In 1900, Planck discovered that energy is emitted in discrete packets (quanta). A desperate solution to a mathematical problem that gave birth to modern physics.
🌃 A Night of Desperation in Berlin
On October 7, 1900, physicist Heinrich Rubens visited his colleague Max Planck at his home in Berlin. He brought with him recent measurements of black-body radiation — and bad news. The equation Planck had been defending for months, known as the Wien-Planck law, did not match the experimental data at long wavelengths. Planck was 42 years old, a professor of theoretical physics at the University of Berlin, and his life was about to change that evening.
Planck worked feverishly as soon as his visitor departed. Within just a few days he constructed a new equation combining two already known approaches — Wien's law for short wavelengths and Rayleigh's law for long ones. On October 19, 1900, he presented his formula at the German Physical Society (Deutsche Physikalische Gesellschaft). Rubens and Kurlbaum immediately compared the formula with their data: it fit perfectly at every wavelength. But Planck himself acknowledged that without a physical explanation, his equation was merely a “lucky intuition.”
☀️ The Black-Body Radiation Problem
To understand what exactly Planck solved, we need to go back a few years. In 1859, Planck's teacher Gustav Kirchhoff had posed a fundamental question: how does the intensity of electromagnetic radiation from an ideal black body depend on the frequency and temperature? A black body completely absorbs all radiation that falls upon it — it reflects nothing. In thermal equilibrium, it emits radiation with a characteristic spectrum that depends only on temperature.
Kirchhoff predicted that this spectrum would be described by a “universal function” — something so fundamental it was later called “Kirchhoff's challenge.” In practical terms, if you heat a metal object, it first glows red, then orange, then white. The Sun, with a surface temperature of about 5,777 Kelvin, shines primarily in the visible spectrum. The question was: which mathematical formula precisely describes this spectral distribution?
💥 The “Ultraviolet Catastrophe”
At the end of the 19th century, two approaches competed. Wilhelm Wien proposed in 1896 a law that fit very well at short wavelengths (high frequencies) but failed at long ones. Lord Rayleigh proposed in 1900 a formula based on the equipartition theorem of classical statistical mechanics, which worked at long wavelengths but led to an impossible prediction: at high frequencies, energy tended toward infinity. Paul Ehrenfest named this problem the “ultraviolet catastrophe” in 1911.
Classical physics assumed that every oscillation mode of an electromagnetic field in a cavity carries energy kBT. But the number of oscillation modes increases proportionally to the square of the frequency — meaning the higher you go in the spectrum, the more modes exist. Multiplying “constant energy per mode” by “infinite modes” gives infinite emission. Something was deeply wrong with the fundamental rules.
😬 “An Act of Desperation”
After the October 19 presentation, Planck began what he later described as “the hardest work of my life.” He sought a physical basis for his formula. Traditionally, Planck had been deeply skeptical of Ludwig Boltzmann's statistical thermodynamics. He did not believe in atoms, considered the second law of thermodynamics absolute rather than statistical. But nothing else worked.
In what he himself called “an act of desperation” (ein Akt der Verzweiflung), Planck turned to Boltzmann's method. It was the only lifeline that could make his formula work. On December 14, 1900, he presented his new theoretical derivation at the German Physical Society. His central assumption was unprecedented: electromagnetic energy cannot be emitted or absorbed continuously, but only in discrete “packets” (quanta), with energy:
E = hν
where h is Planck's constant (approximately 6.626 × 10−34 J·s) and ν is the frequency of the radiation. This relationship means that the energy of each quantum depends exclusively on the frequency: higher frequency = larger minimum energy packet. At ultraviolet frequencies, the packets become so large that thermal energy is insufficient to activate them — and the radiation “freezes out.” This explained why the ultraviolet catastrophe never occurs in practice.
🧪 A Reluctant Revolutionary
It is worth emphasizing: Planck was no revolutionary. He was a conservative thinker, deeply attached to classical physics. He himself initially considered the quantum hypothesis “a purely formal assumption... in reality I did not think much about it.” He never proposed that light itself consists of particles — that was done by Einstein five years later, in 1905, with the theory of photons. Planck spent years trying to “bring back” quanta within the framework of classical physics, without success.
Max Born later wrote about Planck: "He was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from announcing the most revolutionary idea which ever has shaken physics."
⚛️ The Legacy: From Quanta to Quantum Mechanics
Planck's discovery triggered a chain of events that transformed physics. Einstein, in 1905, used the formula E = hν to explain the photoelectric effect — if light energy is transmitted in quanta (photons), then only photons above a critical frequency can eject electrons from a metallic surface, regardless of the light's intensity. Niels Bohr, in 1913, applied quanta to the structure of the atom. Werner Heisenberg, in 1925, founded matrix quantum mechanics. Satyendra Nath Bose, in 1924, developed the statistical mechanics of photons which led to a theoretical derivation of Planck's law.
The constant h proved ubiquitous: it appears in Heisenberg's uncertainty principle (ΔxΔp ≥ ℏ/2), in the energy levels of the hydrogen atom, in the tunneling phenomenon, in quantum electrodynamics. Since 2019, Planck's constant also defines the kilogram: 1 kg is based on the value h = 6.62607015 × 10−34 J·s, a change that replaced the physical prototype of the platinum cylinder in Paris.
🏅 The Man Behind the Constant
Max Karl Ernst Ludwig Planck was born on April 23, 1858 in Kiel. He had exceptional musical talent — he played piano, church organ and cello, possessed absolute pitch and loved Schubert and Brahms. His physics professor Philipp von Jolly discouraged him from pursuing theoretical physics, telling him that “in physics there is nothing significant left to be discovered.” This prediction proved spectacularly wrong.
Planck studied in Munich and Berlin, where Helmholtz and Kirchhoff taught. He received the Nobel Prize in Physics in 1918 "for the services he rendered to the advancement of physics through his discovery of energy quanta." His life was marked by tragedies: his first son was killed at Verdun in 1916, his two daughters died in childbirth, and his son Erwin was executed by the Nazis in January 1945 for his participation in the plot to assassinate Hitler. Planck died on October 4, 1947 in Göttingen, at the age of 89.
Today, the Max Planck Society (Max-Planck-Gesellschaft) is Germany's premier research organization, with 83 institutes across a wide range of disciplines. The constant h, introduced as a mathematical artifice on that evening in 1900, is today a fundamental constant of nature — not only of quantum physics, but of humanity's entire system of measurement.