The golden jubilee of the Dutch Physical Society in April 1971was concluded with a lecture by Samuel Goudsmit on the history of thediscovery of the electron spin. Actually, his could hardly be calleda polished lecture; it was a grandiose artistic performance, full ofwit and emotional involvement. Goudsmit, then at the end of hisscientific career, gave a very personal account of how chance and theguidance by Ehrenfest, their far-sighted supervisor, led him andUhlenbeck to formulate their remarkable discovery. When, in connectionwith the present book , the questionturned up how to discuss the early history of electron spin, mythoughts returned to that day, nearly twenty five years ago, when Ihad been impressed by Goudsmit's truly humane wisdom. After weighingvarious alternatives I thought: why not let the master speak forhimself? Thus I came to translate Goudsmit's historic lecture. Itstext was not meant to be published as a paper, but Goudsmitsubsequently consented to its publication from a tape recording. Apart from a few minor changes I have triedto present Goudsmit's very personal style by giving a literaltranslation of the words spoken in Dutch. A number of references tothe papers mentioned by Goudsmit have been added.
J.H. van der Waals
Goudsmit delivering his lecture in 1971.
Today I will talk a little about history. The history of thediscovery of the electron spin by George Uhlenbeck and myself. Thatis tricky; I don't like the history of physics, I have always beenagainst the way in which the historians wrote about it in earlierdays. Nowadays it is better; someone like Martin Klein, that is real,he brings something new. But the earlier historians always describedphysics as if it had been done by three or four people and theyforgot that these famous people could only do their work because ofthe many others who also made contributions. They can't help it sincethat is the way they have learnt it from the ordinary historians. Youhear about a man like Hitler .... and they forget the millions wholent him the necessary support.
Then, today, there are other people who are interested and theyare the psychologists. They want to know why you became a physicist,why you did all you have done, and start to interrogate you aboutthat. They want to know about your family, hoping that yourgrandfather was a great chemist or a great mathematician, and thenthey are always terribly disappointed when they come to me. Because,when I first registered as a student in Leiden the Beadle said: "TheRector would like to see you a moment". He took me to that room withall those portraits of famous people and there, next to the portraitof Hugo de Groot, hung a large painting of a famous jurist. "Here",he says, "is your grandfather", I reply: "I have never heard of thisman". The great jurist's name being Goudsmit, my reply made himangry. Actually, with my own family the psychologists could donothing. My grandfather was a tourist guide in Hotel des Indes in theHague, my mother had a millinery, and my father a wholesale businessin seats ...... for water closets.
What the historians forget - and also the physicists - is that inthe discoveries in physics chance, luck plays a very, very greatrole. Of course, we do not always recognize this. If someone is richthen he says "Yes, I have been clever, that is why I am rich"! Andthe same is being said of some one who does something in physics"yes, a really clever guy.....". Admittedly, there are cases likeHeisenberg, Dirac and Einstein, there are some exceptions. But formost of us luck plays a very important role and that should not beforgotten.
And this is relevant because, when I went to Leiden, I ended upwith Ehrenfest. Ehrenfest's classes were small and one had a verygood interaction with one's professor. And Ehrenfest was alwaysworried when we interrupted our classes when we had to go somewhere.Once I had to accompany my father to Germany, because of hisbusiness, and then Ehrenfest said: "Do you again have to interruptyour classes?" But my father could not travel alone. Then he asked:"Where are you going?" When I told him, he said: "Nearby is auniversity and there is a spectroscopist, Paschen. You are interestedin spectroscopy (I had become interested in it through my high-schoolteacher Lohuizen), go and have a look". That was important; I havedone it. I went to visit Paschen, who did not treat me as a studentbut as a colleague. And he showed me the experimental set up which hehad for the study of the spectral line of ionised helium, whichentirely confirmed Sommerfeld's relativistic electron orbits. I didnot understand a bit of it. But, I think, I managed to hide my lackof understanding and after my return to Leiden I have nicely studiedall this. One of the things which stuck to me is that in Paschen'sexperiments on the helium line, its fine stucture and therelativistic explanation, there was a forbidden component which wasobviously present. The following summer I was sent for a stay toPaschen, and Paschen and Back have taught me the techniques ofspectroscopy. And when I talked to the theoreticians about thatforbidden component ......... but you know how theoreticians are...... they then say: "Poor experiments". That forbidden line alreadywas an important milestone. I shall recount a few more of thesemilestones.
