By 1900 many physicists felt their subject was nearly complete. Newton's mechanics, Maxwell's electromagnetism and the laws of heat seemed to explain almost everything. A few small puzzles remained. One of them, the color of the light given off by hot objects, would overturn the classical picture of the world and replace it with something far stranger.

Packets of energy

A poker in a fire glows red, then orange, then yellowish white as it heats. When physicists applied the classical laws to the light inside a hot oven, they got an absurd answer: an infinite amount of energy at short wavelengths. In 1900 the German physicist Max Planck found a formula that matched the measurements, but only by assuming that energy is given off and absorbed in tiny separate packets, called quanta, rather than in any amount at all. The size of each packet depends on frequency: higher frequency light comes in bigger packets. Planck at first saw this as a mathematical device, not a fact about nature.

Einstein took it literally. In 1905 he tackled the photoelectric effect, in which light knocks electrons out of a metal. Puzzlingly, even dim ultraviolet light could free electrons, while bright red light could not, however intense. Einstein proposed that light itself comes in particles, later called photons, each with an energy set by its frequency. A single ultraviolet photon carries enough energy to free an electron; a flood of red photons, each too weak, cannot. Einstein's Nobel Prize of 1921 was awarded for his explanation of the photoelectric effect, not for relativity. Light, it seemed, was both a wave, as Young had shown, and a stream of particles.

The quantum atom

An atom is a tiny, dense nucleus surrounded by electrons. Classical physics said an electron circling a nucleus should give off light continuously and spiral inward in a tiny fraction of a second. Atoms plainly do not collapse. In 1913 the Danish physicist Niels Bohr proposed that electrons in an atom can occupy only certain allowed energy levels, and that the atom gives off or absorbs light only when an electron jumps between levels. His model was soon replaced by a fuller theory, but its central idea of fixed energy levels survives.

In 1924 the French physicist Louis de Broglie made a bold suggestion: if light waves can act like particles, perhaps particles such as electrons can act like waves. In 1927 experiments by Clinton Davisson and Lester Germer in the United States, and by George Paget Thomson in Scotland, showed electrons forming interference patterns, just as waves of light do. Erwin Schrödinger had already written an equation for these matter waves in 1926. Max Born then argued that the wave does not describe where the electron is, but the probability of finding it in each place when we look.

Uncertainty and strangeness

In 1927 Werner Heisenberg showed that the more precisely a particle's position is pinned down, the less precisely its momentum can be known, and the reverse. This uncertainty principle is not a complaint about clumsy instruments. It reflects the wavelike nature of matter itself.

Quantum theory predicts experimental results with astonishing accuracy, yet it says many individual outcomes are a matter of chance until measured. Einstein disliked this deeply and argued about it with Bohr for decades. In a 1935 paper with Boris Podolsky and Nathan Rosen, he pointed to what is now called entanglement, in which two particles share one quantum state, so that measuring one immediately tells you what will be found for the other, however far apart they are. He took this as a sign that the theory was incomplete and that hidden details had been left out. Experiments since the 1970s, honored with the 2022 Nobel Prize in physics to Alain Aspect, John Clauser and Anton Zeilinger, have found that entangled particles show correlations that no theory of hidden local properties can explain. Entanglement cannot be used to send messages faster than light, but it is real. Physicists still disagree about what quantum theory says reality is like, even though nobody disputes its predictions.

Worked example: the quantum in your devices

Quantum theory can sound remote from daily life, but it runs much of it. A laser works because many atoms are lifted into a higher energy level and then triggered to drop back together, releasing a flood of identical photons. Lasers read barcodes, carry internet traffic down glass fibers and reshape the cornea in eye surgery.

The transistor, invented at Bell Labs in 1947, controls currents using the quantum behavior of electrons in materials such as silicon; a modern phone contains billions of them. An LED glows with a color fixed by the energy step that electrons drop across inside it. Hospital MRI scanners rely on a quantum property called spin in the hydrogen nuclei of the body. None of these could have been designed with the physics of 1900. The strangest theory in science turned out to be one of the most practical.