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Einstein and the Quantum
The Quest of the Valiant Swabian
By A. DOUGLAS STONE PRINCETON UNIVERSITY PRESS
Copyright © 2013 Princeton University Press
All rights reserved.
ISBN: 978-1-4008-7404-0
CHAPTER 1
"AN ACT OF DESPERATION"
On the evening of Friday, October 19, 1900, Max Planck, the world's leading expert on the science of heat, was experiencing a physicist's worst nightmare. Little more than a year earlier, he had staked his considerable reputation on a theory that purported to solve the outstanding problem of his field: the relationship between heat and light. Tonight at this meeting of the German Physical Society, the hall filled by the men who had been Planck's closest colleagues for over a decade, another scientist would announce publicly what Planck already knew — that the theory he had worked on for the past five years was almost certainly in error. This theory, which built on the work of his close friend Wilhelm Wien, was expressed in terms of a mathematical formula known as the Planck-Wien radiation law.
One of the scientists who had discovered the failure of the Planck-Wien law, Ferdinand Kurlbaum, was scheduled to speak first that night. A friend and close colleague of Planck's, Kurlbaum had no plan to attack Planck's theory on mathematical or logical grounds. Planck after all was the world's greatest expert on this topic and universally respected for his deep understanding of thermodynamics (the physics of heat flow and energy). Kurlbaum would simply present the hard data he and his collaborator, Henrich Rubens, had painstakingly collected to test the predictions of the Planck-Wien theory. The data would show (to quote Richard Feynman) that "Nature had a different way of doing things."
If Planck had been an experimenter himself, like Rubens and Kurlbaum, his reputation would have been less in jeopardy on that night. But Planck was a new breed of physicist, a theoretical physicist, with no laboratory or instruments. The theorist's job was (and is) simply to predict and understand physical systems, from stars and planets to atoms and molecules, using mathematical deductions from known and accepted physical laws. Very rarely (experience tells us about twice a century) theorists may also successfully propose some amendments to the laws of physics; but mostly they are master craftsmen, whose reputation depends on how well they use their intellectual tools. There had of course been great theory-building physicists before Planck: Isaac Newton, James Clerk Maxwell, and Ludwig Boltzmann, to name three of relevance to our story, but only at the end of the nineteenth century had the division of labor been formally recognized by academe, and the theoretical physicist, who divined nature by thought alone, became a recognized species. When Planck had taken up his post at the University of Berlin in 1889, it was the only chair of theoretical physics in Germany, and one of only a handful in the world.
Because a theorist has no measurements to report and no inventions to demonstrate, he is judged solely on whether his theoretical predictions describe important phenomena and are confirmed by experiment. An experimenter can go into the lab and make a great discovery without necessarily knowing what he is looking for, sometimes without even recognizing the discovery when it is first found. Many a Nobel Prize has been awarded for just such serendipity. In short, a good experimentalist can also be lucky. A good theorist, on the other hand, has to be right. Experimentalists are playing poker; theorists are playing chess. Chess games are not lost by "bad luck." The problem for Planck that night was that he had made a serious error in the contest with Nature, which was being exposed by Kurlbaum just now as Planck waited for his turn to speak. He needed to come up with an endgame that would preserve, at least temporarily, his reputation as a theorist.
So what was the problem on which the estimable Professor Planck had stumbled? It was the deceptively simple question of how much a heated object glows. The great Scottish physicist James Clerk Maxwell had demonstrated in 1865 that visible light and radiant heat are different expressions of the same physical phenomenon — the propagation of electrical and magnetic energy through empty space at the speed of light. The difference between visible radiation (i.e., "light") and thermal radiation is only their wavelength. For light, that length is about one-half of a millionth of a meter; for thermal radiation it is twenty times larger, or about ten millionths of a meter (which is still about eight times smaller than the width of a human hair). Such radiation arises when energy, originally stored in atoms (matter), is emitted; it can then be transmitted as an electromagnetic wave over large distances and be reabsorbed by matter. In any enclosed space this happens over and over until the electromagnetic (EM) radiation and the matter share the energy in a balanced manner (they are "in equilibrium").
Thus matter is continually emitting and absorbing radiation — all objects are glowing, whether we can see their radiation or not. What determines if we can see it is the temperature of the object; at room temperature objects glow with primarily thermal (infrared) radiation, a wavelength that our eyes can't see (except with "night-vision" goggles). The red glow of heated metal appears when the metal becomes hot enough to emit just a little of its EM radiation as visible light. The surface of the sun, which is even hotter, emits most of its radiation at visible wavelengths.
The central problem of the physics of heat, the one that Max Planck had worked on for the past five years, was to understand and predict precisely, with a mathematical formula, the amount of electromagnetic energy coming out of an object of a given temperature at each wavelength. This formula is the law of thermal radiation; physicists had known such a formula should exist for over three decades, but finding the correct law and understanding it theoretically had frustrated the best minds of the era. Einstein himself commented somewhat later, "It would be edifying if the brain matter sacrificed by theoretical physicists on the altar of this universal [law] could be put on the scales; and there is no end in sight to this cruel sacrifice!" In 1899, roughly a year and a half earlier, Planck thought he had found the answer, and had proudly announced his conclusions to the very same audience he was scheduled to address this evening. At that earlier meeting he had derived mathematically the equation that generated a universal curve, or graph, with temperature on the horizontal axis and EM energy on the vertical.
The current speaker, Kurlbaum, was presenting his and Rubens's measurements of just this curve, as Planck waited in the audience to respond. The data made a neat straight line, showing that the infrared energy radiated by an object increased proportional to the increasing temperature. On the same graph the prediction of the Planck-Wien law was plotted, giving a rainbow-shaped curve with not even a passing resemblance to the actual measured data points.
