Einstein, Specific Heats, and the Early Quantum Theory Author(S): Martin J

Home , Ernest Solvay

Einstein, Specific Heats, and the Early Quantum Theory Author(s): Martin J. Klein Source: Science, New Series, Vol. 148, No. 3667 (Apr. 9, 1965), pp. 173-180 Published by: American Association for the Advancement of Science Stable URL: http://www.jstor.org/stable/1715511 . Accessed: 02/08/2013 11:35

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

American Association for the Advancement of Science is collaborating with JSTOR to digitize, preserve and extend access to Science.

http://www.jstor.org

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions 9 April 1965, Volume 148, Number 3667 SCIENCE

them also to realize the impossibility of getting along by means of half- way measures. Planck himself was a conservative thinker, but he was completely convinced that physicists would Einstein, Specific Heaits, have to accept and incorporate into their future theories a fundamental dis- and the Quantum Theory continuity of the energy, even though Early it meant giving up something as basic as the Hamiltonian differential equa- Einstein's quantum theory of specific heat first shovved tions of motion (5). He was by no means sure, however, that the time was the power of the new concept of energy quarlta. quite ripe for a general acceptance of this idea of quanta. Somewhat bitter . had him Martin J. Klei personal experience taught that the partisans of a scientific theory are not so easily convinced by rational argument as they ought to be, and that his own estimate of the importance During the month of June 1911 tion with pleasure. "TIhe whole enter- of a problem was not always widely some 25 of Europe's most eminent prise is unusually applealing to me," shared (6). This attitude had prompt- physicists received invitations to take he wrote, "and I har-dly doubt that ed his negative response to Nernst's part in a select international confer- you are its soul" (2). first tentative proposal for such a meet- ence whose purpose it would be to The opening lines of Solvay's let- ing the previous year. In Planck's view confront the scientific crisis provoked ter, based on a draft by Nernst (3), the necessary precondition for the con- by the quantum theory (1). The in- stated some of the diifficulties facing ference was a widespread feeling that vitations were sent by Ernest Solvay, physics. the current defective state of physical the industrial chemist who theory was "intolerable-for every Belgian According to all appe had made a fortune with his new now irI the midst of a ]new development true theorist," a feeling that would process for manufacturing sodium car- of the principles on which the classical draw these true theorists to seek coun- bonate and who used his millions to kinetic-molecular theory of matter was sel together. But in 1910, at least, based. The de, of this he support a variety of worthy causes. systematic velopment doubted that such sharp feelings theory leads, on the one hand, to a radia- Solvay had an amateur's interest in the tion formula that disagrees with all ex- were widely enough shared as yet; he basic questions of physics, but it must perimental results; from this same theory thought, in fact, that only a few others have been apparent to the recipients are deduced, on the otherr hand, assertions -like Einstein, Lorentz, Wien, and of his letter that not even the most on the subject of specificc heats . . . that Larmor-saw the urgency of these are likewise refuted measure- devoted amateur could have by many questions. He had no question about planned ments. It has been shovvn, especially by the agenda, chosen the membership, Planck and Einstein, that these contradic- the urgency in his own mind, of or indeed realized the urgency of the tions disappear if one s(ets certain limits course. "For I can say without exag- problems for which the meeting was on the motions of electtrons and atoms geratlon," he wrote to Nernst, "that to be convened. It did not take much oscillating about an equilibrium position for ten years, without interruption, of but this (the principle energy quanta); nothing in physics has so searching to locate the origin of the interpretation in turn d[eparts so much basically force that had directed Solvay's en- from the equations of m otion used up to stimulated me, agitated me, and ex- thusiastic philanthropy, since Solvay's now that its acceptance Nwould necessarily cited me as these quanta of action" letter asked that all replies be ad- and indisputably entail ai vast reform of (7). dressed to Professor Walther Nernst our current fundamental theories. in Berlin. Among those who immedi- A decade had alread y gone by since ately recognized the role of the famous Max Planck had intiroduced energy Planck's Radiation Formula German physical chemist was Albert quanta into physics in1 his successful Einstein, then professor at Prague, who attempt to derive the correct descrip- Einstein was surely the one physicist wrote to Nernst accepting the invitation of the measured black-body ra- about whom Planck did not have to diation spectrum (4). It had taken worry. Einstein, early and independent- The author is professor of physics at Case much of that decade fo or even the initi- ly, had recognized the real inevitability Institute of Technology, Cleveland, Ohio. This ates he of of the incorrect radiation article was read to the History of Science So- to experience t impact hopelessly ciety in Montreal, 29 December 1964. Planck's radical depaLrture and for formula that followed from classical 9 APRIL 1965 173

