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EinsteindeHaas - On the history of the Einstein—de Haas...

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Unformatted text preview: On the history of the Einstein—de Haas effect '. helpsi v i Einstei V. Ya. Frenkel’ i Elect“ . . . . . ; paper < A. F. [rifle Phystcotechmcal Instztute of the Academy of Scrences of the USSR, Leningrad , they ha Usp. Fiz. Nauk 128, 545—557 (July 1979) The far This article contains information on Einstein’s experimental work. It pays main attention to three of his 15 signifit studies (1915-1916) aimed at experimental demonstration of Ampere molecular currents. It treats the an expt content of these studies, their prehistory, and the peculiar reevaluation of their results after the discovery ' f publica of the spin of the electron. 1t traces the effect of these studies on Einstein’s attitude toward the Stern- change Gerlach experiments and the studies of Uhlenbeck and Goudsmit, and also points out their genetic tie below. with the well-known work of Einstein and Ehrenfest. i PACS numbers: 01.65. + g, 01.60. + q, 03.65.32 ,_ Einsi papers Germa first pl CONTENTS alone. 1. Introduction .................................................................. 580 Natum 2. Einstein’s first publications on molecular currents ..................................... 580 ad dem 3. Einstein’s second paper ......................................................... 582 g mam c 4. Einstein’s views on his studies on Ampere currents .................................... 583 simple 5. Prehistory of Einstein’s studies .................................................... 584. ; tion of 6. Further studies ................................................................ 585 ’ 9 study 1 7. Electronspin.Closingremarks...................................... ............. 586 star-tin References ...................................................................... 587 " Langey of Am; ‘ 1820,i netic fl‘ . It becal 1, INTRODUCTION years later, Einstein together with Ehrenfest “daily _ netic fj _ . K [became absorbed] for many hours in one experimental ; of a ce The studies to demonstrate the existence Of Ampere study” (as Ehrenfest wrote to A. F. Ioffe5) in trying to :' netizec molecular currents, Whmh this article tahes as Its establish the existence of an effect that Einstein had ‘ electri topic, are the major but far from sole ev1dence of - , . . . . . predicted. wrote Einstein’s concern w1th experimental studies. The f for a :1 opinion current among many physicists that Einstein : . himself never “worked with his hands” but delegated There is an article of the experimentalist Einstein % 9‘5er performance of the appropriate experiments to his co- that he wrote jointly With his friend, the PhYSiCiah held S, authors or assistants is erroneous and lacking in any H- Miihsam. This was a short and elegant study on a curren real basis—we shall confirm this assessment by direct method of determing dimensions of channels in filters.6 T curren citation of his studies. Along this line, the appendix It describes an idea for an instrument for measuring . to his early (1902) article is noteworthy. It was con- the largest dimension 0f particles that can pass ‘2 . APOt' cerned with the thermodynamic theory of the potential through a given filter and an experimental test of m ”.58 difference between metals and solutions of their salts, this idea. out m ‘ and an electrical method of studying molecular forces theory was developed on its basis. Einstein writes, “I wish to I (“£th excuse myself in closing for proposing here only an 2- EINSTEINIS FIRST PUBLICATIONS ON equatu overall plan for the laborious experiments while per— MOLECULAR CURRENTS g Whlle I sonally not involved in experimentation. Yet this paPe_1‘ Having confined ourselves to these cursory remarks, L $021210: will still reach its aim If someone involves himself'With we shall now proceed to treat a series of papers of not ac experimental. St‘def’f molecular forces upon becoming Einstein of 1915—1916 on Ampere currents. These not ret acqualnted w1th lt' papers, which were written in part with W. de Haas of ator. (1878—1960) as coauthor, are concerned with theo- _ argum Further it is worth recalling that, upon proposing in retical study and experimental demonstration of the ‘i dynam 1908 a new principle for measuring small amounts of now well-known phenomenon that has become called the ; radiatj electricity,2 Einstein took part in studies to design the Einstein—dc Haas effect. As we see it, they deserve a statior appropriate instrument, which was described in an ar- special treatment for a whole set of reasons. First, “inade ticle by the brothers P. and C. Habicht, his Swiss they played a large role in studies of the magnetic pro- ' friends. They especially recall in their paper3 Ein— perties of substances and atoms, practically up to the —— stein’s participation in the studies to build and test this discovery of the methods of EPR and ferromagnetic , instrument. In 1921 Einstein spent much time on ex— resonance. Second, these are precisely the studies in *2 ”As we periment with canal rays; he performed the corres- which Einstein appears for the first time as the author g; espec; ponding experiments jointly with H. Geiger.