Articulation of Quantum Theory Summary

  • Last updated on November 10, 2022

In attempting to resolve anomalies in the traditional explanation of radiation emitted from certain heated objects, Max Planck restricted the object’s “resonators” to discrete (or quantized) energies, an ad hoc solution that proved to have revolutionary implications.

Summary of Event

Although Max Planck has traditionally been closely associated with the origin of quantum theory, some scholars have come to question whether he actually proposed the theory’s basic idea: that radiant energy is transmitted in discrete packets. Planck was reluctant to accept the idea of quantized energy. In his autobiography, he credits Albert Einstein with the idea. The question of Planck’s precise contribution to quantum theory therefore naturally arises. Quantum theory Physics;quantum theory Planck, Max [kw]Articulation of Quantum Theory (Dec. 14, 1900) [kw]Quantum Theory, Articulation of (Dec. 14, 1900) [kw]Theory, Articulation of Quantum (Dec. 14, 1900) Quantum theory Physics;quantum theory Planck, Max [g]Germany;Dec. 14, 1900: Articulation of Quantum Theory[6550] [c]Physics;Dec. 14, 1900: Articulation of Quantum Theory[6550] [c]Science and technology;Dec. 14, 1900: Articulation of Quantum Theory[6550] Einstein, Albert Clausius, Rudolf Boltzmann, Ludwig Eduard Wien, Wilhelm

During the first fifteen years of his scientific career, Planck devoted his efforts to clarifying, developing, and applying the laws of thermodynamics to a variety of problems. The first law of thermodynamics (the law of conservation of energy) states that, although energy can be changed into different forms, the total energy of an isolated system remains the same. The second law of thermodynamics, which involves the direction of energy flow, states that heat energy moves spontaneously from hot to cold regions or, more generally, that the amount of useless energy in an isolated system (called entropy) increases when an irreversible process occurs in that system.

This phenomenon of irreversibility fascinated Planck, who became an avid student of the writings of Rudolf Clausius, who, in 1865, had introduced the term “entropy” as a measure of the amount of thermal energy incapable of doing work (later seen as a measure of a system’s disorder). Planck came to believe that the second law of thermodynamics had absolute validity. During the 1880’s and 1890’s, he tried to convince his fellow physicists that entropy constitutes a principle of irreversibility, and—largely through Ludwig Eduard Boltzmann’s statistical arguments about the equipartition of energy in describing the behavior of a gas—Planck’s views on entropy prevailed. Clausius, Rudolf

During the 1890’s, Planck became interested in measurements of the radiation from very hot objects being made at a technical institute in Berlin. The theoretical construct used to understand this radiation was the “blackbody,” an idealized object that totally absorbs all radiation falling on it. By the laws of thermodynamics, this perfect absorber must also be a perfect emitter of radiation. Experimenters found that they could approximate a blackbody with a hollow metal box containing a pinhole. After heating the box to a uniform temperature, researchers studied the radiation emitted through the pinhole. They were surprised to discover that this radiation did not depend either on the type of metal or the size and shape of the box.

The “blackbody radiation” depended only on the temperature, and when the brightness (or intensity) of this radiation was plotted as a function of its color (or wavelength) for various temperatures, a set of humplike curves was generated. With higher temperatures, the curves kept their basic shape but their maxima shifted toward the shorter wavelengths (the ultraviolet portion of the spectrum). A family of these curves, the “normal spectral energy distribution,” represented for Planck “something absolute.” He very much wanted to find a satisfactory theoretical explanation of these experimental curves.

Wilhelm Wien Wien, Wilhelm , who studied blackbody radiation both experimentally and theoretically, devised an equation that accounted for the experimental results at high frequencies but not at low frequencies. The English physicist Lord Rayleigh Rayleigh, Lord , on the other hand, formulated an equation that fit the low frequencies but not the high. Wien had also found an empirical relationship between the temperature and the wavelength at the peak of the curve, and Boltzmann Boltzmann, Ludwig Eduard had discovered a relationship between the temperature and total radiated energy. However, no scientist had been able to provide a theoretical explanation of the entire family of curves.

For several years, Planck toiled at solving the mystery of the energy distribution of radiated heat by relying solely on the principles of thermodynamics. He chose this path, because these principles had, for him, absolute validity. He did not need to know about the ultimate nature of the atoms making up the metal box. However, he did posit that the box’s walls contained what he called “simple linear oscillators or resonators.” (He did not describe exactly what these oscillators were, but some scholars have interpreted them as idealized atoms.) Heating the walls set the oscillators into vibrations, causing radiant energy to stream into the cavity and then to emanate from the pinhole. Planck found that he could derive Wien’s Wien, Wilhelm formula, explaining some aspects of this radiant energy, when he assumed a simple relationship between the energy and entropy of these oscillators as they absorbed and emitted radiation.