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions physics, and he had seen further, by formed in 1911. His views on the cor- Einstein's View of Quanta far, into the implications of Planck's puscular properties of radiation were correct radiation formula than anyone sufficiently heretical that there was no Einstein's attitude toward the con- else, including Planck himself (8, 9). great rush of attempts to put them cept of quanta differed sharply from It is not quite true to say that Planck to the test of experiment. Planck's. Planck had quantized the did not have to worry about Einstein: When the list of subjects to be energy of a charged oscillator inter- Einstein's views did concern him, but treated at the Solvay conference was acting with electromagnetic radiation that was because Planck thought they drawn up, probably by Nernst and in order to justify, to derive, the radia- went much too far. Planck had no Planck with revisions by H. A. tion formula he had proposed, a for- doubt that his own new constant h, Lorentz, who was to preside, Einstein's mula he already knew to be in agree- and the discreteness of the energy that ideas on the structure of radiation ment with experiment. The energy its introduction implied, would be in- were not on the agenda. Solvay's let- quanta, whose magnitude had to be corporated into the fundamental the- ter of invitation listed the principal proportional to the frequency of the ory of the future, but he was not at subjects to be discussed, and appropri- oscillator for thermodynamic reasons, all ready to accept the startling con- ate individuals were asked to prepare gave Planck a first suggestion of what clusions that Einstein claimed to have written reports on them. These reports the constant h in his radiation formula drawn from the radiation formula. would be distributed to all members might signify. (He had been con- For Einstein had argued, as early of the conference well in advance of vinced from the outset that this con- as 1905, that the observed form of the the meeting and were intended to pro- stant would take its rightful place with spectral distribution of black-body ra- vide a basis for the discussions to take the velocity of light, the gravitational diation forced a radical revision of ac- place at Brussels. The plans for the constant, and the electronic charge as cepted ideas on the nature of radi- meeting called for reports on both the the fundamental natural constants.) ation (10). Even without having a classical theory of the key problems (13). Planck saw the quantization of real theory of radiation, and guided and their modifications according to the oscillator's energy as the way to only by his incomparable insight into the ideas of the new quantum theory. achieve the radiation law; he would the statistical meaning of the second Thus Lorentz was to discuss the ap- have avoided even that radical step if law of thermodynamics, he asserted plication of the equipartition theorem he could have, but he certainly did not that electromagnetic radiation must to radiation with its disastrous impli- want to abandon any more of the es- show a granular structure. Despite all cation of the Rayleigh-Jeans distribu- tablished structure of theory than he the evidence for the wave theory of tion, and Planck would report on his absolutely had to. light there were circumstances when own radiation theory. In a similar pair- Einstein, on the contrary, had ar- light would have to be considered as ing, James Jeans was asked to discuss gued from the empirically confirmed made up of a collection of independent the classical theory of specific heat radiation law to the existence of energy particles of energy-light quanta. Ein- (some of whose consequences had led quanta. Where Planck saw quantiza- stein's first arguments were essentially to puzzles of longer standing than those tion as a sufficient condition for ob- independent of Planck's theory of the in the theory of radiation), and Ein- taining the radiation law, Einstein radiation spectrum, and even of stein, whose extreme ideas on radia- claimed that the radiation law de- Planck's radiation formula, since Ein- tion were not specifically called for, manded the existence of quanta as a stein used only the experimentally was invited to report on the quantum necessary consequence. And to Ein- well established form of the high-fre- theory of specific heat. stein quanta represented a basic aspect quency spectrum (the Wien distribu- Einstein's first paper on the quantum of the structure of radiation, rather tion). In later papers Einstein gener- theory of specific heat had appeared than just a particular property of oscil- alized this work and showed in sev- in 1907 (12). It was his earliest work lators of a certain type. Once Einstein eral ways that the Planck radiation on the quantum theory of matter, in had recognized the significance of what spectrum implied that light must show contrast with the quantum theory of his friend Paul Ehrenfest would later both wave and particle properties- radiation. This theory of specific heat, call the Rayleigh-Jeans catastrophe what we now call the wave-particle less radical in its consequences and (14), and he recognized it very early, duality. He was convinced that the fu- easier to grasp than his attempts to he never stopped probing and pon- ture theory of radiation would have understand radiation, clearly had to be dering the implications of Planck's ra- to be a fusion of wave and corpuscular reckoned with. For, by 1911, it al- diation law, searching for a clue that theories (11). ready had considerable experimental might suggest the ideas that could re- Planck was not prepared to give up support, both direct and indirect, and place classical theory. The paper en- the description of radiation as a con- this support had come in large part titled "Planck's theory of radiation and tinuous phenomenon in space and from Walther Nernst's laboratory in the theory of specific heat" (12), time, the description provided by the Berlin. The obvious power of Ein- which Einstein sent to the Annalen electromagnetic wave theory of light. stein's ideas in accounting for Nernst's der Physik in November 1906, report- He could argue, somewhat vaguely, data had made Nernst into an en- ed an entirely new set of connections against assumptions tacitly made by thusiastic proponent of the quantum that he had found in the course of Einstein, but their disagreement was theory and probably played no small his probing. not sharp enough for an experimental part in his drive to organize the Sol- He had been reworking Planck's test. Einstein had, to be sure, made vay Congress. It is this important role derivation of the expression for the detailed predictions about a good many played by Einstein's quantum theory average energy of one of the oscilla- phenomena, but the experiments were of specific heat that I propose to de- tors that absorb and emit electromag- difficult and had not yet been per- scribe here. netic radiation. Planck, a novice in 174 SCIENCE, VOL. 148

