In his previous post and the one before that, John Howard explored the history of blackbody radiation. Here, he describes how Max Planck was persuaded to derive a formula for blackbody radiation. Planck presented his formula in December of 1900 to the German Physical Society in Berlin, ushering in the quantum era.

In the late summer of 1900, Otto Lummer and Ernst Pringsheim carefully measured the spectral distribution of the thermal radiation from a blackbody radiator, and H. Rubens and his colleague Kurlbaum made a similar set of measurements at various temperatures. They then plotted their results and compared the results with the two theoretical predictions—of Wilhelm Wien for high frequencies, and Lord Rayleigh for lower frequencies. They found good agreement with the Wien formula, except that the Rayleigh formula was definitely better at low frequencies.

I have read two different accounts of how H. Rubens related to the young thermodynamicist Max Planck that the Wien formula did not fit well at low frequencies. According to one story, Rubens attended a seminar at the University of Berlin shortly after plotting his data.  At the tea and social hour before the event, he saw Planck, joined him for tea, and reported his results. In the other version, Planck invited Rubens and his wife to a Sunday lunch at Planck’s home; after their meal, the two physicists discussed the partial failure of the Wien formula.

Planck was indeed very interested, as less than a year earlier he had carefully worked to put Wien’s derivation of his formula on to a more solid thermodynamic foundation. After the seminar (or the lunch) was over, Planck spent the rest of that day looking for an “interpolation formula” that would reduce to the Rayleigh prediction at low frequencies, and to the Wien formulation at higher frequencies.

After several hours, he succeeded in finding such a formula. It was generally similar to the Wien formulation, but with an additional exponential term in the denominator. He sent a note with his proposed formula to Rubens, who returned to Planck two days later and said that interpolation formula fits everything, so it must be right! Planck said later that finding that formula was “just a lucky guess.”

 At a Berlin meeting of the German Physical Society in mid-October of 1900, Kurlbaum gave a short paper on the Rubens-Kurlbaum measurements, following which Planck arose with some comments and sketched his modified formula on the blackboard. The attendees were pleased with this ad hoc formula; now Planck was faced with the more daunting challenge of producing a satisfactory scientific derivation of that “interpolation formula.” Planck labored over that derivation for about two months, calling it the “hardest labor of my life,” before presenting his detailed derivation to a meeting of the Physical Society in mid-December 1900.

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By John Howard

Prompted by the recent OPN article about Lord Rayleigh and Otto Lummer, John wrote his previous post on the early history of blackbody radiation. Here, he picks up where he left off in that history--in 19th century America and the work of Thomas Edison.

In the United States, a bright, hard-working young Thomas Edison with a knack towards invention had taught himself telegraphy. In 1869, when he was 22, had applied for a job at a brokerage firm in New York City.  While he was waiting to be interviewed, the stock ticker broke down, and he was the only one who knew how to fix it. He was immediately hired—and at a better wage than he had expected.

Within a year, he had designed a much improved stock ticker, and he sold his model to the firm for $40,000. With this money, he bought a building near Newark, N.J.; hired two or three assistants; and began a lifelong career of practical inventions. Of his early inventions, he was most proud of the phonograph. In 1878, at the age of 31, he announced that he was turning his attention toward designing an electric light. In his laboratory in Menlo Park, he worked as much as 20 hours a day.

Edison and his assistants tried hundreds of filaments, until finally, in October 1879, he had a light bulb with a carbon filament that successfully stayed lit for 40 hours. (His team then turned to other materials for filaments, and ultimately settled on tungsten.)

With the invention of the electric light bulb, many scientists and engineers turned their attention to the radiation from lamp filaments and hot incandescent bodies. The General Electric Company began a laboratory at Nela Park in Cleveland for its lamp division, and blackbody radiation was a primary research subject. In Germany, the Siemans company urged the German government to found the Physicalische-Techniche Reichsanstalt (PTR) and even donated a building and land near Berlin University to house that research organization.

In 1887 Hermann Helmholtz joined the PTR as its first director, bringing with him his assistant Otto Lummer, who headed the research effort on blackbody radiation. Lummer constructed a heated sphere with a small hole to emit blackbody radiation, and, in the late summer of 1900, he and Pringsheim studied blackbody radiation over a wide variety of temperatures. Working with them was a young graduate student, Heinrich Rubens of the University of Berlin, a guest worker at PTR.

In early 1900, Lord Rayleigh turned his attention to the problem of blackbody radiation. He was an expert in acoustics, and he had many times calculated the formation of acoustic standing waves in a resonant cavity; why not try that same approach to standing waves of blackbody radiation in a blackbody cavity? He counted up all the possible standing waves, assumed that there was an equal probability for each to occur, and that each standing wave represented an energy of kT of radiation.

When he then calculated the total blackbody radiation, he found to his surprise that he disagreed by a factor of eight with the published value calculated by Wien. He nevertheless published his calculation. He promptly received a note from a bright young Cambridge graduate, James Jeans, who said that he thought Rayleigh had only counted the number of possible standing waves in one octant of the possible directions of x, y, z; he should have counted from minus infinity to plus infinity for the entire range of standing waves. Rayleigh agreed with Jeans immediately, and dropped a note to Nature, renaming his Rayleigh distribution to the more proper Rayleigh-Jeans distribution of standing waves.

The bright young Jeans now had his name linked to the much better known physicist Lord Rayleigh. However, even with this correction, the Rayleigh-Jeans equation appeared only to represent the true spectrum of blackbody radiation at long wavelengths (or low frequencies).

Then, in the late summer of 1900. . .

John’s next post will cover how the work of Lummer, Pringsheim, Planck, and others contributed to the development of an interpolation formula that would reduce to the Rayleigh prediction at low frequencies.

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