Bolzmann’s criticism of this analysis forced Planck to study the interrelationship between entropy and probability, which in turn led him to develop a statistical analysis of the number of ways of distributing a certain amount of energy among many oscillators of a certain frequency. To get a match with experimental results, he needed to construct this distribution in multiples of an energy element. It is unclear whether he intended these energy elements to correspond with actual physical entities, such as quantized energy packets, or whether he used them simply as convenient calculational devices in his combinatorial analysis.

Max Planck.

(Library of Congress)

Until 1978, when science historian Thomas Kuhn argued that Planck did not discover the quantization of radiant energy, Planck’s work was commonly interpreted to indicate that he had understood oscillators as actually emitting radiation in multiples of a definite energy that was proportional to its frequency. The proportionality constant, h, which came to be called “Planck’s constant,” is an extremely small number that has the units of mechanical action. Planck saw this constant as a “mysterious messenger” from the microworld. He insisted that the “introduction of the quantum of action h” into physicists’ theories about the atom “should be done as conservatively as possible.” He knew that the classical wave theory of light had been shown to be true with many experimental observations, and he therefore wanted to preserve a model in which radiation was continuous rather than discrete.

Nevertheless, Planck must have realized that he had accomplished something very important, because on December 14, 1900, when he first made his ideas on quantum theory public, he told his son Erwin that he had just made a discovery “as important as Newton’s.” On the other hand, he saw his greatest claim to fame in his radiation-law formula, because it agreed perfectly with energy distributions of radiations determined in laboratories for all wavelengths and temperatures. The task of interpreting this equation and Planck’s formula relating energy and frequency fell, for the most part, to others.


The person who most profoundly understood the significance of Planck’s work on quantum theory was Albert Einstein Einstein, Albert . He wholeheartedly embraced the idea of quantized energy and used it extensively in his work. For example, he used light quanta to explain the previously inexplicable photoelectric effect, an achievement for which he received the 1921 Nobel Nobel Prizes;physics Prize in Physics. Planck had won the 1918 Nobel Prize for “his discovery of energy quanta.” By extending the discontinuity of energy to light, as well as to the entire electromagnetic spectrum, and by his quantum studies of the interactions between light and matter, Einstein revealed the great power of the quantum idea.

In 1913, Niels Bohr Bohr, Niels developed his quantum theory of the hydrogen atom, using quantized electron energy states to account for the hydrogen spectrum. The full-fledged importance of the quantum idea became clear in quantum mechanics, developed in the 1920’s by such eminent physicists as Louis de Broglie Broglie, Louis de , Werner Heisenberg, and Erwin Schrödinger. So momentous was this new quantum theory that it has become the dominant theoretical tool for helping physicists and chemists understand the microrealm of atoms and molecules.

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Brush, Stephen G. Cautious Revolutionaries: Maxwell, Planck, Hubble. College Park, Md.: American Association of Physics Teachers, 2002. Brush, a historian of physics, argues that Planck intended his quantum hypothesis as a mathematical device, not a physical discontinuity. Includes bibliographical references.
  • citation-type="booksimple"

    xlink:type="simple">Cline, Barbara Lovett. Men Who Made a New Physics. Chicago: University of Chicago Press, 1987. Originally published as The Questioners in 1965, this reprint provides general readers with an accessible account of the evolution of quantum theory. The two chapters on the early work of Planck are particularly well done. Index.
  • citation-type="booksimple"

    xlink:type="simple">Duck, Ian. One Hundred Years of Planck’s Quantum. River Edge, N.J.: World Scientific, 2000. Surveys the history of quantum theory from Planck’s discovery of the quantum to the end of the twentieth century. Includes bibliographical references and indexes.
  • citation-type="booksimple"

    xlink:type="simple">Heilbron, J. L. The Dilemmas of an Upright Man: Max Planck as a Spokesman for German Science. Berkeley: University of California Press, 1986. This brief biography by a respected historian of science surveys Planck’s life and achievements against the background of political turmoil in Germany. Extensive bibliography, index.
  • citation-type="booksimple"

    xlink:type="simple">Kuhn, Thomas S. Black-Body Theory and the Quantum Discontinuity, 1894-1912. New York: Oxford University Press, 1978. This narrative analysis of Planck’s great “discovery” is a controversial reinterpretation of Planck’s ideas and writings. Kuhn maintains that the revolutionary idea of quantized energy did not originate in Planck’s work but in the work of Albert Einstein, Paul Ehrenfest, and Hendrik Lorentz. Extensive notes with references to primary and secondary sources, bibliography, and index.

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