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions statistical mechanics in 1900 despite of the spectral distribution and the theory, and that the range of phenom- his 20 years of work in thermody- average energy E of the oscillators in ena which could be clarified by such namics, had adapted an old illustra- equilibrium with the radiation, a theory included the properties of tive argument of Boltzmann's to his matter as well as those of radiation. = purposes. Planck's line of reasoning p(v,T) (87rv2/c3) E, (4) Einstein was showing in a new way did not, however, really bring out the where c is the velocity of light. If we how deeply the foundations of clas- fundamental way in which he had de- change to the notation introduced by sical physics had been undermined. viated from Boltzmann's basic assump- Planck, where k is used to denote tions. Einstein began his paper with (R/No) and h is used instead of a new derivation of this equation for (R/No)i8, the result is the usual form Specific Heats of Solids the average energy, going back to the for the Planck distribution law, fundamentals of statistical mechanics The contradictions to which Ein- p(^,T) - as he had independently redeveloped stein referred in the passage quoted (87rv2/c') (h^)[exp (hv/kT) - 1-1. (5) them a few years earlier. He showed above concerned the violations of the again that a consequent treatment by Einstein proceeded to comment on equipartition theorem that were ex- the classical methods gave the this argument and its implications. It hibited in the specific heats of solids. equipartition result for the average indicated, above all, the point at which The early calorimetric measurements energy E of an oscillator, the kinetic theory of heat had to be of Dulong and Petit had shown that modified in order that it be in accord the heat capacities of the elements in E = (1) (R/INo)T, with the radiation law. This, in turn, the solid state had a common value, raised a point of principle (12, if these heat were where R is the universal gas constant; major capacities always pp. 183-4): taken for a gram atomic This No is Avogadro's number, the number weight. Dulong-Petit rule provided a of molecules in a gram molecular While up to now molecular motions rough method for weight of any substance; and T is the have been supposed to be subject to the estimating atomic weights and temperature. This result had its roots same laws that hold for the motions of generally served as one of the the bodies we perceive directly (except few indications in the basic classical assumption that early that a kinetic- that we also add the postulate of complete molecular theory of solids might also equal regions of phase space should reversibility), we must now assume that, be The be given equal weights in the averag- for ions which can vibrate at a definite possible. Dulong-Petit rule found a ing process. In Einstein's own way of frequency and which make possible the simple explanation if the ther- of between radiation and mal motions of the interpreting the probabilities used in exchange energy atoms in the solid matter, the manifold of possible states were taken to be simple harmonic os- statistical mechanics this meant that the must be narrower than it is for the bodies cillations about of system spent equal fractions of any in our direct experience. We must in fact positions equilibrium. Each long time interval in regions of equal assume that the mechanism of energy atom would have three in- transfer is such that the vibrations of this phase volume. To avoid the equiparti- energy can as- dependent type, and, sume only the values 0, hv, .... tion result and to arrive at Planck's 2hv, since the average energy of such a nhv, .... harmonic expression for the average energy of an simple oscillation is just T from oscillator one had to drop this assump- This was by no means all, for Ein- (R/N) the equipartition theorem tion and replace it with another: only stein went on to write: (see Eq. 1), the total energy of one those regions of phase space in which mole of the solid would be I now believe that we should not be 3N,,(R/N) T. The heat capacity per the energy took on the discrete values satisfied with this result. For the following mole is the temperature derivative of 0, e, 2,, . . ., ne, . . . were to question forces itself upon us: If the ele- this have non-zero weights, and these in- mentary oscillators that are used in the expression, 3R, or about 6 calories tegral multiples of the unit energy E theory of the energy exchange between per degree. radiation and matter cannot be of the oscillator were to be weighted interpreted So far there is no contradiction, of in the sense of the present kinetic-molec- course. But this explanation of the Du- equally. On this new assumption the ular theory, must we not also modify the average energy could readily be cal- theory for the other oscillators that are long-Petit rule proved too much, since culated and had the value used in the molecular theory of heat? the rule is only a rule and a number There is no doubt about the answer, in of elements have heat capacities much E e [exp (Noe/RT) - 1]-I. (2) my opinion. If Planck's theory of radiation smaller than the Dulong-Petit value. strikes to the heart of the then we matter, These exceptions occur particularly If the quantum of energy, e, is set must also expect to find contradictions between the kinetic-molecular among the lightest elements such as equal to where /3 is the present (R/No)/,v, theory and experiment in other areas of beryllium, boron, and carbon. It was constant h/k and is the v frequency the theory of heat, contradictions that can also well known before 1900 that these of the oscillator, in order be resolved the ultimately by route just traced. In same elements had heat capacities that to satisfy the displacement law, the my opinion this is actually the case, as I varied rapidly with temperature and average energy can be written in the try to show in what follows. that approached the Dulong-Petit value form These remarks show how inade- at temperatures well above room tem- this paper of Einstein's is de- The E- (RINo) f3v [exp (/3v/T) - I]-. (3) quately perature (15). difficulty was to scribed by those who refer to it as find "some escape from the destruc- The frequency spectrum of black-body simply an application of the quan- tive simplicity of the general conclu- radiation, p (v, T), could then be ob- tum theory to solids. It would be more sion," as Rayleigh expressed it in a tained by using a result Planck had to the point to say that the paper very similar connection (16). derived from classical electromagnetic was written to show that there was, The situation was, however, even theory, expressing the proportionality or would have to be, a quantum more disturbing, as Einstein pointed 9 APRIL 1965 175

