Quantum generations, p.13
Quantum Generations, page 13
The Leiden measurement-to-knowledge philosophy has been termed “sophisticated phenomenalism” and should be distinguished from the crude empiricism in which experiments replace, rather than supplement, theoretical work. In spite of its emphasis on precision experiments, Kammerlingh Onnes’s research program was far from unrelated to theory. What may appear as an obsession with the conquest of new low-temperature ranges was not solely motivated in either simple curiosity or a wish to lay claim to the unkown territory before his competitors (although these factors undoubtedly played a role). Contrary to Michelson and other arch-experimentalists, Kammerlingh Onnes had a solid training in mathematics and was deeply inspired by Dutch theorists such as Lorentz and Johannes van der Waals. Before starting on his great program in cryogenics, he had worked in thermodynamics and molecular physics, and he was especially interested in testing the consequences of the molecular theory of van der Waals. In 1880 van der Waals had formulated the “law of corresponding states,” which Kammerlingh Onnes independently developed the following year. According to this law, all substances obey the same equation of state when their pressure, temperature, and volume are expressed as multiples of the values these variables have at the critical point. In 1894 Kammerlingh Onnes stated in clear words the theoretical basis for embarking on a program to liquefy gases: “I was induced to work with condensed gases by the study of van der Waal’s law of corresponding states. It seemed highly desirable to me to scrutinize the isothermal lines of the permanent gases especially of hydrogen at very low temperatures” (Gavroglu and Goudaroulis 1989, 51). The same message, the intimate connection between the Leiden low-temperature experiments and the theories of van der Waals, was contained in Kammerlingh Onnes’s statement of 1908, quoted above, after he had succeeded in liquefying helium.
SUPERCONDUCTIVITY
One of the properties investigated at the Leiden laboratory was electrical conductivity in metals. The theory generally accepted at the time was based on a work that the German physicist Paul Drude had published in 1900 largely the same theory that is today presented in college-level textbooks. Drude suggested that metallic conduction was the result of the motion of free electrons under the influence of an external electric field and that the electrons, which he originally assumed to carry both negative and positive charges, had properties like a gas. In a metal, the conduction electrons were supposed to be in thermal equilibrium with the ions and neutral atoms. Assuming for simplicity that all electrons possess the same thermal velocity u, and that u is much larger than the drift velocity, Drude derived for the electric conductivity (the inverse of the resistivity) an expression of the form σ = e2nλT–½; here, λ is the mean free path and n the number of free electrons per unit volume. In 1905 Lorentz developed a more sophisticated theory by replacing the unrealistic assumption of equal-speed electrons with electron velocities distributed according to the Maxwell-Boltzmann law. And yet, after lengthy calculations, he arrived at a formula that differed from Drude’s only by a numerical factor. The theory of electrical conduction continued to be developed in still more sophisticated versions, by J. J. Thomson, Owen Richardson, Niels Bohr, and others. In these versions, from 1910 to 1915, the electrons in a metallic conductor were conceived as a gas or vapor satisfying the law of ideal gases. It was hoped in this way to find a mechanism for the interaction of electrons and metal atoms that would explain the blackbody radiation law. No satisfactory explanation was found, however, and the electron theories were no more successful in accounting precisely for the variation of resistance with temperature.
It was known experimentally that the resistance of pure metals varied proportionally with the absolute temperature, that is, σ ~ T–1, at least down to 20 K. This posed a problem, for it agreed with the Drude-Lorentz formula only if it was arbitrarily assumed that nλ ~ T–½, and neither Drude’s theory nor its successors were able to calculate n and λ as functions of T. Moreover, experiments made at very low temperatures during the first decade of the century disagreed with both the T–½ dependence and the T–1 dependence. Investigations made by Dewar and others of the temperature dependence of resistance about the boiling point of hydrogen indicated a flattening trend of the resistance function for very small temperatures. This was taken to imply one of two possibilities: either that the resistance would approach a nonzero value asymptotically or that it would reach a minimum and then, for even smaller temperatures, increase indefinitely. The latter possibility was widely assumed to agree well with theory. Close to absolute zero, free electrons would supposedly “freeze” and condense onto the atoms; then the density of free electrons would approach zero and, according to the Drude-Lorentz formula, the resistance would increase drastically. Kammerlingh Onnes, among others, found this an attractive hypothesis. In 1904 he described it as follows:
It seems as if the vapour of electrons which fills the space of the metal at a low temperature condenses more and more on the atoms. Accordingly, the conductivity, as Kelvin has first expressed it, will at a very low temperature reach a maximum and then diminish again till absolute zero is reached, at which point a metal would not conduct at all, any more than glass. The temperature of the maxima of conduc tivity [lies] probably some times lower than that of liquid hydrogen. At a much lower temperature still, there would not be any free electrons left, the electricity would be congealed, as it were, in the metal. (Dahl 1984, 6)
Armed with his newly produced amounts of liquid helium, Kammerlingh Onnes decided in 1910 to examine the question systematically. The experiments were made in collaboration with Cornelis Dorsman and Gilles Holst, and it was Holst who performed the actual measurements. Yet the report was authored only by Kammerlingh Onnes. The Dutchmen first used a platinum resistance and compared their data with earlier measurements of gold resistances of known purity. The results made Kammerlingh Onnes conclude, “It appears that by descending to helium temperatures the resistance is still further diminished, but when these temperatures are reached the resistance attains a constant value quite independent of the individual temperature to which it has been brought” (ibid.). He realized that even small impurities might affect the result significantly and believed that these masked the real variation of resistance with temperature. Observing that the sample richer in gold showed less resistance than the other sample, he suggested that the resistance of pure metals would vanish asymptotically as the temperature approached zero and become practically zero at 5 K. This was a bold guess. And, like most bold guesses, it was wrong.
