Book: The Origin and Development of the Quantum Theory

Context and Purpose
Planck recounts the scientific problem that drove the emergence of the quantum idea: the stubborn discrepancy between experimental measurements of blackbody radiation and the predictions of classical physics. Measurements of thermal radiation spectra, particularly at short wavelengths, refused to conform to the laws derived from classical electrodynamics and thermodynamics. The goal was to reconcile observed spectral distributions with the principles of energy conservation and entropy.
He frames the narrative as a step-by-step intellectual response to empirical puzzles. The account emphasizes the humility and caution with which new hypotheses were adopted, presenting quantization not as an a priori revolution but as a pragmatic device compelled by data.

Historical Narrative
The story opens with the development of laws for thermal radiation, Kirchhoff's identification of blackbody universality, Stefan and Boltzmann's temperature law, and Wien's displacement law. Early theoretical attempts produced approximate formulas that fit parts of the spectrum but failed at extremes. The classical approach culminated in formulas that predicted an "ultraviolet catastrophe," a divergence at short wavelengths that contradicted experiment.
Planck describes how an empirical interpolation, suggested by matching low- and high-frequency limits, led to a formula that agreed with measurements. This successful formula, however, lacked a firm microscopic justification until Planck himself provided a derivation based on a radical new assumption about the exchange of energy.

Core Idea: Energy Elements
The decisive hypothesis introduced energy elements proportional to frequency, E = hν, where h is a new universal constant. Radiation exchange between matter and the electromagnetic field was modeled via resonant oscillators, and these oscillators could only emit or absorb energy in discrete increments. Quantization of energy exchange, rather than quantization of radiation itself initially, served as the mathematical device that yielded the correct spectral law.
Planck stresses the modesty of the original claim: the quantization was a formal step to obtain the correct entropy and distribution, not an immediate assertion that energy is physically discontinuous in all processes. Nonetheless, the constant h emerged as a fundamental parameter, linking thermodynamics, electrodynamics, and statistical mechanics.

Statistical Reasoning and Entropy
Boltzmann's ideas about probability and entropy are central to the derivation. Planck adopts a combinatorial approach, counting the ways energy quanta could be distributed among oscillators, and relates this counting to the entropy through Boltzmann's principle. This statistical underpinning allowed the derived spectral distribution to satisfy both the Wien and Rayleigh-Jeans limits and to match precise measurements.
The route through statistical concepts forced a reexamination of the foundations of thermodynamics and the role of microscopic hypotheses. Planck reflects on the tension between deterministic classical mechanics and the probabilistic character introduced by his counting method.

Immediate Reception and Development
The quantum hypothesis provoked mixed reactions. Some contemporaries, including Einstein, extended and radicalized the idea by proposing light quanta, while others sought to reconcile quantization with classical theory. Subsequent work by Bohr, Sommerfeld, and others built upon Planck's constant to craft early quantum models of atoms and spectra, gradually shifting the theoretical landscape.
Planck reports the slow but inexorable conversion of a pragmatic mathematical device into a cornerstone of a new theoretical framework. The initial reluctance of many physicists gave way as more phenomena demanded discrete-energy explanations.

Implications and Legacy
Quantization inaugurated a fundamental revision of physical thought: classical assumptions about continuous energy exchange and equipartition no longer held universally. The constant h provided a new natural scale, linking thermodynamic temperature, frequency, and action, and signaled the necessity of a deeper theory to replace classical mechanics in atomic domains.
Planck views the origin of the quantum theory as illustrative of scientific progress: empirical stubbornness compels conceptual innovation, and cautious hypotheses may evolve into revolutionary principles. The lecture closes on a note that acknowledges both the provisional nature of early quantum ideas and their profound and lasting impact on the understanding of nature.