Max Planck: Founder of Quantum Theory

Max Planck’s scientific career spanned some of the most turbulent times in German history—the Wilhelmian Empire, the Weimar Republic and the Third Reich. Through it all, he advanced and protected physics, with his own research evolving from theoretical physics that was firmly grounded in thermodynamics to his blackbody distribution law, which forced him to invoke non-classical ideas.

 

feature5-img1.jpgPortrait of Max Planck.

Wikimedia Commons/Deutsches Bundesarchiv

Max Planck didn’t set out to develop a new theory for how the universe works. When he started the work on blackbody radiation that would lead him to discover energy quanta, he had initially believed—like the other physicists of his day—that energy was a continuous quantity. He was disturbed that he had had to quantize it in order to get his equations to work. As he stated in his 1920 Nobel lecture: “It was completely indispensable for obtaining the correct expression for entropy [in his derivation of the blackbody distribution law] … it proved elusive and resistant to all efforts to fit it into the framework of classical physics.”

Furthermore, Planck wrote: “ … The introduction of the quantum of action has not yet produced a genuine quantum theory.” But his 1899 discovery of the new fundamental constant, Planck’s constant, is now an intrinsic feature of quantum mechanics—the “genuine theory” that Planck had sought. That field was pioneered in 1926 by the works of Max Born, Werner Heisenberg, Pascual Jordan, Erwin Schrödinger and Paul Dirac.

Planck lived to witness the development of quantum mechanics—and he eventually accepted it and its successes in physics. Nevertheless, scholars still debate whether Planck should be credited as the founder of quantum physics, given that discontinuous energies did not appear to be part of his conception of reality. Rather, they served as a heuristic device that he needed to get the math right. It wasn’t until 1906 when Albert Einstein derived the Planck distribution law from first principles in conjunction with his theoretical work on the production and transformation of light, which posited the light quantum and the mechanism of the photoelectric effect.

In spite of differing opinions over Planck’s role in quantum physics, no one disputes that the man made exemplary contributions to theoretical physics, physics education, and service to the physics community over the many decades in which he served as the spokesman for German science.

Early life, education and interests

Planck came from a family devoted to the study of religion. His great-grandfather and grandfather were both professors of theology at the University of Göttingen, and his father, Johann Julius Wilhelm von Planck, had studied church law; he was also a professor of jurisprudence, first at Kiel and later at the Ludwig-Maximilians Universität in Munich. Planck’s mother, Emma Patzig, Johann’s second wife, came from a family of pastors.

Planck was born on 23 April 1858 in Kiel, Germany. He attended Maximilians-Gymnasium in Munich, where he studied languages, mathematics, history and music. After graduating at the age of 16, he studied physics and mathematics at the University of Munich from 1874 to 1877. Following that, he spent two semesters at the University of Berlin, where he took courses given by the mathematician Karl Weierstrass and the physicists Gustav Kirchhoff and Hermann von Helmholtz.

Planck received his doctorate in 1879 from the University of Munich; his thesis was a study of the second law of thermodynamics. In 1880, he received his Habilitation (the right to teach in German universities) with his paper, “Equilibrium states of isotropic bodies at different temperatures.”

Planck loved music; he was an accomplished pianist who played throughout his adult life. He often hosted a musical trio: Planck played the piano, while his son Erwin played the cello, and Albert Einstein (who joined them from 1914 on) played the violin. He also enjoyed hiking in the mountains, often with Erwin. (Even at the age of 85, he could still manage to ascend 3,000-m peaks in the Tyrolean Alps.)

Planck’s family

Planck’s parents instilled in him strong values and an attachment to family, which he carried into his own family. In 1887, he married Marie Merck, the daughter of a Munich banker and the younger sister of a school friend. He and his first wife raised four children: twin daughters Grete and Emma and two sons Karl and Erwin. Marie died in 1909 after 22 years of marriage, and Planck remarried a year and a half later. His second wife, Marga von Hoesslin, was the daughter of a Munich painter. Shortly afterward, Planck’s third son Hermann was born.

