Max Planck’s Rough Road to Quantum Theory

Max Planck’s Early Life

Max Planck (1858–1947) was born in Kiel, (in modern day Germany), the sixth child to the distinguished jurist and professor of law at the University of Kiel, Johann Julius Wilhelm Planck and his second wife, Emma Patzig. His family culture would bestow in Planck’s life and work a sense of excellence in scholarship, incorruptibility, idealism, reliability, and generosity.

In 1867, when Planck was nine, his father received an appointment at the University of Munich. The family moved and Planck enrolled in the city’s Maximilian Gymnasium where his interest in physics and mathematics was piqued. However, Planck excelled in his other studies as well, in particular music. Thus at the time of graduation, now 16, Planck had the difficult decision of choosing a future in either music or physics; he chose physics.

Max Planck’s Early Work

In 1879, Planck , now twenty-one, received his PhD for his thesis on the second law of thermodynamics and the entropy concept. Thermodynamics, especially the entropy concept, would remain a central theme throughout most of Planck’s work. Unfortunately, Planck’s career was off to a slow start, as he was unable to make much of an impression with his work on the entropy concept. One reason for this may simply have been that this area of study was still relatively new.

More disappointment followed when Planck discovered much of his work on entropy theory had already been done by Willard Gibbs (1839–1903). Moreover, his work on the thermodynamics of dilute solutions lacked the chemical insight so successfully applied by others such as Jacobus Henricus van’t Hoff (1852–1911). However, his efforts weren’t in vain and the skills that he’d been finely honing were finally going to serve him well.

The Blackbody Radiation Challenge

By the 1890s, hardly a physicist in Berlin was unaware that Kirchhoff, Boltzmann, and Wien had secured a role for thermodynamics in the solution of the blackbody problem. Thus when in 1894 Planck embarked on the blackbody problem, he expected his beloved tools of thermodynamics – in particular the entropy concept – which he had been polishing for some time on physical chemistry problems, to serve him well. Several things enticed Planck about the blackbody problem, including that he had been commissioned by several electricity companies to develop light bulbs that would provide the most light output for the least amount of energy used.

In early 1899, at the time of his fifth publication recounting his efforts, the Wien-Planck law was in excellent agreement with experimental measurements. Although falling short of his overall goal, Planck was convinced he’d successfully derived the universal function for the blackbody spectrum that Kirchhoff had challenged physicists to find some forty years prior. However, his victory would be short-lived. By the spring of 1900, improved experimental techniques revealed new results showing discrepancy with the Wien-Planck law. It was beginning to look as if Planck’s almost six years of effort had been in vain.

The Cost of Being Right

On December 14, 1900, Planck presented a new derivation; he had now been victorious in his search for the blackbody spectrum. Further, he had gained his desired physical insight into the interaction between matter and radiation. Nonetheless, the price he paid was quite high.

He had to appeal to Boltzmann’s method of obtaining the total number of microstates in order to obtain an expression for entropy. To be sure, Boltzmann’s method wasn’t mainstream at all, and considered by most to be questionable at best. Moreover, unlike Boltzmann – who was able to neatly dispose of those annoying chunks of energy in the end – Planck was stuck with them for good since their elimination resulted in complete and utter failure of his theory.

Coming to Terms with Energy Quanta

A full acceptance of this rather devious character of energy meant all of physics, as Planck had known it, would drastically change forever. Understandably, Planck was reluctant in his new role as a revolutionary, and he did very little to promote the discontinuous, or discrete nature of energy, which today we call energy quanta (or quantum for a single “chunk”).

He held to the idea that quanta of energy were a mathematical artifact, and hoped that further refinements to his theory would lead back to the “old familiar physics” (classical physics) with less drastic results. He – and pretty much everyone else – chose to focus on the remarkable accuracy of Planck’s Radiation Law, rather than the annoying energy quanta that it implied. It took almost eight years, after he first presented his quantum theory of discrete energy, before Planck could finally admit it represented the fundamental nature of energy:

“… there exists a certain threshold: the resonator does not respond at all to very small excitations; if it responds to larger ones, it does so only in such a way that its energy is an integral multiple of the energy element hv , so that the instantaneous value of the energy is always represented by such an integral multiple.”

While Planck and others may have been hesitant in their acceptance of the energy quanta, there was one who embraced it almost immediately.

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