If I talk in the first person, then there are two reasons. First:lack of modesty, and second: as I tell that history, I can only speakabout my own experiences. You know, when Uhlenbeck tells the historyof spin then he tells a different story. I don't think either of uslies. But if someone is lying then it is a little more I than he.
I was interested in spectral lines and the first thing I did ....I found a formula for the doublets in the spectra, claiming that itwas exactly the same formula as used by Sommerfeld for the X-raydoublets. And I told this to Ehrenfest. At that stage it was allwrong but Ehrenfest never discouraged anyone and said: "That's nice,we'll publish it". And there was a short little piece in"Naturwissenschaften" and a very lengthy article in "ArchivesNéerlandaises des Sciences exactes et naturelles", which waspublished in Holland in french to be sure that nobody would read it.Of course, as a young student I was very proud of it.
Now, what happened? Two and a half years later exactly the samework was done, the very same formula, by Millikan in America, andKoster gave a seminar about it in Leiden. Of course he did not knowthat I had already done so. At the end of the seminar I said: "I havespoken about the very same, here, two and a half years ago".
Now there is an important point I want to make. Do I have to getrecognition from the historians that I was the first? I had simplyguessed it while Millikan, when he obtained the formula, had newexperimental material which demonstrated its correctness. One did notunderstand that the formula was correct, but the new experimentaldata made it clear that he was the one who had the right formula. Hehad reasons for it, I had simply guessed, I could not even convinceEhrenfest, and it was published in french .....
In these days Kronig came from America and he came to Leiden; wecollaborated in spectroscopy and worked on the intensities in theZeeman effect for which we found the exact expressions. Of course, it was quite different from today;there was no quantum mechanics at the time, don't forget that thisdid not yet exist! One had to guess these little formulae; onedeveloped a feeling for them. It is just as with veterinary and humanmedicine. People can tell one where it hurts, but a veterinary doctorhas to guess where it hurts. A horse or a cow cannot tell that. Andso it is with these little formulae. It is really curious ...... itwas a kind of numerology, and it is a miracle that we arrived at thecorrect expressions which later could be derived by quantummechanics. Now, when it is derived it becomes quite simple. If oneknows some mathematics, then one can derive all those things. We hadto guess at them; I had a feeling for that. And that is the wayKronig and I did those things.
Well, Ehrenfest soon found out that I was not a propertheoretician and then he sent me to Amsterdam. Three days a week Iwas part-time assistant with Zeeman and things were quite differentduring those days. For instance, Wednesday evenings I took the trainback to Leiden and then had a feeling I ought to switch; the jokesone heard and recounted in Amsterdam could not be used in Leiden.That was not done; they were not proper enough. In Amsterdarn it wasquite friendly. Professor Zeeman, of course, was somewhat more formalthan I had been used to.
And I did something else at the time. The Pauli principle waspublished early in 1925 . I am convinced thatalthough it is one of the most important publications in physics, whoreads it now, of the younger generation, will find it hard tounderstand. Even that one will not understand it all. And I wrote anote in May that the Pauli principle becameeasier to understand when introducing different quantum numbers. Thequantum numbers I used for Pauli's principle were mL andms; ms being always the same, plus or minus1/2. (In those days it was slightly different, one used 1 and 0, butthat does not really matter.) And if you used these for the Pauliprinciple, then it became much simpler ......., as one does today ofcourse. You people don't know that such a change was necessary butPauli had introduced different quantum numbers. As a mathematiciansaid, the change amounted to a simple linear transformation - whichis trivial, mathematically trivial of course, but not so for theunderstanding and in teaching.
Well, I had introduced those quantum numbers, but if I had been agood physicist, then I would have noticed already in May 1925 thatthis implied that the electron possessed spin. But I was no goodphysicist, I am no good physicist and thus I did not realize this.
I sent my note to Copenhagen to get an opinion from Kramers andKronig; Kronig then having left for Copenhagen. I received a longletter from Kronig about other things but he did not say anythingabout my note. That did not interest him, apparently. This is anotherimportant point, besides Paschen's forbidden line, the forbiddenfine-structure component. That was all in the spring of 1925. ThenUhlenbeck appears on the scene.
