Albert Einstein's contributions will be studied as long as our civilization exists. But while scientists from their student days on will, on the whole, know of his work indirectly through the textbooks, Einstein's actual words, in his wide-ranging publications and correspondence, will be scrutinized chiefly by the historians of science. One may hope that Ein stein would have approved; not only did he publish many essays on his torical developments in science,' but he was on record, more than once, that a means of writing must be found that conveys the thought processes that lead to discoveries - showing how scientists thought and wrestled with their problems. Moreover, Einstein made the task of the historian easier than did many other scientists, because of the characteristic frank ness and consistency in his writings. These traits of his will aid my task to speak about some of the early steps on his path to relativity - steps that made that path a high road and caused the other, more fashionable ones of that day to be seen eventually as blind alleys.
"Recognize the nnity o/ % comp/ex o/ phenomena "
When viewed in terms of Einstein's early publications/ the road that brought him to the threshold of relativity began in apparently quite unimpressive territory. Einstein's first published article, entitled "Con sequences of the capillarity phenomena," was sent to the Annn/en dcr Physih in December 1900, a half year after Einstein had graduated from the Eidgenossische Technische Hochschule in Zurich and a half year be fore his getting his first temporary job as a substitute teacher.
At the time, all the excitement in physics lay in a quite different direc tion. ft was just a few years after the discovery of X-rays, radioactivity,
Einstein and tEe cn/tMre o / science
the etectron. New experiments) findings and new theories chased one another rapidly. Einstein was not ready for any of that. As he charac terized it )ater, he was in the midd!e of years of "groping in the dark." He often remarked that his forma) training had been spotty, a)though on his own he had worked his way through the vo)umes of ctassic lectures of Kirchhoff, Hetmhottz, Hertz, and Bottzmann's GastEeorie, not to speak of Ernst Mach, to whose work Michete Besso had introduced Einstein soon after their first meeting in 1896. Einstein confessed tater, "f had no technics) knowledge."^ But he added: "ft turned out soon that the gen era) overview [a//geweine UEersicEf] over physica) connections is often more va)uab)e than speciahst knowtedge and routine."
But capillarity was by no means as du)) as it now may seem. Even some five years !ater, a tong paper on capillarity by G. Bakker in the famous votume 17 of the Anng/en der PEysiE starts with the panegyric: "The theory of capiUarity of Laplace was one of the most beautifu) achieve ments of science"; he goes on to sing the praises of the subject as handted by Gauss, Young, Gibbs, and F. Neumann. Young Nie)s Bohr's first re search, comptetcd in 1906, was on the closely retated probtem of surface tension of water. For Einstein the capillarity paper was the first of nine pubtications indicating his deep interest in thermodynamics and, tater, statistica) mechanics, which he published in the Anna/en Jer PEysiE be tween 1901 and 1907/
The probtem to which Einstein is attending, in this first paper and in the next one, is "the probtem of molecular forces." The mechanica) work done in a cycte that invotves isotherma) increases of surfaces of tiquids should be zero; but, he says, this is contrary to experience. Therefore, "there is nothing )eft to do but to assume that the change in surface area is attended by a conversion of work to heat." He promises to proceed from the simplest assumptions [AnnaEmen] about the nature of mo)ecu)ar forces of attraction, and check their consequences in terms of their agree ment with experiment, fn this work, he says, "! )et myself be guided by anatogy with gravitationa) forces." At the end of the paper, he sum marizes:
We can now say that our fundamental assumption has been validated: to each atom there corresponds a mo)ecu)ar force of attraction which is independent of the temperature and inde pendent of the way the atom chemically combines with other atoms. . . . The question whether and in what respect our 58
Einstein's scienti/ic progruw; /orw^twe ye<rrs $9 forces are related to gravitational forces must be left com
pletely open.
What preoccupies him here, as he writes in a letter to his friend Marcel Grossmann (April 14, 1901), is "the question concerning the inner relationship of molecular forces with Newtonian forces at a dis tance."^ Now, this is not a problem without ambition! Newton himself, who had hoped for a relationship between gravitational forces and mo lecular forces, would have been not uninterested to read this work.
The idea for Einstein's work seems to have been based on Wilhelm Ostwald's AZ/geweine CEemie. This is the book first mentioned in all of Einstein's writings. Indeed, he sent a reprint of the paper to the scientist- philosopher Ostwald on April $, 1901, together with a request for a job in Ostwald's laboratory and the remark that his book had stimulated this paper. Ostwald, on his side, was not overwhelmed; he did not even reply. But Einstein's interest in the program of the unification of the forces of nature was making its tentative first appearance right here. Ele felt he was working on important problems, and despite his inability to find a steady job, he was evidently in good spirits. In the letter to Grossmann he says he is as merry as a bird, and he adds: "It is a magnificent feeling to recognize the unity [EinEeit/icEEeit] of a complex of phenomena which to direct observation appear to be quite separate things." It is only April 1901, but this is already a familiar Einstein, here searching for bridges between the phenomena of microphysics and macrophysics, between capillarity and gravitation.