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions out after describing the facts I have stein took it for granted that the vibra- that year Walther Nernst proposed a just summarized. By 1906 there were tions which contribute to the heat ca- new theorem, which eventually took good reasons to believe that atoms had pacity included those whose frequen- on the enviable status of a new law an internal structure and that they con- cies could be measured by a study of of thermodynamics, that established an tained, in some way, electrons. Ein- the optical absorption of the solid, at essential relation between the thermal stein referred in particular to Drude's least in certain cases (17; see also 9, behavior of matter at temperatures work on dispersion which indicated p. 34). From the known value of the near absolute zero and problems of that, while the infrared-absorption fre- constant /3, he readily estimated that pressing and even practical interest to quencies of solids could be assigned unless the optical absorption occurred chemists (18). I do not intend to re- to ionic vibrations, ultraviolet-absorp- at wavelengths greater than several mi- view Nernst's reasoning here, but I tion frequencies seemed to be as- crons, the corresponding vibration must point out that Nernst was con- sociated with electronic vibrations. would make no contribution to the cerned with chemical equilibria in But if this were the case then once heat capacity at room temperature. gases at high temperatures. Thermody- again the equipartition theorem would Only when the wavelength absorbed namics left one without a method for demand too much, since it would re- was greater than about 50 microns calculating the essential constant in the quire a full contribution of (R/No) (well into the infrared) would the condition for equilibrium, and Nernst from each electronic vibration, and the full equipartition value of the specific found that this gap could be filled if heat capacity would have to be far heat be observed at room temperature. he postulated that entropy differences greater than the Dulong-Petit value. The data available to Einstein were between all states of a system disap- Einstein had displayed the contradic- consistent with these results, and his pear at absolute zero. Evidence avail- tions; he now proceeded to resolve estimates of infrared-absorption fre- able to Nernst made this look plausi- them with one stroke. For if his view quencies from specific heat values were ble, but much work had to be done of the universality of the quantum remarkably good, considering how before "the new heat theorem" would hypothesis was correct ("if Planck's oversimplified a model of the solid he rest on secure foundations. theory strikes to the heart of the mat- had used. Nernst discussed this theorem in his ter"), then the average energy of any Even more striking than this unex- Silliman Lectures at Yale in the fall oscillator is not given by the equipar- pected new relationship between op- of 1906 and remarked on its implica- tition value, (R/No)T, but rather by tical and thermal properties was the tions for calorimetry (19): the expression of Eq. 3. In this case, general theorem implied by Einstein's however, the energy and specific heat eouations: the specific heat of all For the specific heats of liquids or solids at the absolute zero, our hypothesis on the of the solids must become vanishingly small depend frequencies requires that every atom shall have a atomic vibrations in the solid. Einstein at sufficiently low temperatures. The definite value for the atomic heat, inde- made the simplest possible assumption exceptions to the Dulong-Petit rule pendent of the form, crystallized or liquid here, recognizing explicitly that he was were not to be considered as excep- (i.e. amorphous), and of whether it is in chemical with other atoms. he took all tional at all; they were just substances combination probably oversimplifying: Numerous measurements by different ex- decrease atomic vibrations to be independent that exhibited the universal perimenters have shown, in full agreement and of the same frequency v. The of specific heat with decreasing tem- with each other, that the atomic heats in energy, U, of 1 mole of the solid perature at relatively high tempera- the solid state decrease greatly at low but at the time it is would then be given by the equation tures, because of their light atoms and temperatures, present fre- impossible to calculate the limiting value correspondingly high vibrational toward which tend. For want of a U = 3R/3v - 1-1; they [exp (/pvT) (6) quencies. Diamond, for example, had better assumption I believe we can set the specific heat follows at once by a specific heat that did not approach for the present the value of the atomic differentiating U with respect to the the Dulong-Petit value until it was heats at absolute zero for all elements to 1.5. Of course it is somewhat heated to over 1000?C, equal temperature. If the specific heat is temperatures unsatisfactory to calculate with such a plotted as a function of temperature, and its specific heat fell off to almost doubtful value; but on the one hand we or rather of (T/f3v), one obtains a a tenth of that value when it was are obliged for the sake of the following curve that rises smoothly and mono- cooled to only -50?C. A test of the calculations to make some assumption, and on the other hand it makes little difference tonically from zero at the origin and theory for other materials, particularly for the following purposes what value approaches the equipartition value, 3R, for the large class that did obey the the atomic heat has between the limits asymptotically when (T/f3v) becomes Dulong-Petit rule, would, however, re- 0 and 2. large. Roughly speaking, the heat ca- quire experiments at low temperature. pacity is negligibly small when (T//3v) Just such experiments were even then This uncertainty in the behavior of is less than 0.1, and has about the being planned and would soon be car- the specific heats at low temperatures equipartition value when (T//3v) is ap- ried out at Berlin, but not for the pur- had to be removed in order to test preciably greater than one. Since light pose of testing Einstein's ideas. the theorem and then to use it freely. atoms would be expected to vibrate at As Nernst pointed out in a paper higher frequencies than heavier ones, read to the Prussian Academy a month other things being equal, this result A New Law of Thermodynamics later (20), it would be enough to fol- already gave a qualitative insight into low the specific heats down to the boil- why the light elements had anomalous- The zero of the absolute temperature ing point of hydrogen, or in many ly low heat capacities at room tem- scale introduced by Kelvin is the only cases only to the boiling point of oxy- perature. temperature with an absolute signifi- gen, in order to observe the limiting The implications of Einstein's spe- cance, but the absolute zero seemed behavior. cific heat equation went much further to have no particular interest for phys- These measurements presented a ma- than these qualitative remarks. Ein- icists prior to 1905. In December of jor experimental problem. Earlier 176 SCIENCE, VOL. 148

