In 1894, at the opening of a new laboratory at the University of Chicago, the American physicist Albert Michelson repeated a view he credited to an eminent colleague: the great principles of physics were probably settled, and "the future truths of physical science are to be looked for in the sixth place of decimals." Within a decade, measurements made to just that kind of precision had begun to break physics open. This course tells the story of that break.

A confident century ends

By 1900 physics rested on three great pillars. Newton's mechanics described motion, Maxwell's equations described electricity, magnetism and light as one field, and thermodynamics described heat and energy. Together they explained a huge range of phenomena, and many physicists believed the remaining work was a matter of tidying up.

Not everyone was so sure. In April 1900 Lord Kelvin gave a lecture at the Royal Institution in London, later published as "Nineteenth Century Clouds over the Dynamical Theory of Heat and Light." He described two clouds hanging over the theory of heat and light. One was the failure of experiments to detect the earth's motion through the ether, the medium that light waves were thought to travel in. The other was a puzzle about how energy is shared out among the parts of a body. The first cloud would lead to relativity. The second, in a roundabout way, pointed toward the quantum.

The blackbody problem

Heat any object enough and it glows: dull red, then orange, then white. In 1860 Gustav Kirchhoff showed that an ideal object called a blackbody, an object that absorbs all the light falling on it, would give off a spectrum of colors that depends only on its temperature, not on what it is made of. A small hole in the wall of a hot oven behaves almost exactly like one. Kirchhoff posed a challenge: find the universal formula for that spectrum.

The problem was not only abstract. In Berlin, the Imperial Physical and Technical Institute, known by its German initials PTR, measured glowing bodies with great care, partly because the answers mattered to industry, especially electric lighting. Physicists such as Otto Lummer, Ernst Pringsheim, Heinrich Rubens and Ferdinand Kurlbaum built instruments that could measure radiation deep into the infrared.

Theory struggled to keep up. A formula proposed by Wilhelm Wien in 1896 fit the data at short wavelengths but drifted away from the new infrared measurements. A different line of reasoning, based squarely on classical physics, gave what became known as the Rayleigh-Jeans formula, after Lord Rayleigh's work in 1900 and James Jeans's in 1905. It worked at long wavelengths but predicted that a hot body should pour out ever more energy at shorter and shorter wavelengths, without limit. That cannot be true, since a warm stove does not blast out deadly ultraviolet light. In 1911 Paul Ehrenfest named this failure the "ultraviolet catastrophe."

Planck's formula and its price

Max Planck was a professor in Berlin, 42 years old, a careful and conservative man who believed deeply in the laws of thermodynamics. On a Sunday in early October 1900, Heinrich Rubens and his wife visited the Plancks, and Rubens described his latest results. New infrared measurements by Rubens showed clearly where Wien's formula failed. That evening Planck worked out a new formula that blended the two known behaviors, and he presented it on October 19. It matched the data almost perfectly.

A formula that fits is not yet an explanation, and Planck spent the next weeks looking for one. To find it he turned to Ludwig Boltzmann's statistical approach to entropy, which counts the ways energy can be arranged among many parts. Planck had long distrusted this method. To make the counting work, he treated the energy of the tiny vibrating parts of the oven's walls as coming in small, separate amounts, each in proportion to the frequency of vibration. The constant linking energy to frequency is now called Planck's constant. On December 14, 1900, he presented to the German Physical Society a derivation that split energy into finite elements. That date is often called the birthday of quantum theory.

Many years later, in a letter of 1931, Planck described the step as something done out of desperation, by a man ready to give up almost any earlier conviction except the basic laws of thermodynamics.

A revolution almost nobody noticed

For several years hardly anyone saw anything revolutionary in Planck's work, and Planck least of all. He regarded his energy elements as a formal device, not a fact about light itself, and he spent years trying to fit them back into classical physics. Revolutions in science are often recognized only in hindsight. The person who opens the door may not want to walk through it.

Worked example: the evidence at the decimal point

Picture the data as it stood in 1900. At short wavelengths, Wien's formula fit well. At long wavelengths, Rubens and Kurlbaum's infrared readings bent away from Wien and toward the classical Rayleigh formula.

Planck's response had two stages, and it helps to separate them. First he found a curve that joined the two regions smoothly, an act of skilled guesswork. Then he asked what physical assumption would produce that curve, and found that only an unwelcome one would: energy divided into pieces. Michelson had been right that precise measurement matters, but wrong about what it would deliver. The sixth decimal place did not polish old principles. It overturned them.