‘I Three of experimental investigations. Third, a study of them and in 580 Sov. Phys. Usp. 22(7), July 1979 0038-5670/79/070580-08$01.10 © 1980 American Institute of Physics 580 581 st “daily (perimental n trying to :tein had Einstein 'sician tudy on a : in filters.6 ' measuring n pass l test of y remarks, pers of These ie Haas a theo- n of the 3 called the deserve a . First, gnetic pro- ' up to the iagnetic studies in the author ldy of them (sics 580 helps in understanding the lively interest with which Einstein reacted to the discovery of the spin of the electron and participated in the discussions about the paper of Unlenbeck and Goudsmit. Finally and fourth, they have an interesting and rather long prehistory. The fact is paradoxial (in the face of the mentioned significance of these studies) that their result involved an experimental error, and in several years after their publication, their treatment had undergone a substantial change. We shall pay special attention to this problem. below. i Einstein and de Haas presented the discussed set of papers on Feb. 19, 1915 in Berlin at a meeting of the German Physical Society chaired by H. Rubens. The first publication of this set was signed by Einstein alone. It was printed in the May issue of the journal Natumissenschafien in 1915 with the title "Experiment- al demonstration of Ampere molecular currents”." Its a main content amounts to an unusually graphic and simple theoretical treatment of the problem; a descrip- tion of the fundamental scheme for its experimental study is a small appendix to the‘ main part of the article. Starting with the studies on magnetism of P. Curie, Langevin, and Weiss, Einstein recalls the hypothesis of Ampere that the French scientist had formulated in 1820, immediately after Oersted had shown that a mag— netic field arises around a conductor bearing a current. It became clear after Oersted had shown that a mag- netic field appears not only as a certain inner property of a certain class of solids when permanently mag- netized, but it also arises under the influence of an electric current. “This state of affairs,” Einstein wrote, “must seem unsatisfactory to physicists striving I for a unitary understanding of nature?” cisely why Ampere had proposed that the magnetic field surrounding a magnetic object is caused by currents flowing in the molecules, or molecular currents. This is pre- t Another remark of general nature that Einstein made r in his article" cannot help but arouse attention. He points out in a footnote to the text of his paper, “Ampére’s theory in its modern, electronic form also faces the difficulty that, according to Maxwell’s electromagnetic equations, the electrons should lose energy by radiation while performing their circular motion, so that the ' molecules or atoms should lose their magnetic moment in time or have already lost it, which of course does I) not actually happen.” Amazingly, here Einstein does not recall Bohr: the classical paper “On the structure of atoms and molecules” directly begins with general arguments about the “inadequacy of classical electro- dynamics” and contains a postulate on the absence of ' radiation loses in the revolution of an electron in a ' stationary orbit about the nucleus to resolve this I “inadequacy.” f l 1’As we know, Einstein presented an analogous argument with especial force in connection with the equality of gravitational and inertial mass that Eotvos had discovered. 581 Sov. Phys. Usp. 22(7), July 1979 The joint paper of Einstein and de Haas9 also contained a rather extensive theoretical part, partially repeating material of Ref. 7. We note some new, curious argu- ments expressed in it “against” Ampére’s hypothesis. The authors stress that the concept of currents flowing without resistance has aroused doubts as to the validity of the hypothesis of molecular currents even in the pre-Maxwell period. Maxwell’s theory added a new difficulty to this: an electron moving in a circular or— bit should continuously emit. Finally, a complication has arisen in the 20th century: the existence of a mag- netic moment of the molecule as T-o 0 means that the “energy of circular motion must be the so—called zero- point energy—a concept that arouses a quite under- standable resistance in many physicists.”9 This is the fundamental importance of Eq. (1) (see below) and the concepts associated with it. The authors also point out that the experiment that they proposed enables an ac- curate determination of the ratio of the charge of an electron to its mass.” In closing the theoretical part he points out that also the rotation of a magnetic object alters its magnetic state, and this can in principle also be employed to test Ampére’s hypothesis (though, as he points out, this test is