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions workers had been content to measure Vibrational Frequency and they departed from the theory average values of the specific heat over only at very low values of the specific wide temperature intervals (21), and One key aspect of the situation was heat, where the theoretical predictions Nernst had to develop new methods in taken up by Frederick Lindemann, were definitely below the measured order to determine the specific heat the young English physicist who was values. at definite temperatures, a particularly Nernst's student and collaborator dur- Nernst described these results in sev- delicate job at low temperatures where ing this period. The single parameter eral papers written early in 1911 the magnitudes are small. It was not in Einstein's equation for the specific (26). He was now thoroughly con- until February 1910 that Nernst be- heat of a solid was the vibrational fre- vinced not only that Einstein's result gan to report his results (22). He and quency; once this was fixed the value was essentially correct, but also that his co-workers had studied a wide of the specific heat was determined its verification was a strong argument variety of elements and compounds for all temperatures. Einstein had al- for the quantum theory that lay behind from room temperature down to liquid ready argued (12) that this vibra- it. He wrote, air temperatures; all had shown a tional frequency must be identical with marked decrease in heat as the optical absorption frequency as de- I believe that nobody who has acquired, specific of a termined the method of "residual by long years practice, reasonably the temperature was lowered. Nernst by reliable sense for the experimental test remarked that "one gets the impres- rays." He had also pointed out that of a theory (never by any means a simple sion that the specific heats are con- not all thermal vibrations are optically- matter) will be able to contemplate these verging to zero as required by Ein- active, since the vibrating particle could results without becoming convinced of the of the stein's This seems to be be a neutral atom rather than a mighty logical power quantum theory." theory, which immediately clarifies all Nernst's first reference to Einstein's charged ion (24). Einstein had not, the essential features. work: he reported qualitative agree- however, given a general way of re- ment with Einstein's equation, and lating the vibrational frequency, which His lecture, "On modern problems announced that his co-workers F. A. determined the thermal behavior, to in thermodynamics," delivered to the Lindemann and A. Magnus were in other measurable properties of the Prussian Academy of Sciences on 26 the process of examining the degree solid. In June 1910 Lindemann sub- January 1911, gave Nernst the op- to which there was also quantitative mitted a paper to the Physikalische portunity to discuss the matter at agreement. Zeitschrift which offered a method of greater length and also to become even Nernst had more to say about this filling this gap (25). His reasoning more eloquent on the subject of the quantitative agreement a month or so was based on a very simple and quantum theory (27). He now de- later when he lectured on his work plausible physical assumption. At the scribed Planck's introduction of the to the French Physical Society (23). melting point of the solid its struc- hypothesis of energy quanta as an in- This time he quoted Einstein's equa- ture is disrupted, and so Lindemann novation in the same class as those tion, described its connection with assumed that the amplitude of atomic due to Newton and to Dalton. The "that old enigma," the Dulong-Petit vibrations at the melting temperature quantum theory, he said, was, to be rule (an especially relevant connection must be some definite fraction of the sure, still only a rule for calculation- to note when lecturing in France), interatomic distance in the crystal. "a very odd rule, one might even say and reported that the data so far ob- This assumption allowed him to ex- a grotesque one"-but it had so proven tained agreed very well with Einstein's press the vibrational frequency simply its fruitfulness in Planck's work on specific heat formula. The support in terms of the melting temperature, radiation and Einstein's on molecular that Einstein's result gave to the new the molecular weight, and the density. mechanics that it was the duty of sci- heat theorem did not escape Nernst's He was led to results that agreed well ence to take it seriously and investi- attention, either. But he admitted free- with optical absorption frequencies gate it from as many sides as pos- ly that Einstein's theory gave to spe- where they had been measured, and sible. cific heat measurements an intrinsic in- also with the frequencies deduced from Nernst did more than declare him- terest that he himself had not been the specific heat data by means of self a supporter of the quantum the- aware of when he planned his experi- Einstein's formula. This work was done ory: he took it seriously enough to mental program. What is most strik- with Nernst's "constant helpful inter- try to apply it to new problems and ing in Nernst's remarks about Ein- est"; Lindemann's results surely served to develop it further. He sketched out stein's work is the glaring omission of in turn to fortify Nernst's growing be- the way in which the quantum theory any reference to the quantum theory. lief in Einstein's work. might account for the old problem of In April 1910 Nernst was obviously The new data that Nernst obtained the specific heats of diatomic gases by convinced of the importance of Ein- on specific heats down to liquid hydro- quantizing the rotational motion, and stein's result, but he was not ready gen temperatures had the same effect. he argued that the basic qualitative yet to accept or at least to comment All the materials measured behaved in features of Einstein's result ought also on the theory that had led to this accordance with theoretical expecta- to apply to the specific heats of liquids. result. tions; even lead, whose specific heat Nernst's best known venture into the This reluctance did not persist much had not fallen more than 10 percent in quantum theory was the paper he longer. Nernst apparently turned his going from room temperature down wrote with Lindemann in July 1911 attention almost immediately to the to liquid air temperature, showed al- offering a revision of Einstein's theory twin problems of extending his mea- most a 50-percent drop in the addi- of specific heats (28). The revision surements to liquid hydrogen tempera- tional 60 degrees of cooling down to was called for because of the discrep- tures and acquiring a full grasp of the liquid hydrogen temperature. Nernst's ancy, already mentioned, between the quantum theory behind the specific experimental curves had the shape and theory and experiment at the lowest heat formula. structure required by Einstein's theory, temperatures. Nernst and Lindemann