Einstein's second paper, again, looks not very promising on the sur face. It is entitled "Concerning the thermodynamics of potential differ ence between metals and fully dissociated solutions of their salts, and concerning a new method to investigate molecular forces." It is dated April 1902., some two months before he started his job at the patent office. Over a year has elapsed since his first paper.
He begins with a section entitled "A hypothetical extension of the second law of the mechanical theory of heat." His earlier method now has undergone a significant change. In the first paper he had started with the phenomena, listed reams of experimental data from the literature, and discussed consequences drawn from them, as was more or less the rule in papers of the time. Now, in the first section, he postulates a state ment of the second law which he recognizes to be outside the limits set by the available phenomena. By generalizing (yerg/Zgeweinern) beyond ex-
6o
perience, he proposes to adopt the following statement: "One remains in harmony with experience when one appiies the second taw to physicai mixtures upon whose individual components are acting any arbitrary conservative forces." Moreover, he warns quickly, "We will rely on this hypothesis in what follows even if it does not appear to be absolutely necessary." He has now begun to go for discoveries of postulates frankly beyond the "present experience." The appeal of the geneM/ixabofi is taking over, and becomes a directive for research.
The third paper follows, sent in from Bern in June 190Z. ft is entitled "Kinetic theory of thermal equilibrium and the second law of thermo dynamics," the first of three papers in 1902.-04 extending Boltzmann's ideas in thermodynamics and statistical mechanics. Einstein introduces an interpretation of statistical probability in which systems run through the various possible states over and over in irregular fashion, unlike ther modynamic descriptions in which equilibrium states once reached are persisted in indefinitely. This is an important bridge to his future work. His power has begun to show now, although it did not attract much attention at the time. Without having read J. Willard Gibbs' E/e?Ment<3ry pnMcip/es o/ stgtishca/ wecEawfcs, which appeared in the same year, Einstein is getting some of the same results.
The introductory paragraph of the third paper lays forth the ambition to generalize:
Despite the success of the kinetic theory of heat in the area of the theory of gases, it has so far not been possible, by the laws of mechanics alone, to provide a sufficient foundation for the general theory of heat. Maxwell's and Boltzmann's theories have come close to this goal. The purpose of the following considerations is to fill the gap. At the same time there will be given an extension of the second postulate which will be of importance for the application of thermodynamics. Moreover, a mathematical expression for entropy will be obtained, from a mechanical point of view.
The first numbered section follows immediately and is entitled "1. Mechanical picture B;VJ] for a physical system." The only footnote in this paper is to Boltzmann's GasfBeone, where, incidentally, the important term is also used in one of the headings.
As if to make sure that we take seriously what is implied by this term, Einstein comes back to it toward the end of his paper, In one sentence he gives the main conclusion: "The second law thus appears as a neces
sary consequence of the mechanical world picture jnotwend/ge Fo/ge des wecFnniscFen We/tFi/des]." With this, he has used the term in print for the first time. He was to return to it often later, not feast in his two great critiques of the "mechanicat worfd picture" in his "Autobiographicaf notes" of 1946, and of the whole unsatisfactory devefopment from the mecFnniscFe Frogrninw of the nineteenth century to our Fendges We/t- Fi/d, as speffed out in his earlier lecture on "Aether and relativity theory" (192-0).
So as of 1902, we see the twenty-three-year-old Einstein entering pub licly on the ground where the great fight among German scientists has been in progress between the chief rival world conceptions, one holding to mechanics and the other to electrodynamics as the ground of funda mental explanation. In this 1902 article, he is still concerned with inves tigating the mechanical world picture as one of the main options. And while he finds it there of use, he ends with a suspicion: "The results are more general than the mechanical representation used to arrive at them." Soon he will see it is in fact far too limited; it cannot handle, for example, Brownian movement. He will also find that its most prominent alterna tive, the so-called electromagnetic world picture, cannot handle fluctua tion phenomena of light. And even the victory of one of the conceptions would, as he later expressed it, leave us with "two types of conceptual elements, on the one hand, material points with forces at a distance be tween them, and, on the other hand, the continuous fields . . . an inter mediate state in physics without a uniform basis for the entirety."* He will have to try to build his own We/tFi/d.