George Uhlenbeck had interrupted his research to become tutor ofthe children of the Netherlands ambassador in Rome. He must have donethis very well because one of them later made it to ambassador inWashington, Van Rooyen. But, as Ehrenfest said: "there in Italy hehas learnt nothing of those new things, there they only knowclassical physics". And George Uhlenbeck, who was there, has alsostudied classical physics; when he came home in the summer Ehrenfestsaid: "You should work together with him for a while, then he maylearn something about the new atomic structure and all that spectralbusiness". What he clearly thought, of course, was: "Perhaps I mightlearn a little bit of real physics from Uhlenbeck".
Leiden 1924. From left to right: Dieke, Goudsmit, Tinbergen, Ehrenfest, Kronig, Fermi. Note: Tinbergen later changed from physics to economy and became the first Nobel laureate in economy (1969).
So Uhlenbeck knew nothing about the new physics, but yet he did animportant thing for the modern physics that was to come. Ehrenfesthad written him a letter in which he said: "I have read an article bya young man, it looks nice and one ought to try and see him". Well,in those days, when your professor wrote you, you did it. And GeorgeUhlenbeck went to see that young man; the young man just came backfrom Germany and was totally discouraged. He had spent a semester inG?ttingen and there they had given him a treatment: "Well thatman cannot know anything, besides being too small he never studiedanyplace worthwhile". So the young man really got discouraged andmeant to give up physics. But Uhlenbeck said: "Don't do that beforeyou first talk to Ehrenfest; come and see Ehrenfest." And the mancame to Leiden and stayed for two or three months with Ehrenfest, ofwhich I can show a picture. A well-known picture that you may haveseen before: there is that young man, Enrico Fermi. And underEhrenfest's encouragement it dawned on him that he really was acompetent physicist. And if you look at Fermi's career ....... thoseare the days in which he really became a great physicist.
In any case, Uhlenbeck came to the Hague - where I lived and helived there too. I had promised to write a short article for"Physica", then in Dutch, and I did it together with him, which wasreally great. Because he knew nothing, but was so good; he asked allthose questions I had never asked, and from that collaboration tomake things clear emerged a few, as we now know, important results.One of the first results that came out was a new interpretation ofthe spectrum of hydrogen. We had Sommerfeld's hydrogen spectrum, andfor formal reasons and because I had investigated all those things,we obtained a new interpretation of the hydrogen spectrum. The newterm scheme. I have a picture of it, but you know it because that iswhat you learn today. On the left is the old Sommerfeld scheme, onthe right the real one ........... And the curious thing is that I,because I knew all these intensity rules and so forth, had alreadyguessed the correct formulae. That was my contribution; that I knewwhich formulae one had to take. One took the classical expressionsand instead of integral quantum numbers one put in half integralquantum numbers and did a few other things, it was like magic, but itnevertheless precisely fitted, and what I found so delightful - ifyou really believed it - then the "forbidden" line which Paschen hadseen was not forbidden but a real spectral line which ought to bepresent and that gave me a lot of fun.
And this, of course, is something I want to say again; peopledon't believe it. In the beginning when you do something you neverknow whether it is important or not, and we absolutely had no ideathat a new interpretation of the hydrogen spectrum was important.Therefore, this was published in "Physica", in Dutch. We also had an article about those quantumvectors L and S, the coupling of quantum vectors, allthat tommy rot, I don't know how you call it, and that was sent offto the "Zeitschrift für Physik". Do you note the difference? Wedid not know what was important. Everyone worked on those quantumvectors and that was published in the "Zeitschrift für Physik".The hydrogen spectrum was published in "Physica", but you note, thisspectrum pointed in the right direction.
The old and the new term scheme of hydrogen . The scheme shows the multiplet splitting of the excited states of the hydrogen atom with principal quantum number n=3, presented by Goudsmit in the form in which it appeared in the original publications of1926. The assignment in the current notation has been added at the right. With the development of quantum mechanics the notation changed. The quantum numbers L and J now usedfor the orbital and total angular momentum, respectively, correspond to K-1/2 and J-1/2 in the figure. The "forbidden component" referred to by Goudsmit is of the type 3 2P1/2 --> 2 2S in which the total angular momentum is conserved and L changes by plus or minus 1.
