? De Broglie’s answer: wrap the electron’s wave around its orbit. If a whole number of wavelengths fits the loop, the wave closes on itself and reinforces – a stable standing wave, like a guitar string’s note. If not, the wave comes back out of step and cancels itself out. The allowed orbits are simply the ones where the wave fits. Try the slider: only whole numbers work.

Particles are waves; waves that fit are the allowed states; and watching a wave changes what it does. But what exactly is waving? Water waves are water; sound waves are air. The electron’s wave, it turns out, is made of something much stranger: complex numbers – numbers with a direction. That’s Chapter 2.