Planck's Quantum Hypothesis (1900): The Birth of Quantum Theory

Max Planck’s quantum hypothesis, presented in Berlin on 14 December 1900, solved the problem of black-body radiation by assuming that energy is exchanged only in discrete packets, or quanta. To make his formula fit the experimental data, Planck introduced a new constant of nature, now called Planck’s constant. Though he regarded the step as a mathematical expedient, it is generally taken as the birth of quantum physics.

Background: the black-body problem

When an object is heated it glows, first dull red, then orange, then white. In 1859–1860 the German physicist Gustav Kirchhoff showed that for an ideal “black body”, one that absorbs all radiation falling on it, the spectrum of this glow depends only on temperature, not on the material. In practice, a good black body can be made from a hollow box with a small hole: almost any light entering the hole is trapped, and the radiation escaping from it when the box is heated is close to the ideal. Finding the formula for that spectrum became a major goal of physics.

The question also had practical weight. German industry was developing electric lighting, and the Physikalisch-Technische Reichsanstalt (PTR), the national standards laboratory in Berlin, made precise measurements of radiation to set standards for lamps. In 1896 Wilhelm Wien proposed a formula that matched measurements at short wavelengths well.

By 1899–1900, however, careful work at the PTR by Otto Lummer and Ernst Pringsheim, and by Heinrich Rubens and Ferdinand Kurlbaum at long infrared wavelengths, showed that Wien’s law failed. In June 1900 Lord Rayleigh in Britain proposed a different law based on classical physics that worked for long wavelengths but not for short ones.

Max Planck

Max Planck (1858–1947), born in Kiel, became professor of theoretical physics at the University of Berlin in 1889 (full professor from 1892). He was an expert in thermodynamics and had worked on black-body radiation since 1894, hoping to explain the irreversible flow of heat from first principles. He was a cautious, conservative scientist, the opposite of a revolutionary by temperament.

Planck had come to physics despite discouragement. As a student in Munich he was reportedly advised by his teacher Philipp von Jolly that almost everything in physics had already been discovered. He chose theory anyway, writing his doctoral thesis on the second law of thermodynamics, and in Berlin he succeeded Gustav Kirchhoff in the chair of theoretical physics. Colleagues valued his clarity and integrity, qualities that later made him a respected spokesman for German science.

October 1900: the right formula

On Sunday 7 October 1900 Rubens and his wife visited the Plancks and told him about the new long-wavelength measurements. That evening Planck found a formula that blended Wien’s law at short wavelengths with the observed behaviour at long ones. He presented it at a meeting of the German Physical Society on 19 October 1900. Rubens compared it with his data overnight and found excellent agreement. Over the following years, ever more precise measurements across the whole spectrum confirmed the formula, which has never needed correction.

A formula that fitted was not yet an explanation. Planck now needed to derive it from physical principles.

December 1900: the quantum

Planck modelled the walls of the black body as a collection of tiny electrical oscillators exchanging energy with the radiation. To calculate their entropy he turned to the statistical methods of the Austrian physicist Ludwig Boltzmann, which Planck had previously resisted. Boltzmann’s method required counting the ways energy could be shared among the oscillators, and that counting worked only if the energy was divided into finite elements.

Planck set the size of each energy element equal to h multiplied by the frequency of the oscillator, where h was a new constant. He presented this derivation to the German Physical Society on 14 December 1900. From his formula and the measurements, he calculated values for h and for Boltzmann’s constant k, and from them good estimates of Avogadro’s number and the charge of the electron.

Planck later wrote that the step had been an act of desperation, taken because nothing else would yield the right result. He expected that the energy elements would eventually be explained away within classical physics.

At the time, almost no one recognised the step as radical. Listeners at the Physical Society were impressed mainly that the formula fitted the data so well. Planck’s own papers of 1900 and 1901 presented the energy elements briefly, and the full strangeness of the idea, that an oscillator could not hold any amount of energy but only whole multiples of a smallest unit, emerged only gradually as others examined the derivation.

Myths and facts

Myth: Planck was trying to solve the “ultraviolet catastrophe”. The classical prediction that a black body should emit unlimited energy at short wavelengths is now often called by that name, but the term was coined by Paul Ehrenfest in 1911. Planck in 1900 was not reacting to it; he was trying to explain precise measurements from the PTR.

Myth: Planck immediately proposed that light is made of particles. He quantised the energy of the oscillators in the walls, not the radiation itself. The idea that light comes in quanta was Albert Einstein’s, in 1905.

Consequences

For several years few physicists, Planck included, thought the quantum was physically real. That changed in 1905, when Einstein used light quanta to explain the photoelectric effect (see Einstein’s miracle year). In 1907 Einstein applied quanta to explain how the heat capacity of solids falls at low temperatures, and in 1911 the first Solvay Conference in Brussels gathered leading physicists to discuss the quantum problem.

In 1913 Niels Bohr used Planck’s constant to explain the spectrum of hydrogen with a quantised model of the atom, building on Rutherford’s nucleus. In the mid-1920s Werner Heisenberg, Erwin Schrödinger, Paul Dirac and others developed full quantum mechanics, in which h sets the scale of every quantum effect. Because h is so tiny, quantum effects are invisible in everyday life but dominate the behaviour of atoms, electrons and light.

Legacy

Planck received the 1918 Nobel Prize in Physics, awarded in 1919, “in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta”. He became a leading figure in German science and an early supporter of Einstein’s relativity. His later life was marked by personal tragedy: his elder son Karl was killed at Verdun in 1916, and his son Erwin was executed in January 1945 for links to the July 1944 plot against Hitler. Planck died in Göttingen on 4 October 1947. In 1948 Germany’s main research organisation was renamed the Max Planck Society in his honour.

Planck’s constant is about 6.626 × 10⁻³⁴ joule-seconds. Since 20 May 2019 its value has been fixed exactly, and the kilogram is defined through it, so the quantum Planck reluctantly introduced now anchors the international system of units.

Timeline

• 1859–1860: Gustav Kirchhoff defines the black-body problem.
• 1896: Wilhelm Wien proposes his radiation law.
• 1899–1900: PTR measurements reveal deviations from Wien’s law.
• 1900, 7 October: Rubens tells Planck of new data; Planck finds his formula.
• 1900, 19 October: Planck presents the radiation formula in Berlin.
• 1900, 14 December: Planck presents its derivation using energy quanta.
• 1905: Einstein proposes that light itself consists of quanta.
• 1919: Planck receives the 1918 Nobel Prize in Physics.
• 2019, 20 May: The SI is redefined with Planck’s constant fixed exactly.

Why it matters

Planck’s hypothesis broke with the assumption, unquestioned since Newton, that energy changes smoothly and continuously. The quantum idea grew into the theory that explains atoms, chemistry, semiconductors and lasers, building on the earlier electromagnetic picture of light (see Maxwell’s electromagnetic theory).