When the day came I had to tell Uhlenbeck about the Pauliprinciple - of course using my own quantum numbers - then he said tome: "But don't you see what this implies? It means that there is afourth degree of freedom for the electron. It means that the electronhas a spin, that it rotates". Now, I can also exactly tell you thedifference between Uhlenbeck and me as physicists. In those days, allthrough the summer when I told Uhlenbeck about Landé andHeisenberg, for instance, or about Paschen, then he asked: "Who isthat?" He had never heard of them, strange. And when he said: "Thatmeans a fourth degree of freedom", then I asked him: "What is adegree of freedom?" In any case, when he made his remark, it was luckthat I knew all these things about the spectra, and I then said:"That fits precisely in our hydrogen scheme which we wrote about fourweeks ago. And if one now allows the electron to be magnetic with theappropriate magnetic moment, then one can understand all thosecomplicated Zeeman-effects. They come out naturally, as well as theLandé formulae and everything, it works beautifully".
And that was it: the spin; thus is was discovered, in that manner.Of course we told Ehrenfest about it and then summer was over and Iwent again to Amsterdam and various episodes followed. Naturally, Ifound it wonderful, because in the formalism which I knew it fittedperfectly. And the rigorous physics behind it I did not fathom. ButUhlenbeck, being a good physicist, started to think about it. ......"A charge that rotates"......? He claims that he then went to Lorentzand that Lorentz replied: "Yes, that is very difficult because itcauses the self energy of the electron to be wrong".
And Uhlenbeck also tells you that ........ We had just written ashort article in German and given to Ehrenfest, who wanted to send itto "Naturwissenschaften". Now it is being told that Uhlenbeck gotfrightened, went to Ehrenfest and said: "Don't send it off, becauseit probably is wrong; it is impossible, one cannot have an electronthat rotates at such high speed and has the right moment". AndEhrenfest replied: "It is too late, I have sent it off already". ButI do not remember the event, I never had the idea that is was wrongbecause I did not know enough. The one thing I remember is thatEhrenfest said to me: "Well, that is a nice idea, though it may bewrong. But you don't yet have a reputation, so you have nothing tolose". That is the only thing I remember.
Well the note was submitted and published .Directly, the next day, I received a letter from Heisenberg and herefers to our "mutige Note" (courageous note). I did not even know weneeded courage to publish that. I wasn't courageous at all. I think Istill have Heisenberg's letter. In it he writes a formula ......... Idid not understand a bit of it. And then he says somewhere: "Whathave you done with the factor 2?" Which factor? Not the slightestnotion, and the formula given without derivation.
I told you, the spin fitted nicely into the whole formalism. But,of course, we also ought to have made a quantitative calculation ofthe size of the splittings. If one believed in the spin, then thespin can be "up" or "down", and what is the difference in energy -does it come out correctly? We had the formulae already, but was itpossible to derive these formulae? We did not do that because weimagined it would be very difficult. Now every beginning student doesit; what do you call him? ..... a freshman, a greenhorn? He manages,but we didn't know how to do it, and therefore we had not done it.Luckily we did not know, because if we had done it, then we wouldhave run into an error by a factor of 2. That would not have fitted,but we did not know; all other things fitted perfectly, yet this doesnot.
Well, we were discouraged but, again, it was a matter of luck.Just in those days Lorentz celebrated the fiftieth anniversary of hisdoctorate. And Bohr and Einstein and many other great scientists cameto Leiden. And Bohr had seen our note and was quite interested. Everyday we had a meeting, a get together with Bohr, Einstein andEhrenfest about the problem of the spin and all those things, atEhrenfest's home. There we learned a lot.
In passing I have to mention a typical Ehrenfest anecdote, notsuch a nice one, perhaps. Lorentz lived in Haarlem and all thesecelebreties, Rutherford, Madame Curie, Bohr, Einstein and very manyothers travelled by train, a special train, from Leiden to Haarlem.And the week before one of those rare fatal train accidents hadoccurred and I said to Ehrenfest: "Wouldn't it be dreadful if thattrain had an accident?" And Ehrenfest replied: "Yes, that would bedreadful, but think of all the young physicists who then could getjobs ......".
Bohr was highly optimistic, in particular when he saw that I hadalready all the formulae for the fine structure. And he thoughtperhaps, that it [i.e. the factor 2] is something trivial; probablysomething relativistic. I have never understood the argumentprecisely. When Bohr and Einstein were talking together at theEhrenfests', I did not understand a bit of it.