Sadly, the death of Planck’s first wife was the first of many family losses that Planck endured in his later years. He also lost his elder son Karl to the First World War, and both of his daughters died from complications of childbirth between 1917 and 1919. These deaths deeply affected Planck.

The destruction that came with the Second World War brought additional tragedy. An Allied bombing destroyed Planck's home, his library and all his private papers. He also learned that his granddaughter Emma had attempted suicide, and his second son Erwin was executed by the Nazis in 1944. Erwin had previously worked for the Defense Ministry and as Secretary of State in the Reich Chancellery, and he was working as a businessman when he was put to death for his alleged participation in the failed assassination plot to kill Hitler in July 1944. Planck wrote to Hitler himself with a personal appeal to spare his son’s life. His letter went unanswered.

Career accomplishments

From 1885 to 1889, Planck served as associate professor for theoretical physics at the University of Kiel. He replaced Heinrich Hertz. In 1887, Kirchhoff, the director of the Institute of Theoretical Physics at the University of Berlin, passed away. Shortly afterward, an academic search was launched for his replacement. The final candidates included Ludwig Boltzmann, Heinrich Hertz and Planck; after the first two declined, Planck was offered an associate professorship, which he accepted. In 1892, he was promoted to full professor.

Planck taught a six-semester course on theoretical physics, and he soon became well known as an excellent teacher. The Austrian physicist Lise Meitner called Planck “the best lecturer I ever heard.” Planck taught physics for 40 years, supervised 25 doctoral students and took part in 650 doctoral examinations. Many of his students excelled in physics in their academic careers; Max von Laue and Walther Bothe each received Nobel Prizes. When Planck served as the Rector of the University from 1913 to 1914, he established a professorship for Einstein and called him to Berlin; they became close friends.

Similarly, Planck’s service to the scientific community was outstanding. He facilitated the merger of the local Physical Societies in Germany in 1898; the resulting new institution became the German Physical Society. From 1905 to 1909, Planck served as its president. The Society published the world’s leading physics journal at that time, Annalen der Physik.

In 1894, Planck was made a full member of the Prussian Academy of Sciences. From 1912 to 1938, he served as the secretary of the theoretical physics section and the physical-mathematical section of the Berlin Academy of Sciences. In July 1930, Planck was made the president of the Kaiser Wilhelm Society (KWS) for the Advancement of Science, a position he held for seven years. He worked hard during that time to save the KWS from the racist policies of the Third Reich.

At the age of 75, Planck continued to promote physics in Germany; he kept his positions in the Berlin Academy of Sciences, the KWS, and the university until 1938. In 1938, Planck formed a new KWS for physics—the Max Planck Institute for Physics; Peter Debye was the director.

 

feature5-img2.jpgMonument to Max Planck by Bernhard Heiliger, Humboldt-Universität Berlin.

Wikimedia Commons

Planck’s derivation of the blackbody distribution law

Planck built on the work of other prominent scientists of his day, beginning with Kirchhoff, to develop his famous blackbody distribution law. (See p. 3.) His aim was to use the principles of thermodynamics and electrodynamics to derive a theory that could accurately describe the distribution of energy over the frequencies comprising blackbody radiation.

Planck knew that blackbody radiation does not depend on the material forming the cavity; therefore, he could postulate that the cavity walls are composed of a collection of damped Hertzian resonators (linear oscillating electric dipoles), each of which would be a massless spring or harmonic oscillator containing an electrical charge. Planck used Hertz’s 1889 theory of electric dipole radiation to build his model.

When the cavity was to be heated, the accelerating charges would radiate according to Maxwell’s equations, and they also absorbed energy from the resonator radiation. Planck stated the problem as follows: “In the steady state, how is the energy [of the cavity] distributed over the vibrations of the resonators and over the frequencies of the radiation, and what is the temperature of the total system?”