New experiments in 1911 made use of mercury, which could be obtained in a highly purified form. An initial experiment, reported in April, seemed to confirm Kammerlingh Onnes’s suspicion of an asymptotically vanishing resistance. But when more precise experiments were conducted the following month, they showed a variation that was altogether unexpected, a sudden change to zero resistance at a temperature close to 4.2 K (figure 6.1). In his Nobel lecture of 1913, Kammerlingh Onnes described the discovery as follows: “The experiment left no doubt that, as far as accuracy of measurement went, the resistance disappeared. At the same time, however, something unexpected occured. The disappearance did not take place gradually but abruptly. From 1/500 the resistance at 4.2 K drops to a millionth part. At the lowest temperature, 1.5 K, it could be established that the resistance had become less than a thousand-millionth part of that at normal temperature. Thus the mercury at 4.2 K has entered a new state, which, owing to its particular electrical properties, can be called the state of superconductivity.” Further experiments made between 1911 and 1913 proved that mercury’s superconductivity was there to stay, whereas neither platinum nor gold showed a similar behavior. Yet mercury was no anomaly, for in December 1912 it turned out that tin and lead were superconductors too; the disappearance of resistance was found to occur at 3.78 K for tin and 6.0 K for lead. Contrary to expectations, it was realized that impurities had no effect on the new phenomenon. Moreover, it was definitely confirmed that the vanishing of resistance occurred abruptly and that the “knees” on the resistance curve were experimental artifacts.
The term “superconductivity” first appeared in a paper written by Kammerlingh Onnes in early 1913. Now there was a name for the puzzling phenomenon, but an understanding of what the name covered was completely lacking. For a time, Kammerlingh Onnes did not fully realize the novelty of the phenomenon and he continued to think of it as an extreme case of ordinary electrical conduction, that is, within the framework provided by the Drude-Lorentz theory. Perhaps, he thought, it was caused by a sudden increase in the mean free paths of the electrons. This idea, together with the results obtained for lead and tin, made him believe that superconductivity might be a general low-temperature state for all metals. But this was clearly a matter to be decided experimentally, and experiments proved that superconductivity was limited to a few elements. Within the area of experimental superconductivity progress followed quickly, notwithstanding the lack of theoretical understanding. In 1913 the first superconducting magnet was constructed at Leiden, and in 1914 Kammerlingh Onnes and his team began a study of the effect of strong magnetic fields on the superconducting state. A new discontinuity turned up, namely, the existence of a certain critical value of the field above which the zero resistance vanished abruptly and mysteriously. The critical field strength was found to increase with a decreasing temperature. The effect of a supercritical magnetic field thus had the same effect as heating the metal. Yet another novel phenomenon was left to the puzzled theoreticians.
Figure 6.1. Superconductivity revealed: Kammerlingh Onnes’s 1911 curve of the resistance of mercury versus tem perature.
It is sometimes claimed that Kammerlingh Onnes also discovered super-fluidity in 1911. The weak basis for this claim is that the Leiden group performed measurements of the variation of the density of liquid helium with the temperature and obtained results that suggested a maximum density near 2.2 K. However, the sharp change in density a manifestation of helium’s superfluidity was firmly established only several years after World War I, in 1924. Even then, Kammerlingh Onnes did not consider it a particularly interesting phenomenon that deserved a detailed study. Although what he observed in 1911 was indeed a superfluid property, it took many years until it was realized to be a manifestation of a genuinely novel phenomenon. Observation is a necessary but not sufficient precondition for discovery, and it was only in 1938 that superfluidity attained the status of discovery.