9 APRIL 1965 177

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions proposed that Einstein's result for the the elastic constants of a solid and The Solvay Conference molar heat capacity at constant vol- the vibrational frequencies responsible ume, Cv, for optical absorption. Neither Suther- For 5 days the 21 physicists talked. land nor Madelung (31), who had in- Solvay's staff had seen to it that the - 3R(313/T)2 exp (3v/ T) dependently proposed essentially the group was handsomely housed at the [exp (T^/T) ' (7) same idea, discussed the relationship Hotel Metropole, where the meetings also be replaced by the equation between these vibrational frequencies took place; they had no need to and the specific heat, but Einstein concern themselves with anything less 3R exp C -= (O^/T)2 (tvl/T) naturally seized upon this additional weighty than the pressing problems of - ' 2L [exp (v/T) 1]2 relationship. On the basis of an ad- physics. The presiding officer at all exp (8) (fzv/2T) (f3v/2T) 8) mittedly crude model of the interac- sessions was H. A. Lorentz, who need- [exp (,l3v/2T) - 1]2 J tions within the solid, Einstein could ed all his brilliant insight, encyclopedic The predictions of this new specific calculate the vibrational frequency knowledge, and linguistic fluency to heat formula did not differ qualitative- from the compressibility and other keep the discussions focused and to ly from Einstein's, but the Nernst- data. The agreement, for the one case keep the participants in real contact Lindemann formula accounted for the where Nernst's specific heat data per- with each other. The formal papers data in a much more satisfactory way, mitted Einstein to compare the fre- ranged from James Jeans's attempt to without the introduction of any new quency determined from his own spe- explain all of the apparent failures of parameters. cific heat equation, was "really sur- the classical theory without any re- While Nernst and Lindemann origi- prising." course to the ideas of quanta to Ein- nally arrived at their result empirically, In the second of these two papers stein's arguments for the absolute in- they attempted to give it a theoreti- (32) Einstein emphasized that his the- evitability of the quantum structure of cal significance by associating the term ory could not be expected to account radiation. Discussion of the papers was apparently containing "half-quanta" fully for the measured specific heats intense and often very pointed. Poin- with the potential energy, and the term because in reality the vibrations in a care dismissed Jeans's attempts with in "whole quanta" with the kinetic crystal were not monochromatic, as he the remark: "That is not the role of energy of the vibrating atoms in the had originally assumed for the sake physical theories. They ought not in- crystal. The details need not concern of simplicity. He attempted to do troduce as many arbitrary constants as us here, but it is quite clear that something with a model of interacting there are phenomena to be ex- Nernst now looked upon himself as atoms, taking into account the rapid plained" (1, p. 77). Einstein com- something of a quantum theorist. transfer of vibrational energy from one plained that Planck's use of the Boltz- atom to its neighbors, but he could mann relation was "a bit shocking," not bring this to any positive result. and that his way of proceeding de- A Review of the Problem While he was "tormenting himself" prived the relation of any physical con- with this calculation, he received from tent (1, p. 115). 13y this time, the summer of 1911, Nernst the proof sheets of the first One thing this first Solvay Congress the invitations to the Solvay Congress report on the Nernst-Lindemann form- certainly did accomplish was to sharp, had been received and, for the most ula (33). Einstein immediately recog- en the issues. Planck's fear that hardly part, accepted. Einstein, in Prague, nized this as a valuable empirical equa- anyone would feel the "intolerability" was preparing his review on "The cur- tion, but he was evidently unconvinced of the unresolved problems could now rent status of the problem of specific by the theoretical foundations that the be dismissed. At the final session in heats" (7, pp. 407-435). He had not authors had proposed for it. Instead Brussels such a thoughtful observer as devoted any large fraction of his ef- Einstein interpreted the Nernst-Linde- Marcel Brillouin expressed his own forts to this problem in the 4/2 years mann formula in line with his own conclusions, granting that they might since his first paper on the subject view that there was a whole spectrum seem "pretty timid" to the younger had been written. Having once estab- of vibrational frequencies in the solid: and bolder spirits present: "It seems lished the basic point, the necessity of Nernst and Lindemann had, in effect, certain that from now on we will have applying the quantum hypothesis to the assumed a very simple form for this to introduce into our physical and vibrational motions in solids, he had spectrum, with equal numbers of vibra- chemical ideas a discontinuity, some- turned his attention back to matters tions at only two frequencies, 1v and thing that changes in jumps, of which he considered more fundamental-the v/2. Einstein was sure that the true we had no notion at all a few years quantum structure of radiation and the spectrum was more complex, even ago" (1, p. 451). And Langevin re- deepening implications of his relativity though he could not see how to de- marked that the power of the quantum theory. Einstein saw no likelihood that termine it (34). theory to discover totally unexpected the theory of the specific heat of The divergent views held by Nernst relationships among phenomena as ap- solids would point the way toward and Einstein on the significance of the parently distinct as optical absorption the new foundations that physicists Nernst-Lindemann formula were aired frequencies and specific heats had to would have to construct for their at the congress in Brussels, where both be acknowledged. science. men discussed the subject of specific The indirect effects of such a meet- He did not, however, ignore the sub- heats. But this difference of opinion ing are incalculable. How significant ject completely, but returned to it in between two leading proponents of the was it, for example, that Niels Bohr two papers published early in 1911. quantum theory was very minor com- heard a first-hand and enthusiastic ac- In the first of these (29) he followed pared to the fundamental disagree- count of the proceedings from Ernest up a connection, originally suggested ments that were expressed and dis- Rutherford when Bohr visited him in by William Sutherland (30), between cussed at Brussels. Manchester a few weeks after Ruther-