His calculation for the probabilities of the various distributions of energy in the collection of resonators followed from Boltzmann’s distribution for gas molecules. Planck relied on his knowledge that the walls of the blackbody cavity contained resonators with both energy and entropy distributions. However, at equilibrium, the total entropy (resonators and radiation field) was a maximum and could be calculated using a combinatorial analysis that had been developed by Boltzmann.

Boltzmann had written that there is a proportionality between entropy, S, and lnW, with W denoting the possible permutations of the molecules (Boltzmann’s term was “complexion”). Planck wrote this as an equation: S = klnW. Although this calculation is now known as the Boltzmann equation, Planck was the first to express it as such, and it was he who named the constant of proportionality, k, the Boltzmann constant.

Planck realized that probabilities are only valid for countable configurations of molecules. Moreover, in order to make the configurations countable, he needed to introduce his energy elements. In Planck’s words in his 1901 Annalen paper: “To find the probability that N resonators have a total energy Un, it is necessary to suppose that Un is not continuously divisible, but is an integral multiple of finite identical parts. We call such a part an energy element ε.”

To proceed with the calculation, Planck wrote that the distribution of the energy among the N resonators of frequency ν. He divided the energy of each resonator into small, finite amounts and wrote UN = Pε, where P is an integral number that represents the number of “energy elements” that are distributed among the N resonators, P = UN/ε. Planck wrote, “If the ratio calculated is not an integer, we take P for an integer in the neighborhood.”

In his next step, he interpreted the symbol W as the number of ways to distribute P energy elements ε among the N resonators. Planck used the Stirling approximation, which states that N! (N factorial) is approximately equal to NN for very large values of N, to calculate the number of permutations, and from that, the entropy and the average energy of the resonators.

Planck’s equation of the blackbody spectrum had two universal constants: h, Planck’s constant, and k, Boltzmann’s constant. Planck derived Wien’s displacement law and realized that, for the internal consistency of his equations for the entropy of a single resonator, « was required to be proportional to the frequency n of the resonator: ε = hν. Planck thought of ε = hν as a mathematical postulate devoid of physical reality. Thus, Planck derived the blackbody spectrum equation:

Feature5-Equat1.jpg

where ρ is the energy density of the radiation of frequency between ν and dν, c is the velocity of light in a vacuum, and T is the absolute temperature.

Planck’s equation was in agreement with the precision measurements of the blackbody spectrum, and it covered the spectral range from short to long wavelengths. In 1902, the second volume of Heinrich Kayser’s Handbook of Spectroscopy became the first monograph to include Planck’s equation and its derivation.

Planck’s place in quantum mechanics

Planck was initially uncomfortable that his equations had forced him to quantize energy. But he eventually came to accept quantum mechanics as the field was shaped by his colleagues. Once the theoretical significance of quantized energy was developed by Planck, it entered into the 1918-1922 atomic theory of Niels Bohr, and then into the Heisenberg’s quantum mechanics developed in 1926 and beyond.

Although Planck had come to change his scientific views over his career, he once mordantly suggested that true paradigm shifts don’t occur until those who are entrenched in old ways of thinking begin to die off: “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

A dedicated scientist

Although sometimes thought of as a conservative man, Planck was not afraid to take a stand for what he believed in. For example, he fought the Education Ministry when they blocked the appointment of Lise Meitner, a student of Boltzmann’s, to the physics department at the University of Berlin on the basis of her gender. Planck even hired Meitner as an assistant for two years. She became an exceptional scientist and one of his closest friends.

He also fought to save one of the first institutes formed by the KWS—the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry—when its existence was threatened by the policies of the Third Reich. Fritz Haber, the director of the institute, had been born to a Jewish family but converted to Christianity at the age of 24.

In April of 1933, Hitler announced his “Law for the Restoration of the Professional Civil Service,” which obligated Haber to dismiss all the members of his institute who were of Jewish descent. Haber was morally unable to comply with the regulation, which would have required him to dismiss most of his researchers. On 30 April 1933, he resigned his directorship and immigrated to Switzerland.