more complex experimentally). And yet another remark, now of a “geomagnetic” character: a corresponding effect can be employed to explain the phenomenon of terrestrial magnetism: it is not fortuit- ous that the axis of rotation of the Earth and its mag- netic axis approximately coincide. Before proceeding to present the essence of the study, Einstein writes, “In the past three months I have performed (my italics—V. F.) experiments jointly with de Haas—Lorentz in the Imperial Physicotechni- cal Institute that have firmly established the existence of Ampere molecular currents.” The design of the experiments is based on the follow— ing simple “argument,” as the author called it. An electron moves uniformly in a circle of radius r at the velocity v=21rrn, where n is the number of revolutions per second. This means that the angular momentum here is Mmh=mvr =2m1rrzn (m is the electron mass). On the other hand, according to Ampere, the magnetic moment Mmagnof a loop having the current i=en, where e is the charge of the electron, is mefiennrz. Hence, upon converting to vector notation we get Mmech: 2_’” MM“: 9.31m“: _1.13. 10-7Mm,g,.. (1) Einstein considered it obvious that the magnetic mo- ment is determined by the rotation of the electron, so that the vectors Mme}. and MM,“ lie in opposite direc- tions. Equation (1) is generalized to the case of an 2”I‘he stated remark is very characteristic of Einstein: in two papers in 1905 [on the quantum theory of radiation and on methods of determining the dimensions of molecules (Brownian movement)] he stresses the importance of the fact that the theory that he had developed offers a new method of deter— mining Avogadro’s number. V. Ya. Frenkel' 581 , iffykfitpékb‘e‘uwna ensemble of “loops” bearing a current. Here the left— hand side will contain the total angular momentum of the object, and the right-hand side the total magnetic moment. Einstein makes the simple remark that the total angular momentum of the object should remain constant in the absence of external rotational moments. Hence a change in the magnetization of the object, which entails a change in the corresponding “electronic” component of its angular momentum, must be compen— sated. This compensation is carried out by transfer of angular momentum of the electrons to the solid (rod) as a whole: when its magnetization is changed it must begin to rotate. Figure 1 reproduces the diagram of the experiment that Einstein proposed. The iron rod S is suspended by a thin filament coaxially inside a solenoid supplied with current. A change in the direction of the current alters the magnetization of the rod, and consequently causes it to rotate. By fastening a small mirror to the rod, one can register the studied rotation by observing a light beam reflected from it onto a scale. The article closes by describing an important experi— mental detail: the winding of the solenoid was supplied with alternating current whose frequency coincided with the intrinsic frequency of torsional oscillations of the rod, and also it was stated that application of this resonance method made it possible to overcome experi- mental difficulties and to confirm quantitatively Eq. (1) given above. The article,9 which contained a detailed description of the experiment, and which was submitted to Verhandlun- gen on Apr. 19, 1915, was signed by Einstein and de Haas. Hence we see that the first article was intended to emphasize that the idea of the entire study as a whole and the corresponding experiments belonged to Einstein, while both authors took part in developing the appara- tus for carrying out the experiments themselves. This circumstance, in addition to the reference cited above from Ref. '7, is confirmed by two facts. First, Ref. 10, which de Haas published alone on the same topic as Ref. 9, called the corresponding effect the “Einstein effect”— it kept this name for some time in the German litera- ture (before it received its present name of the “Ein- stein—de Haas effect”). Second, in 1916 Einstein pub- lished an independent article that dealt only with the experimental side of the topic under discussion (see below). ‘ The paper of Einstein and de Haas describes and discusses the features of their experimental setup (Fig. 2), which was a realization of the model of Fig. 1 that was proposed in Ref. 7, and they also analyze the FIG. 1. FIG. 2. sources of possible errors and ways to overcome them. ' 1;. The authors write down and solve the equation for the E: torsional oscillations of the soft-iron rod S, undergoing E the test, and interrelate the measurable quantities via 1! the constant A =2m/e, which they propose as the quan- tity being sought, or more exactly, the one to be veri- fied, since the specific charge of the electron had been measured by that time with sufficient accuracy. When the rod is remagnetized, it begins to undergo torsional 3 oscillations. The experiments measured the amplitude i a of the angular oscillations (determined by the deflec- g tion of a light ray directed onto the