178 SCIENCE, VOL. 148

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions ford's return from Brussels? (35). We I got on very well with all the people ideas on the structure of radiation at do know that the 19-year-old Louis here, even with Mme. Curie who is quite that date (38). After a brief descrip- a good sort when one knows her. I got on de whose older brother Mau- tion of the special theory of relativity Broglie, very well with Einstein who made the rice de Broglie was one of the scientific most impression on me except perhaps the report went on in this vein: secretaries of the Congress, read the Lorentz .... He says he knows very little Fundamental as this idea of Einstein's discussions as the manuscript was be- mathematics, but he seems to have had [relativity] has proved to be for the de- a success with them. ing prepared for publication. "With all great (37) velopment of physical principles, its ap- the ardor of my youth," he has writ- plications are, for the present, still close to the limits of the measurable. His study ten, "I was en- A year and a half after the first swept away by my of other questions which are now at the thusiasm for the problems discussed Solvay Congress the four physicists center of interest has proved to be much and I resolved to devote all my ef- from Berlin who had attended- more significant for practical physics. forts to understanding the true nature Planck, Nernst, Rubens, and Warburg Thus, he was the very first to show the of the mysterious quanta that Max -joined forces to recommend that the importance of the quantum hypothesis for the energy of atoms and molecular mo- Planck had introduced ten years Prussian Academy of Sciences take an tions by his deduction of a formula for earlier" (36). unusual step. They proposed that the the specific heats of solids from this hypo- There is no doubt about the enor- Academy elect to full membership and thesis. Although this formula has not mous impression that Einstein made award a research professorship to Al- been confirmed in full detail, it neverthe- less suggested the foundations on his at Brussels. Frederick bert Einstein, only 34 years old at correctly colleagues for the further development of the new Lindemann, who accompanied Nernst the time. The document in which they kinetic-atomic theory. He has also related to Brussels as a scientific secretary to set forth their reasons, properly de- the quantum hypothesis to the photoelec- the Congress, wrote home to his father scribed by Theo Kahan as being "of tric and photochemical effects by establish- which the day after the meeting (37). Linde- unusual interest for the history of mod- ing new and interesting relationships can be checked experimentally, and he mann, the future Viscount Cherwell ern ideas" in science, shows clearly was one of the first to point out the and scientific adviser to Winston that it was Einstein's work on the close connections between the elastic con- Churchill, was still a very impression- quantum theory of matter, and on spe- stants and the optical properties of crystals. able young man. He described Sol- cific heats in particular, in addition to In sum, one can say that there is one for as "a nice the of that in- hardly among the great problems, vay, example, very theory relativity, proved in which modern physics is so rich, to man, unfortunately though with rather fluential, and also shows what even which Einstein has not made some re- liberal views." He went on to write: this eminent group still thought of his markable contribution. That he may some-

Photograph by Benjamin Couprie, Brussels, courtesy of Solvay et Cie., Brussels.

Participants at the first Solvay Conference, 1911. Seated, left to right: Nernst, Brillouin, Solvay, Lorentz, Warburg, Perrin, Wien, Mme. Curie, Poincare. Standing: Goldschmidt, Planck, Rubens, Sommerfeld, Lindemann, De Broglie, Knudsen, Hasenohrl, Hostelet, Herzen, Jeans, Rutherford, Kamerlingh Onnes, Einstein, Langevin. 9 APRIL 1965 179