Anyway, Bohr made one mistake. Instead of Uhlenbeck he invited meto Copenhagen, to see if I might learn something there. That did notwork, of course, and after six weeks he presented me with afirst-class railway ticket, to go back to the Hague. But inCopenhagen there was a young man, Thomas, who was thoroughlyacquainted with the theory of relativity. While I was there he workedout that Heisenberg's factor of two - which seemed lost - actuallyrepresented the relativistic factor and everything was in order.
The man who never cared to believe in the spin was Pauli. And thenBohr said: "On your way home you should stop off at Hamburg andexplain the factor 2 to Pauli". I have tried to do so, but because Idid not really understand it myself I, naturally, was unable toexplain it to Pauli ....... But Pauli did not want to believe it; onmy return Einstein still was in Leiden and I had to explain it to himtoo, which went even worse. I did not manage, but later I received apostcard from Pauli that he had seen Thomas's work and that hebelieved in it.
Part of a letter by L.H. Thomas to Goudsmit (25 March 1926). Reproduced from a transparency shown by Goudsmit during his 1971 lecture. The original is presumably in the
Goudsmit archive kept by the AIP Center for History of Physics.
Well, that would have been the end, as I thought myself. Thomaswas to return to England and wanted to travel via Holland to visitme, so he wrote me a letter. Here is a part of that letter. I thinkthis represents an important point, and in particular the historians,naturally, enjoy such a thing. The historians, they always try totrace someone who, somewhere in a dark chest, has already hiddenEinstein's theory. But this they also found wonderful.
Now this is dead certain. If Kronig had not left Leiden and hadstayed with Ehrenfest, then things would have taken another course.Ehrenfest would have encouraged him and said: "That you ought topublish". With Pauli, of course, it was entirely different. Butadmitting the great difference in this respect, if one looksobjectively ......... In the days that Kronig had that idea then thenew interpretation of the hydrogen spectrum did not exist,mL and ms did not exist, and he may not haveknown about these forbidden components because they did not interesthim. Thus, actually, the material that convinced people that it wasright simply did not exist. Also, Kronig was not really the first.The first one to publish about the quantized electron - Kronig didnot do so - was Compton. For reasons that were totally erroneous, hehad said some four years before in the "Journal of the FranklinInstitute": "Perhaps there exists a quantized rotation of theelectrons". But the reasons he had given were wrong and unconvincing.
Then there was a short paper by Kennard, an American physicist,who had slightly more convincing arguments, but insufficient to makepeople believe him. Urey had thought about it but did not publish it.When Kronig read our paper he published two articles to prove that wewere wrong; in "Nature" and in the "Proceedings of the NationalAcademy" in Washington ....... Therefore, I find it a little strangeif some historians say: "Kronig did it, really, you people did not doit". That is the same historian who says .... that is merely a lineartransformation and, therefore, a trivial contribution.
That is the way the history looks and it is a somewhat curioushistory. Who, precisely, should get credit for it? Such things arenot possible without also giving credit to all other people who havecontributed. But one aspect stands out which is of particularimportance for young people. First: you need not be a genius to makean important contribution to physics because, I do admit, theelectron spin is an important contribution. That I know now, then wedid not know, but now I do. They all told me so.
Then I want to say one more thing: even if you make a minorcontribution, if it is not important, then this gives an enormoussatisfaction. Therefore I do believe that one should not alwaysaspire to tackle what is most important, but try to have fun workingin physics and obtain results.
References
[*] Foundations of Modern EPR,edited by G.R. Eaton, S.S. Eaton, and K.M. Salikhov(World Scientific, Singapore, 1998).
[1] S.A. Goudsmit, De ontdekking van deelectronenrotatie, Nederlands Tijdschrift voor Natuurkunde37 (1971) 386.
[2] S. Goudsmit and R. de L. Kronig,Naturwissenschaften 13 (1925) 90; Verhandelingen KoninklijkeAkademie van Wetenschappen 34 (1925) 278.
[3] W. Pauli, Z. Physik 32 (1925) 794.
[4] S. Goudsmit, Z. Physik 32 (1925) 111;the relation with our current notation is somewhat less trivial thansuggested by Goudsmit in his lecture.
[5] S. Goudsmit and G.E. Uhlenbeck, Physica6 (1926) 273.
[6] G.E. Uhlenbeck and S. Goudsmit,Naturwissenschaften 47 (1925) 953. A subsequent publication bythe same authors, Nature 117 (1926) 264, is followed by a veryinteresting postscript by N. Bohr.
[7] L.H. Thomas, Nature 107 (1926) 514.
