That quantum leap...

January 5, 2001

John Heilbron opens a THES tribute to 100 years of quantum theory with a look at Max Planck's contribution to modern physics.

When, on December 14 1900, Max Planck presented the paper now regarded as the inauguration of quantum theory, neither he nor any of his listeners recognised it as the first shot in a scientific revolution. It was the culmination of four years' hard work in a corner of what Planck called the physical world picture. The general principles of physical science made the strong lines of the picture; the universal constants fixed its dimensions; and the elegance and simplicity of the pattern to which it reduced the confusion and complexity of phenomena made its value.

Planck did not believe that his world picture transcribed the inner nature of things. It was, after all, the work of a human being. But he believed that by gradually eliminating the all-too-human smudges from the design, he could fashion a portrait faithful enough to nature to pass for truth. Just as his friend Albert Einstein used to invoke God as a convenient test and jest - “If relativity theory is wrong, then I am sorry for the dear God” - so Planck liked to say that a proper world picture would have to be intelligible to an intelligent Martian.

To complete his corner of the picture, Planck aimed to describe one of the great scientific problems of his day - black body radiation, roughly what you see when looking into a furnace. This meant specifying the intensity of each colour into which the radiation could be split. Planck was interested in the steady state of this furnace, or black body radiation. Because the intensity of each colour at equilibrium depends only on the colour itself, the temperature, and some universal constants, the problem excited Planck’s interest in the general and eternal.

When a gas is in equilibrium, its molecules fly about in maximum disorder. The mysterious thermodynamic quantity “entropy” is a measure of disorder, so equilibrium in a gas corresponds to a maximum of entropy. Planck accordingly took his central problem to be the application of the law of entropy to the general state of radiation described by Maxwell’s electromagnetic equations.

By 1899, Planck had transformed the problem into one of finding the presumably unique relation between the entropy and energy of what he called a resonator - a microscopic charged billiard ball linked to a perfect microscopic spring. The resonator could exchange energy with black body radiation through electromagnetic forces that pushed and pulled the ball. Eventually, Planck associated a collection of resonators with each colour of radiation. In 1900, experimentalists kept improving their measurements of the furnace spectrum, and Planck concocted relations between the resonator’s entropy and energy to obtain the distribution of the moment.

In October 1900, he found one that fitted the data perfectly. By December, he had contrived a theoretical deduction by recourse to the relationship between the entropy and disorder of a gas specified some years earlier by Ludwig Boltzmann. To make this technique work with radiation, Planck had to calculate as if the sum of the energies of all the resonators associated with a given colour consisted of a very large number of very small elements, each proportional to the quantity (the frequency) defining the colour. This limitation of values available to the energy of the resonators is now taken to be the essence of Planck’s contribution and the first instance of the quantum. The key step for Planck, however, was the extension of the concepts of the mechanical world picture to radiation, and the key result the means to deduce its fundamental dimensions.

He had already signalled that the universal constants that figured in the formula would give a scale “significant for all times and cultures, even extraterrestrial and extra-human ones”. As the accuracy of measurements supporting Planck’s formula increased, so did confidence in the values of atomic constants deduced from it. In 1908, the Nobel prize committees recommended Planck for physics and Rutherford for chemistry. That the value of the electronic charge deduced by Planck from his radiation formula agreed with that found by Rutherford from counting alpha particles figured prominently in the decision. Unfortunately, the academy learned that there was something unorthodox about the energy elements involved in his deduction and refused Planck the prize. Not only Planck, but the high tribunal in Stockholm, missed what we now take to be the significance of December 14.

Planck was an unwitting and reluctant revolutionary. He was also conservative in politics, social views and lifestyle. But he was strong and bold as a physicist. He accepted and developed the theory of relativity because it simplified and dehumanised the world picture. What disturbed most people about relativity was to Planck its greatest attraction. The theory showed that a correct world picture could not be built on common intuition and that theoretical physicists could transcend the limitations of their species. The very concept of a perfectible world picture tantamount to reality indicates Planck’s boldness and independence. For most physicists around 1900, physical theory was a convenient instrument, not an object of true belief.

Theoretical physics as Planck conceived and practised it produced quantum theory and relativity theory and came to be respected as the highest form of science for most of the 20th century. Around 1900 Planck was its dynamic leader and role model. He accomplished much more and much less than the invention of quantum theory 100 years ago.

John Heilbron is a senior research fellow at Worcester College, Oxford, and former professor of history and vice-chancellor at the University of California at Berkeley. He is author of The Dilemmas of an Upright Man: Max Planck and the Fortunes of German Science (Harvard University Press, £11.50, ISBN 0 674 00439 6).



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