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions times have missed the target in his M. Planck, Forlesungen iiber die 7heorie der his paper (12), changing his prediction to speculations, as, for example, in his Wiirmestrahlung (Barth, Leipzig, 1906), pp. the statement that either diamond will ab- 163, 220. As a matter of fact, Planck rec- sorb at 11 microns or it will have cannot no ab- hypothesis of light quanta, really ognized the constant h as a fundamental sorption peak in the infrared, thus allowing be held too much against him, for it is natural constant even before he had intro- for the possibility that the vibrations are not possible to introduce really new ideas, duced the idea of energy quanta, at a time due to neutral atoms. See A. Einstein, Attnn. when h was simply a particular combina- even in the most exact sciences, without Physik 22, 800 (1907). tion of the constants in the Wien distribu- 25. F. A. Lindemann, Physik. Z. 11, 609 (1910). sometimes taking a risk. tion law. See M. Planck, Ann. Physik 1, Preiss. Akad. Wiss. Ber- 120 I thank 26. W. Nernst, Sitzber. (1900); Dr. Joseph Agassi, who Z. Elek- first pointed this out to me. lin, Kl. Math. Phys. 1911, p. 306; References and Notes trochemn. 17, 265 (1911). The quotation is 14. P. Ehrenfest, Antn. Physik 36, 91 (1911). from p. 275 of the latter paper. 1. The proceedings of the first Solvay 15. See, for example, W. Nernst, Theoretische this, 27. W. Nernst, Sitzber. Preuss. Akad. Wiss. Ber- Congress on Physics, were published under Chemie (Enke, Stuttgart, ed. 3, 1900), p. lin, Ki. Math. Phys. 1911, 65 The the editorship of P. Langevin and M. de 175. (1911). quotation is from p. 86. La Thleorie du Rayonnement et les 16. J. W. Strutt, Lord Rayleigh, Phil. Mag. 49, Broglie, F. A. Z. Elek- Quanta (Gauthier-Villars, Paris, 1912). 98 (1900). Rayleigh's remark is quoted by 28. W. Nernst and Lindematin, trochetm. 817 2. This letter is quoted in full in an unpub- Kelvin in his famous lecture "Nineteenth 17, (1911). 29. A. Annt. 170 (1911). lished manuscript by J. Pelseneer, "Historique century clouds over the dynamical theory of Einstein, Physik 34, des Instituts Internationaux de Physique et heat and light," in W. Thomson, Lord Kel- 30. WV.Sutherland, Phil. Mag. 20, 657 (1910). de Chimie Solvay." I should like to thank vin, Baltimore Lectures (Clay, London, 1904), 31. E. Madelung, Physik. Z. 11, 898 (1910). John Heilbron of the project, "Sources for p. 527. 32. A. Einstein, Ann. Physik 35, 679 (1911). History of Quantum Physics," for the loan 17. Optical absorption frequencies were cldeter- 33. W. Nernst and F. A. Lindemann, Sitzber. of this manuscript, and Prof. Pelseneer for mined by the method of "residual rays" de- Preuss. Akad. Wiss. Berlin, KI. Math. Phys. permission to quote from it. veloped by H. Rubens. See, for example, 1911, p. 494. 3. Solvay's letter and Nernst's original German 0. W. Richardson, The Electrotl Theory of 34. The detailed theory of the spectrum was idraft are to be found in the Lorentz Col- Matter (Cambridge Univ. Press, Cam- begun by M. Born and T. von Karman, lection at the Algemeen Rijksarchief in the bridge, 1914), p. 157. Physik. Z. 13, 297 (1912), and almost simul- Wiss. Geittin- Hague. 18. W. Nernst, Nachr. Kgl. Ges. taneously an eminently successful approxi- Kl. 1. For a 4. M. Planck, Verhandl. Deut. Physik. Ges. 2, getn, Math. Phys. 1906, p. mate theory was given by P. Debye, Aisnn. review of Nernst's work see F. Simon's 789 Both refer 237 (1900). See M. J. Klein, Arch. Hist. Physik 39, (1912). papers Guthrie Lecture in Yearbook of the Physical Exact Sci. 1, 459 (1962), for a detailed dis- to Einstein's two articles of 1911. London 1. cussion and bibliography. Society of 19556, p. 35. N. Bohr, Essays 1958-1962 otn Atoomic and Chemistry 5. M. Planck, Ann. Physik 31, 758 19. W. Nernst, Thermodynamics Physics anid Hzttuman Knoswledge (Interscience, (1910). Univ. New Haven, 1913), pp. 6. See M. Planck, Scientific Autobiography (Yale Press, New York, 1963), pp. 31, 83. New York, 63-64. 36. L. de Broglie, Physicien et Peniseur (Edi- (Philosophical Library, 1949). W. Sitzber. Preluss. Akad. Wiss. Ber- 7. Quoted by J. Pelseneer 20. Nernst, tions Albin Michel, Paris, 1953), p. 458; (2). Kl. Math. Phys. 1906, 933. 8. A. Z. 10, 185, 817 (1909); lin, p. see also p. 425 for Maurice de Broglie's Einstein, Physik. 21. See, for example, J. Dewar, Proc. Roy. Soc. see also L. Rosenfeld, Osiris 2, 149 (1936). comments, as well as M. de Broglie. Les Lotidon Ser. A 76, 330 (1905). The new Premiers de 9. F. Reiche, The Quantumi Theory (Dutton, at Nernst's Congres Physique Sol'ay (Edi- technioue was developed sugges- tions Albin Michel, Paris, 1951). New York. 1922). tion A. Eucken, Physik. Z. 10, 586 (1909). by 37. F. W. F. Smith, Earl of Birkenhead, The 10. A. Einstein, Annt. Physik 17, 132 (1905); 22. W. Sitzber. Preutss. Akad. Wiss. Ber- Nernst, and the Primne Minister see also M. J. Klein, in The Natural Philoso- Kl. Math. see Professor (Houghton lin, Phys. 1910, p. 262; par- 43. pher, D. Gershenson and D. Greenberg, ticularly pp. 276 and 282. Mifflin, Boston, 1962), p. Hist. Sci. Eds. (Blaisdell, New York, 1963), vol. 2, 23. W. Nernst, J. Phys. Theor. Appl. 9, 721 38. T. Kahan, Arch. Intern. 15, 337 p. 57. (1910). (1962). Kahan quotes the German text and 11. For a detailed analysis see M. J. Klein, in 24. Actually Einstein originally thought that gives a French translation. An English ver- The Natural Philosopher, D. Gershenson and only the vibrations of positive ions were in- sion is included in C. Seelig, Albert Einstein D. Greenberg, Eds. (Blaisdell, New York, volved, and on this basis predicted that (Staples, London, 1956), pp. 144-146. 1964), vol. 3, p. 1. diamond should have an absorption peak at 39. This work was supported in part by the 12. A. Einstein, Ann. Physik 22, 180 (1907). 11 microns. He recognized his error several National Carbon Company, a division of 13. M. Planck, Antn. Physik 4, 564 (1901); months later and published a correction to Union Carbide Corporation.

one or more straits of some size between North and South America, we are uncertain as to the number of straits, their location, and the time of their existence. It is almost certain that Miocene Mammals and there were straits across the Isthmus of Panama (3), and the distribution Central American of Tertiary marine deposits indicates Seaways a major seaway in northwestern Co- lombia, the Bolivar Trough (Fig. 1). Fauna of the Canal Zone indicates separation of Thus, the separation of North from South America did not depend on the Central and South America during most of the Tertiary. opening of a single strait. In Central America as a whole, however, the distribution of land and water during Ter- Frank C. Whitmore, Jr., and Robert H. Stewart tiary time can be only approximately delineated, because geologic observa- tions, as well as fossil finds, are relatively few and scattered .over a large The fossil mammal faunas of North the geology of this large area, makes tropical region where there are few and South America indicate that the reconstruction of the Tertiary zooge- rock outcrops. A difficulty that faces two continents were separated from ography of the region between the con- the paleogeographer studying the isth- Paleocene or earlier time until the late tinents an exercise involving consider- mian portion of Central America is Pliocene (1, 2). Unfortunately our al- able speculation. While the differences most complete ignorance of the Terti- between the faunas of the two con- Mr. Whitmore is a paleontologist on the staff from and of the U.S. Geological Survey, Washington, D.C. ary land mammals of Central America, tinents, resulting complete Mr. Stewart is a geologist with the Panama together with incomplete knowledge of long separation, prove the existence of Canal Company, Balboa, Canal Zone.

180 SCIENCE, VOL. 148

This content downloaded from 128.103.149.52 on Fri, 2 Aug 2013 11:35:45 AM All use subject to JSTOR Terms and Conditions