Planck attempted to obtain an exemption for Haber’s Institute on the grounds that its science was critical to Germany’s national interests. He first contacted Bernhard Rust, the Reich Minister of Science, Education and National Culture, and, when that attempt failed, he met with Hitler himself. Hitler refused to relent.

It is perhaps not surprising, then, that in a final act of defiance, Planck resigned his position as the presiding secretary of the Prussian Academy of Sciences when it was taken over by the Nazis in 1938.

Although Planck was then 80 years old, he had not yet finished dedicating himself to science. After the war, he became president of the newly formed Max Planck Society for the Promotion of Science in the British zone. Planck served in that role 16 May 1945 to 31 March 1946. At the age of 89, he continued to give public lectures on science and society.

On 28 March 1947 in Bonn, he delivered his last lecture, in which he concluded:

“The only thing that we may claim for our own with absolute assurance, the greatest good that no power in the world can take from us, and one that can give us more permanent happiness than anything else, is integrity of soul, which manifests itself in a conscientious performance of one’s duty. And he whom good fortune has permitted to cooperate in the erection of the edifice of exact science, will find his satisfaction and inner happiness, with our great poet Goethe, in the knowledge that he has explored the explorable and quietly venerates the inexplorable.”

These words exemplify Planck’s life. He died from a stroke on 4 October 1947 at the age 89. He is buried in the cemetery at Göttingen-Grone.

 

feature5-img3.jpgThe laboratory for radiation measurement at the Physikalische-Technische Reichsanstalt (PTR) in Berlin circa 1900. The blackbody is the white cylinder on the optical bench.

Source: Lehrbuch der Physik und Meteorologie, by Müller-Pouilet, ed. L. Pfaundler, Braunschweig, 1909, 10th ed., vol. 2, plate 1.

Theories and precision measurements of blackbody radiation

Scientists’ interest in designing a blackbody cavity was spurred by the writings of Gustav Kirchhoff, who was a professor of physics at the University of Heidelberg. In 1860, Kirchhoff described his radiation law and a hypothetical perfect body that would absorb all of the incident radiation, regardless of frequency or angle of incidence. This so-called “blackbody” would be independent of its material composition; its equilibrium spectrum of radiation or the intensity of radiation in a given frequency range would be a function of the absolute temperature.

Kirchhoff’s law was based on thermodynamics: his first publication stated that the emissivity and absorptivity of a blackbody are equal, and their ratio is a function of the wavelength and the temperature. Kirchhoff suggested the construction of a heated cavity as a source of blackbody radiation—a proposal that was initially ignored by the scientific community.

That began to change when, in the late 1800s, electric lights were installed in Berlin. Efficiency and temperature standards were required, and to fulfill them, scientists at the Physikalisch-Technische Reichsanstalt (PTR) conducted precise measurements. When spectroscopists measured blackbody radiation in the 1880s, they wanted to develop an absolute calibration of temperature and a radiation intensity standard to satisfy the needs of the electrical industry.

This brought scientists back to Kirchhoff’s idea of investigating blackbody radiation. In 1898, German physicists Otto Lummer and Ferdinand Kurlbaum designed a blackbody cavity. Its cylindrical shape contained electrical resistive heating coils that surrounded a porcelain tube blackened with oxides of iron or cobalt. A thermocouple within the cavity measured temperature. The radiation from an aperture was dispersed with a prism and detected.

Lummer and Kurlbaum used a bolometer whose design was inspired by that of the bolometer that the American astronomer Samuel P. Langley had developed in 1881. (Unlike previous radiation detectors, the bolometer measured radiation outside the visible spectrum.) The researchers also designed a spectrobolometer in which they replaced the glass lenses of a standard spectrometer with silvered mirrors and included a prism designed to transmit radiation into the range of longer wavelengths. Soon after, German physicist Heinrich Rubens developed a technique to further improve sensitivity, yielding measures of radiation over a very narrow spread of wavelengths.