The fourth paper, entitled "A theory of the foundations of thermo dynamics," is sent off from Bern in January 1903. It is his only paper published that year. In addition to constructing a We/tFi/d, he is also building a career, and of course a family. He and Mileva Marie are mar ried on January 6, 1903, and in the first of his surviving letters to his friend Besso, Einstein writes in that month: "Well now, I am a married man and lead a nice, comfortable life with my wife. She takes excellent care... and is always cheerful." ** He goes on to describe the fourth paper, which he has just sent off
after much reworking and correction. But now it is completely clear and simple, so that I am quite satisfied with it. After postulating the energy principle and the atomic theory, there follow the concepts of temperature and entropy; with the addi tional aid of the hypothesis that the distribution of states of
6 z Einstein nnd tEe cM/tnre o / science
isolated systems never go into tess probable ones, there follows also the second law in its most general form namely the impos sibility of a perpetuum mobile of the second kind.^
Hindsight makes it easy to see that the structure of the argument in this paper is perhaps its most interesting feature: first, the postulation of general principles, now with hardly a nod to the detailed phenomena; then the derivation of logical consequences; and at the end, the test against experience - in this case, experience of the most general kind.
More than a year later, on April 14,1904, Einstein writes to his friend Conrad Habicht: "In a few weeks we are expecting a young one. 1 now
have found in a very simple manner the relation between the elementary quanta of matter and the wavelengths of radiation."^ In fact, he has just sent off his fifth paper to the Ann%/en derEEysiE, "On molecular theory of heat." This paper announces itself modestly, in the first sentence, as merely an addition to work published the previous year. But the plot has thickened. In his usual introductory paragraph, he sets out the general plan. He will derive an expression for the entropy of a system which is
completely analogous to that found by Boltzmann for ideal gases and postulated by Planck for his theory of radiation. . . . Then a simple derivation will be given of the second law. Thereupon the meaning of a universal constant will be investi gated, which plays an important role in the general molecular theory of heat. Finally there follows an application to the theory of black body radiation, where a highly interesting rela tion is developed between the universal constant mentioned above [he means R/2 N] (one which is determined by the mag
nitude of the elementary quanta of matter and of electricity), on the one hand, and the order of magnitude of the wavelength of radiation, on the other, without making use of any special hypotheses.
Thus Einstein introduces his long-lasting concern with fluctuation phenomena. He shows that the size of energy fluctuations g in the system, and therefore its thermal stability, is determined by a universal constant (which we would write as E = R/N). Having applied it to mechanical systems and thermal phenomena, he then makes the original and daring jump to an "application to radiation": In order to determine the universal constant from the size of observable energy fluctuations, he proposes to go to the only kind of physical system where, he says, experience allows
E i n s t e i n ' s s c i e n t i / i c p r o g r a m . ' ( o r w ^ h y e y e ^ r s 63
one to "suppose" (yermnten) that there %re energy fluctuations - the case of an otherwise empty space filled with thermal radiation. Obviously, by now he has indeed learned to "scent out the path that leads to funda mentals," as he later put it.
There follows now an ingenious argument that shows how much he is at home with borderline cases between two different fields as defined in contemporary physics, not having to choose between one and the other, but rather using both - indeed, "recognizing the unity of a complex of phenomena." He considers a volume y with dimensions of the order of the wavelength X of the radiation in it (y — X^). In that case, the energy fluctuations will be of the same order as the magnitude of the energy itself, or = EE Now he uses the Stefan-Boltzmann law in the form E = cyf* and deduces that X — 0 .4 /T. But "by experience" - Einstein
does not mention that it is Wien's law (1893) - we know that indeed Emax's 0 .2 9 3 /T. So his result has the same general lawfulness with re
spect to T, and the same order of magnitude for the constant. Einstein concludes that in view of the "great generality of our assumptions," this agreement cannot be an "accident." And with that, the paper ends. (The coincidence of prediction within a factor of about 2. remains characteris tically an indication for Einstein that things are going quite well.)
But what a great launching of work, in some eight pages! Fluctuation phenomena will remain one of Einstein's trusted tools, not only in the Brownian motion paper, which is almost ready to come over the horizon, or in the papers on quantum theory of radiation and on Bose-Einstein statistics, but even in some of the smaller papers that have received little notice so far. (There is, for example, one of Einstein's short publications in 1908 on a new electrostatic method for measuring small quantities of electricity. With Conrad and Paul Habicht, friends of the earliest days of the Olympia Academy in Bern, Einstein had been interested in building a device for measuring small voltages by multiplication techniques. In fact, Einstein wrote a patent application for the device, which claimed to measure potential differences down to 5 X 1 0"* volt. He even found a
"clever mechanic" who attempted to build the thing. But Einstein's real interest shows up in the last paragraph of the short 1908 paper that de scribed the device.'" In research, for example on radioactivity, an electro static method of measurement of highest sensitivity might be useful. But "I was led to this plan by thinking how one might find and measure the spontaneous charge appearing on conductors which should exist analo
gously with the Brownian motion that is required by the molecuiar theory of heat.")
The next publication is Einstein's inaugural dissertation on "A new determination of molecular dimensions," dated April 30,190$." We are now in the miraculous year of 1903, the year that will continue to be a challenge for historians of science for a long time. The work does not yet