mirror attached to the rod S and reflected by this mirror onto a scale 145 cm away) as a function of the frequency a.» of the curren supplying the winding of the coil inside which the rod was placed. The amplitude reaches its maximum 0: at the point of resonance when w coincides with the intrinsic frequency mm of the torsional oscillations. It g turns out as a result that " 2 0 h2 =Tm=n27amaxAm]//1_bz. (2) ~ 9:31 eat-Wm": Here we have b=oz/am.x, Aw=wm —w, Q is the moment of inertia of the rod, and J is its total magnetization. Thus, we see that if we take the resonance curve and measure Q and J, we can then determine A. It proved from Einstein and de Haas’s measurements to be 1.11 x10‘7, “in good agreement with the theoretical values of 1.13x10'7. Indeed, add the authors, “this agree- ment might be fortuitous, since we must ascribe an accuracy of about 10% to our measurements; neverthe- less we have shown that the result of circular motion of the electrons described at the beginning of our article is quantitatively confirmed by experiment, at least approximately.”9 i, E F f i- 3,, g, 5*. g g 3. EINSTEIN’S SECOND PAPER Almost exactly a year after the first report on experi- ”I ments involving Ampere currents, on Feb. 25, 1916, Einstein gave a paper at a session of the same German g Physical Society (this time only in his own name) with the title: “A simple experiment to demonstrate Ampere _ ' molecular currents.” As Einstein saw it, the stated . experiment might serve as a lecture demonstration of S? the treated phenomenon: a visible demonstration of the } microscopic properties of matter always impresses! V. Ya. Frenkel' 532 -. for is a a ca the is a Ear ture stuc thec on t Whi< pen: mus gre: in 0 met (not to b it, 1 star qua: that fing come them. tion for the undergoing ntities via the quan- ,o be veri— n had been cy. When 3 torsional amplitude the deflec- ttached to scale 145 the current . the rod mum at ith the lations. It (2) he moment tization. irve and it proved o be 1.11 al values agree— ribe an neverthe- r motion our nent, at on experi- i, 1916, e German me) with Lte Ampere ! stated ration of tion of the ressesl .el' 582 The difficulty of the prior experiments consisted in isolating the relatively weak gyromagnetic effect against the background of the purely magnetic forces acting on the studied rod (cf. Figs. 1 and 2). In order to avoid this difficulty, in the variant of the experiment pro- posed by Einstein, the magnetic field of the coil acts on the iron rod (10 cm long and 0.14 cm in diameter) for a very short time of the order of a millisecond. This is achieved by using a simple discharge circuit in which a capacitor and a quenching resistance are connected to the coils. As usual, an essential part of the apparatus is a device to compensate the magnetic field of the Earth. As investigations showed, for a successful lec; ture demonstration one must carefully center the studied rod. Remarkable in the words of the great theoretician of modern time are the following comments on the point of suspension of the quartz filament to which this rod was attached: “A sufficiently exact sus— pension of the rod by its center (the point of suspension must lie on its principal axis of inertia.—V.F.) faced great difficulties. The aid of Mr. Eger kindly helped me in overcoming them. Ultimately the following amusing method led to the goal. The rod is clamped vertically (not firmly!) on a stand so that the end from which it is to be suspended is inverted downward. Vertically below it, also in an inverted position, one attaches to the stand respectively a cork with a copper pin and the quartz filament. Here the height is carefully chosen so that the quartz filament when raised upward (with a wet finger) in a straight line doesn’t quite touch the flat end of the rod (see Fig. 3——V.F.). Using a gas burner made of a drawn-out glass tube, one heats the end of S with a small flame until a piece of rosin raised from below on the finger will stick to it. The rosin melts and forms a completely symmetrical drop under the action of capil— lary forces. If now one brings the quartz filament into it from below, it is wetted by the rosin and drawn by capillary forces as far as possible into the interior of the drop. This means that it is automatically centered. Now one needs only to cool the rod and the suspension is ready.“1 It is worth pointing out in conclusion that Einstein notes at the end of his article the coincidence of the order of magnitude of the effect with the theoreti— cal prediction, as well as its correct sign [see Eq. (1)]. 4. EINSTEIN’S VIEWS ON HIS STUDIES ON AMPERE CURRENTS Before we proceed it is appropriate to trace out how Einstein evaluated the discussed studies on molecular currents. It is quite remarkable that he performed FIG. 3. 583 Sov. Phys. Usp. 22(7), July 1979 these studies simultaneously with intensive investiga- tions on the general theory of relativity. Perhaps in dicussing and performing th...
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