Waves and particles

The ultraviolet catastrophe

The quantum began, in a sense, with a fireplace. Everything warm gives off electromagnetic radiation, and the hotter it is, the more it gives off and the bluer the color: a stove element glows dull red, then orange, then white. Physicists call an ideal radiator a blackbody; in Berlin they built one as a heated hollow oven with a small hole. By 1900 they could measure how much radiation it emits at each wavelength. The curve rises to a peak and falls away again. A hotter body is brighter at every wavelength, and its peak shifts toward shorter wavelengths.

No theory could explain that curve. The best formula, Wilhelm Wien’s, worked at short wavelengths but failed in the infrared, as new measurements showed in 1900. Classical physics, applied fully, matched the infrared but predicted radiation climbing without limit at short wavelengths. That runaway was spelled out in 1905, and in 1911 Paul Ehrenfest named it the ultraviolet catastrophe.

Planck was not fighting that catastrophe. In October 1900 he found a formula that fit the new data, which had broken Wien’s law, a law he had defended. When he presented its derivation that December, he had to make a strange assumption: the energy of the tiny vibrating charges in a hot body comes only in whole portions, each worth a new constant, h, times the frequency. High-frequency portions are so expensive that the charges rarely hold them, so the curve comes back down.

Planck treated the portions as a mathematical device; historians still argue about how literally he meant them. Three decades later he called the step “an act of desperation.” The formula was accepted at once; the quantum was mostly ignored for years.

Light comes in lumps

The person who took the quantum further was Albert Einstein, with a different puzzle. Shine light on a metal plate and electrons fly out; this is the photoelectric effect. If light were an ordinary wave, brighter light would carry more energy, and the electrons should come out faster. They don’t. In 1902 Philipp Lenard found that brighter light knocks out more electrons, but not faster ones. What makes the fastest of them faster is a higher frequency: blue or ultraviolet light instead of red.

In 1905 Einstein proposed that light itself comes in lumps, quanta that, he wrote, can be “absorbed or produced only as wholes”: less like water from a hose than like shots from a gun, pop, pop, pop. Each quantum, later called a photon, carries energy set by its frequency. Higher frequency means more energetic photons and faster electrons; brighter light means more photons and more electrons. He predicted an exact law, a straight line with the same slope for every metal, and Robert Millikan in Chicago, who called the idea “reckless,” confirmed it in 1916. Einstein kept the waves too: light, he suggested, behaves as a wave on average but delivers its energy in lumps.

The year 1905 invites comparison with Newton’s plague years of 1665–66, as Newton later recalled them. The paper on jiggling particles gave a way to prove that atoms are real. Einstein’s 1921 Nobel Prize, awarded in 1922, was given “especially for his discovery of the law of the photoelectric effect,” not for relativity, which the committee’s expert judged unproven. Einstein’s lesson, in this reading, is never to be confined by what you’ve seen and been taught:

I am enough of the artist to draw freely upon my imagination. Imagination is more important than knowledge.

Albert Einstein, interview in the Saturday Evening Post, October 26, 1929

The same “why not?” runs back to Thales, who, as later writers report, asked why earthquakes couldn’t have a natural cause. Refusing to rule things out has carried humanity into the quantum age, though imagination still needs a test: Einstein’s line counted once Millikan’s data fell on it.

Everything is a wave

So light acts as a wave in some experiments and as particles in others, which seemed absurd. Then the French physicist Louis de Broglie proposed, in 1923 and in his 1924 doctoral thesis, that the same must be true of everything, including electrons, which everyone had taken to be tiny balls. In 1927 electrons bounced off a nickel crystal at Bell Labs in New York, and passed through thin metal films in Aberdeen, Scotland, in exactly the patterns waves make.

The double slit

The clearest way to see this is an experiment with two slits. Fire small balls at a wall with two slits in it, and the balls that get through land as the two single-slit piles added together, with no stripes. Send a water wave at the same wall, and the waves spreading from the two slits overlap. Where crest meets crest they reinforce each other, where crest meets trough they cancel, and the screen shows alternating bright and dark bands, called interference fringes. Thomas Young showed such fringes with sunlight in 1803.

Now send electrons, or photons, one at a time. Each arrives at a single point on the screen, like a particle. But as thousands build up, the points form bands, the interference pattern of a wave. Physicists in Bologna filmed this electron by electron in 1974, and a team at Hitachi in Japan made the famous version in 1989; both split each electron’s wave with a fine wire rather than slits.

Then comes the strangest part. Place a detector at the slits to record which slit each electron passes through, and the bands fade away, leaving the two single-slit piles, as with balls. Nobody has to watch: any physical record of the path erases the bands, even one left on a stray air molecule that no one ever reads. And every dot on the screen is itself a measurement.

In Newton’s world, an observer made no difference. A person watching a planet or a cart was just another body, with no effect unless it exerted a force; in this course’s reading, that is what made reductionism possible. In the quantum world, a measurement that records which way the particle went cannot leave the pattern untouched, even when it gives no push. This is called wave–particle duality. It has been seen in electrons, atoms, molecules, and, as of 2026, clusters of more than 7,000 sodium atoms.

What, then, is the wave of an electron? The answer came fast: in June 1926 Max Born proposed that it tells you probabilities. Where the wave is large, you are likely to find the electron; where it is small, you are unlikely to. Strictly, the probability goes with the square of the wave’s size. In the standard reading, the electron isn’t a little ball sitting somewhere; it is spread through space as a set of possibilities, until a detector registers it, always whole, in one place. The argument about what the wave really is has never ended.