Planck had known that this moment was coming. Rubens was a personal friend, and he and his wife had visited Planck twelve days earlier for Sunday lunch. As physicists are wont, Rubens began talking shop and informed Planck that the law of thermal radiation that Planck had defended ardently for the past two years was badly out of agreement with their new data, which instead showed an intriguing linear variation with temperature. It was on this rather dramatic failure of his theory that Herr Planck would soon be asked to "comment." Thus the impending discussion showed every sign of being exceedingly awkward.
Planck was no longer a young man, although he was famously vigorous, and would climb mountains well into his seventies. At forty-two his hair was receding above his piercing eyes, and it sometimes pushed straight upward in an unruly shock. He had the bushy handlebar mustache sported by many of his Prussian colleagues and was dressed neatly in the academic style: white shirt with high collar, black bow tie and jacket, and pince-nez glasses. As a young man he had gone into science for the most idealistic of reasons: "my decision to devote myself to science was a direct result of the discovery that ... pure reasoning can enable man to gain an insight into the mechanism of [natural laws].... In this connection it is of paramount importance that the outside world is something independent from man, something absolute, and the quest for these laws ... appeared to me as the most sublime scientific pursuit in life." Early in his academic career he had been attracted to the science of heat, thermodynamics, since it is based on two absolute laws. The First Law states that heat is a form of energy, and the Second Law governs the flow of heat and the possibility of converting heat energy to do useful work, as in a steam engine. The Second Law employs the mysterious concept of entropy (roughly speaking, the amount of disorder in a physical system), and Planck had based his career on the interpretation and applications of this profound notion. That was why he was now in trouble.
Planck had not presented the Planck-Wien law of thermal radiation as a conjecture, based on provisional assumptions that he might revise. Quite the contrary. Little more than a year before, standing in front of the very same group of physicists, he had "proved" to them that this law followed from no other assumption than the Second Law of thermodynamics. With crushing certainty he had stated, "the limits of validity of this law coincide with those of the Second Law of Thermodynamics." This was the heavy artillery; the Planck-Wien law was supposed to be as solid as the Second Law itself! Einstein, also an admirer of thermodynamics, has said it is "the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown" (and, so far, he has been right). So if Planck, the world's expert, said that he had derived the law of thermal radiation directly from the Second Law, the case should have been closed. Unfortunately for Planck, the data disagreed.
Thus, when Planck stepped to the podium that night, his aim was not scientific revolution but damage control. Nonetheless, he was a truth seeker; he was not willing to run away from unpleasant facts. Later he scorned the English theorist James Jeans for just such behavior: "He is the model of the theorist as he should not be ..., [because he believes] so much the worse for the facts if they don't fit." Planck stood up and faced the music: "The interesting results of long wavelength spectral energy measurements ... confirm the statement ... that Wien's energy distribution law is not generally valid.... Since I myself even in this Society have expressed the opinion that Wien's law must be necessarily true, I may perhaps be permitted to explain briefly the relationship between the ... theory developed by me and the experimental data."
The "relationship" between them of course is that the Planck-Wien theory is wrong; Planck could not quite bring himself to say that in his remarks. But he did identify a weak point in his earlier arguments and admitted that the Second Law of thermodynamics does not have enough power, on its own, to answer the question. There had to be some further new principle involved. Having lost his guideposts for the journey, but being under such intense pressure to come up with an answer, Planck did something highly uncharacteristic. Planck was not a man to leap impulsively into the unknown; by his own description he was "by nature ... peacefully inclined, and reject[s] all doubtful adventures." Nonetheless, on that October night he had decided to wing it. What followed was the most fateful improvisation in the history of science.
Planck had been fortunate that his friend Rubens had given him warning of the failure of his theory. Moreover Rubens's data provided a huge clue to what was wrong. Earlier experiments had shown that the Plank-Wien law worked very well for visible EM radiation emitted by very hot bodies, that is, for the shorter wavelengths. The new experiments of Rubens and Kurlbaum showed not only that the law failed for the longer, infrared wavelengths emitted by less hot objects, but also showed exactly how it failed. That nice, straight line in the data told Planck that at long wavelengths, contrary to the prediction of the Planck-Wien law, the radiation energy must be proportional to temperature. To Planck the challenge was similar to filling in a line in a crossword puzzle for which the end of the word was known, and now someone had filled in the first letter for him, telling him his original guess was wrong. With a little inspired mathematical insight on the very Sunday night, twelve days earlier, that Rubens had warned him of the problem, Planck had guessed the correct mathematical formula for the law of thermal radiation. Now, at the meeting, he unveiled his new formula, soon to become immortalized as the Planck radiation law. Moreover he took the liberty of sketching how his new law compared to the Rubens-Kurlbaum data; it produced a line perfectly matching the data points. He concluded, "I should therefore be permitted to draw your attention to this new formula, which I consider to be the simplest possible, apart from Wien's expression."
With this great leap of intuition Planck had achieved a draw, but not a victory. Theorists are not supposed to just guess the correct formulas to describe data; they are supposed to derive these formulas from the fundamental laws of physics, which at the time were Newton's laws of mechanics and of gravity, Maxwell's electromagnetic theory, and the laws of thermodynamics. For Planck's new law to be anything more than a "curiosity" (as he himself put it), he would have to connect it to the more general laws of physics. As Planck himself said, "even if the absolutely precise validity of the radiation formula is taken for granted, so long as it had merely the standing of a law disclosed by a lucky intuition, it could not be expected to possess more than a formal significance. For this reason, on the very day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning."
(Continues...)
Excerpted from Einstein and the Quantum by A. DOUGLAS STONE. Copyright © 2013 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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