Although the discovery of superconductivity was a shining peak in the work of the Leiden laboratory, it was only one part of many in a broadly planned research program. Both before and after 1911, Kammerlingh Onnes and his group spent most of their time investigating other properties at low temperatures, including the Hall effect, piezoelectricity, the Curie law, magneto-optics, and radioactivity. It was for “his investigations of the properties of matter at low temperatures which led, inter alia, to the production of liquid helium” that Kammerlingh Onnes was awarded the Nobel prize in 1913. Superconductivity, in retrospect by far the most important of the discoveries, was not mentioned explicitly in the presentation speech. That superconductivity did not immediately arouse a stir was also reflected in the first Solvay Congress of 1911, which took place half a year after the discovery. In Brussels, Kammerlingh Onnes gave a detailed report on electrical resistance measurements in which he vaguely suggested that the vanishing of resistance might be explained with the help of quantum theory. In his Nobel lecture, he similarly suggested that superconductivity might be connected with “the energy of Planck’s vibrators.” The brief discussion following the Solvay report, limited to a question from Paul Langevin, indicates that the physicists gathered in Brussels were not particularly interested in the phenomenon.
Attempts to apply quantum theory to develop an improved theory of electrical conduction, and thereby to explain superconductivity, followed quickly after the 1911 discovery. One of the more promising among the theories, proposed by Wilhelm Wien in 1913, was based on the assumption that electrical conduction was essentially determined by the mean-free path of the electrons. At low temperatures, Wien’s quantum theory led to a quadratic dependence of the resistance on temperature, but it failed to explain the sudden drop in resistance of superconducting metals. Other applications of quantum theory, suggested by Keesom in 1914 and Frederick Lindemann in 1915, were no more successful. What was the cause of the abrupt change in resistance? Why was the phenomenon restricted to a few of the metals in the periodic table? Theory just could not tell. Yet, in spite of the failure, there was no sense of crisis because of the anomaly.
If superconductivity could not be understood theoretically, perhaps it could be used technologically. At an early stage, the Leiden physicists realized the possibility of constructing powerful superconducting electromagnets, where there would be no heat loss even for very large currents. Such powerful magnets were not merely scientifically interesting, but would also be of great use in the electrotechnical industry. It turned out, though, that strong magnetic fields counteracted the superconducting state; the dream of super-electromagnets therefore had to be shelved, at least temporarily. In early 1914, experiments were made with a superconducting lead ring to which was applied a varying magnetic field of strength up to 10 kilogauss. At small field strengths the resistance was zero, but at a critical value about 600 gauss the resistance rose dramatically, in a manner analogous to the resistance-temperature variation. “The resistance increases . . . as if the introduction of the magnetic field has the same effect as heating the conductor,” Kammerlingh Onnes wrote. Further examination of the relationship between resistance and magnetic field had to wait until the 1920s. With the advent of World War I, Leiden was temporarily cut off from its supplies of helium. And without liquid helium, neither superconductivity nor other phenomena at temperatures below 5 K could be studied experimentally.
Low-temperature experiments in Leiden continued after the war ended and new supplies of helium were secured. In 1919 it was established that two more metals, thallium and uranium, are superconducting. The vanishing temperatures were found to be 2.32 K for thallium and about 7.2 K for uranium. On the theoretical side, attempts continued to understand the phenomenon, but progress was notably lacking. The first two Solvay conferences after the war may illustrate the unsatisfactory state of knowledge concerning superconductivity. At the 1921 conference, Kammerlingh Onnes gave an address on “Superconductors and the Rutherford-Bohr Model,” in which he reported on the latest Leiden experiments. He suggested that superconductivity was a nonclassical phenomenon that could be understood only in terms of Bohr’s quantum atom, but neither Kammerlingh Onnes nor others could tell how. He summarized his report in eight questions, including “Since the Rutherford-Bohr atoms unite to make a metal, what happens to their electrons? Do they lose all or only part of their kinetic energy?”
The subject of the fourth congress in 1924 was “The Electrical Conductivity of Metals” and here, superconductivity was discussed by several of the participants. Lorentz, who spoke on the electron theory of metals, concluded vaguely that the electronic orbits in the superconducting states must be irregular or “particular.” Kammerlingh Onnes discussed a possible connection between the electron structures of the few superconducting elements according to Bohr’s new theory of the periodic system. Langevin suggested that the discontinuous vanishing of resistance was perhaps a result of a phase change in the material. He was apparently unaware that the suggestion had already been tested experimentally in Leiden, where Keesom’s x-ray analyses proved that no change in phase was involved. Owen Richardson proposed a model according to which the electrons could move freely along orbits tangential to each other, and Auguste Piccard wondered whether lightning was perhaps a superconducting phenomenon at normal temperature.
Neither the Solvay discussions nor other contemporary attempts to understand superconductivity brought the subject any closer to an explanation than before the war. As Einstein wrote in 1922, in his only contribution to the literature on superconductivity, “With our wide-ranging ignorance of the quantum mechanics of composite systems we are far from able to compose a theory out of these vague ideas. We can only rely on experiment” (Dahl 1992, 106). Incidentally, this was possibly the first time that the term “quantum mechanics” occurred in a scientific publication.