The 1893 work of Wilhelm Wien, an assistant at PTR who excelled in both theoretical and experimental work, was also critical for understanding blackbody radiation. Wien’s displacement law, which was independently and simultaneously derived by Friedrich Paschen, stated that the peak wavelength of the spectrum is shifted (displaced) to higher frequencies when temperature is increased. As Wien explained in his Nobel lecture, “…The radiation energy of a certain wavelength varies with changing temperature so that the product of temperature and wavelength remains constant. Using this displacement law, it is easy to calculate the distribution of the intensity of thermal radiation over the various wavelengths for any temperature, as soon as it is known for one temperature.”

In 1896, Wien applied thermodynamics to electromagnetic radiation in order to derive an equation of the blackbody spectrum called Wien’s distribution law. Prior to May 1899, Wien’s law was consistent with the experimental measurements in the range 0.7 to 6 µm. However, when Lummer and his colleague Ernst Pringsheim analyzed their measurements into the infrared wavelengths (12 to 18 µm) in 1900, their data no longer fit Wien’s law.

That same year, Lord Rayleigh derived a blackbody radiation law, which he called the law of complete radiation. He pointed out some of the implausible conclusions of Wien’s law—for example, the idea that a wavelength approaches a limit as temperature increases. He suggested a modification that used the equipartition theory of statistical mechanics for the case of electromagnetic vibrations in cavity radiation. The equipartition theory states that, at thermal equilibrium, the average kinetic energy is distributed equally for each degree of freedom. This analysis followed Rayleigh’s previous calculation that mathematically characterized the standing sound waves in a cube; in this case he derived an analogous equation for transverse electromagnetic waves in a cube.

Meanwhile, in October of 1900, Rubens and Kurlbaum measured deviations from Wien’s law that increased with longer wavelengths and at higher temperatures. Rubens shared these results with Planck, and he also stated that, at longer wavelengths, Rayleigh’s 1900 radiation law was valid. This is what motivated Planck to begin his theoretical investigation of blackbody radiation.

 


Barry R. Masters is a Fellow of AAAS, OSA and SPIE. He is a visiting scientist with the department of biological engineering, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.

References and Resources

>> M. Planck. Wissenschaftliche Selbstbiographie, Leipzig, JA Barth (1948). Trans. F. Gaynor in Scientific Autobiography and Other Papers, New York, Philosophical Library (1949).
>> M. Planck. Physikalische Abhandlungen und Vorträge, Band I, II, III, Braunschweig, Friedrich Vieweg & Sohn (1958).
>> J. Mehra and H. Rechenberg. The Historical Development of Quantum Theory, 1(2), The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld: Its Foundation and the Rise of its Difficulties 1900-1925, N.Y., Springer (2001) 23-9.
>> J.H. Heilbron. The Dilemmas of an Upright Man, Max Planck as Spokesman for German Science, Berkeley, University of California Press (1986).
>> T.S. Kuhn. Blackbody Theory and the Quantum Discontinuity, 1894-1912, Chicago, the University of Chicago Press (1987).
>> D. Hoffmann. On the experimental context of Planck’s foundation of quantum theory. In: J. Büttner et al. Revisiting the Quantum Discontinuity, Preprint 150 Berlin, Max-Planck-Institut für Wissenschaftsgeschichte (2000).
>> D. Hoffmann, ed. Max Planck: Annalen Papers, Weinheim, WILEY-VCH Verlag (2008).
>> L.F. Beck. ed. Max Planck und die Max-Planck-Gesellschaft, Vol. 20, Berlin, Archiv der Max-Planck-Gesellschaft (2009).

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Max Planck: Founder of Quantum Theory

Max Planck’s scientific career spanned some of the most turbulent times in German history—the Wilhelmian Empire, the Weimar Republic and the Third Reich. Through it all, he advanced and protected physics, with his own research evolving from theoretical physics that was firmly grounded in thermodynamics to his blackbody distribution law, which forced him to invoke non-classical ideas.

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