The problem of blackbody radiation lacked a theory that could correctly reproduce the intensity and color of light emitted at different temperatures. Planck applied statistical mechanics and boldly assumed that a harmonic oscillator can possess only energies that are integer multiples of hν, where h is a constant and ν the frequency. With this assumption he derived the radiation spectrum now called "Planck’s law," matching experimental data perfectly. The idea that energy is discrete rather than continuous shocked the classical physics community of the day. Later, Einstein’s light-quantum hypothesis and Bohr’s atomic model embraced Planck’s quantum concept and developed it further. The notion of quanta underlies modern technologies such as semiconductor lasers and MRI scanners, dramatically influencing society. Planck’s 1900 paper therefore marks a decisive turning point in the history of physics.

The “ultraviolet catastrophe” of blackbody radiation stemmed from the Rayleigh–Jeans formula predicting infinite energy at high frequency. Planck quantized the harmonic oscillator energy levels as E_n = n hν and introduced the partition function Z = Σ exp(−E_n/kT) to compute the mean energy ⟨E⟩. He obtained ⟨E⟩ = hν/[exp(hν/kT) − 1] and used it to derive the spectral energy density I(ν,T) = (2hν^3/c^2)/[exp(hν/kT) − 1]. This expression smoothly coincides with the Rayleigh–Jeans limit at low frequency and Wien’s law at high frequency, matching experimental data. The constant h ≈ 6.626×10^−34 J·s became a cornerstone of quantum theory, appearing in de Broglie relations and the Heisenberg uncertainty principle. Quantization proved crucial for explaining atomic line spectra and the temperature dependence of solid heat capacities, among many puzzling phenomena. While Planck initially regarded quanta as a mere mathematical device, Einstein embraced the physical reality of photons, launching full-fledged quantum physics. Today quantum electronics, quantum information science, and even modern metrology—such as the redefinition of the kilogram fixing h—are rooted in Planck’s constant. The award has been called “the opening of the door to modern physics,” fundamentally reshaping our understanding of energy, information, and matter through quantum theory. Hence Planck’s work provides theoretical foundations that extend beyond physics to chemistry, biology, and engineering.

Planck analyzed an ensemble of one-dimensional harmonic oscillators modelling blackbody modes and recalculated their statistical behavior within Boltzmann’s framework. By discretizing energies as E_n = n hν instead of using a continuum, he removed the ultraviolet divergence and derived I(ν,T) that agrees with experiment. The constant h emerged as a quantum of action later embedded in de Broglie and Schrödinger formulations of wave–particle duality. Planck initially envisioned quantum cells in classical phase space, adopting a compromise rather than a fully non-classical stance. With Einstein’s photon hypothesis and the Bohr–Sommerfeld quantization rule, h appeared in the integral ∮ p dq = n h, revealing the universality of the quantization condition. Planck’s law still serves as a baseline model in modern quantum field contexts, from the Casimir effect and the CMB spectrum to optical cavity quantum noise. Photon statistics derived from the blackbody distribution underpin Bose–Einstein condensation and laser coherence theory, while h features in renormalization-group scale parameters. In recent SI redefinitions using the Kibble balance and Josephson–quantum Hall interlinking, h has been fixed at 6.62607015×10^−34 J·s, embedding quantum standards into metrology. Thus, the 1918 Nobel Prize marks the birthplace of quantum field theory, seeding diverse research topics such as non-commutative operator algebras, field quantization, and informational entropy.