The discovery of the electron spin
                               S.A. Goudsmit


When I went to Leiden, I ended up with Ehrenfest. Ehrenfest's classes 
were small and one had a very good interaction with one's professor. 
And Ehrenfest was always worried when we interrupted our classes when 
we had to go somewhere. Once I had to accompany my father to Germany, 
because of his business, and then Ehrenfest said: "Do you again have 
to interrupt your classes?" But my father could not travel alone. 
Then he asked: "Where are you going?" When I told him, he said: 
"Nearby is a university and there is a spectroscopist, Paschen. You 
are interested in spectroscopy (I had become interested in it through 
my high-school teacher Lohuizen), go and have a look". That was 
important; I have done it. I went to visit Paschen, who did not treat 
me as a student but as a colleague. And he showed me the experimental 
set up which he had for the study of the spectral line of ionised 
helium, which entirely confirmed Sommerfeld's relativistic electron 
orbits. I did not understand a bit of it. But, I think, I managed to 
hide my lack of understanding and after my return to Leiden I have 
nicely studied all this. One of the things which stuck to me is that 
in Paschen's experiments on the helium line, its fine stucture and 
the relativistic explanation, there was a forbidden component which 
was obviously present. The following summer I was sent for a stay to 
Paschen, and Paschen and Back have taught me the techniques of 
spectroscopy. And when I talked to the theoreticians about that 
forbidden component ......... but you know how theoreticians 
are ...... they then say: "Poor experiments". That forbidden line 
already was an important milestone. I shall recount a few more of 
these milestones.

I was interested in spectral lines and the first thing I did .... I 
found a formula for the doublets in the spectra, claiming that it was 
exactly the same formula as used by Sommerfeld for the X-ray doublets.
 And I told this to Ehrenfest. At that stage it was all wrong 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 "Archives 
Néerlandaises des Sciences exactes et naturelles", which was 
published in Holland in french to be sure that nobody would read it. 
Of course, as a young student I was very proud of it.

In these days Kronig came from America and he came to Leiden; we 
collaborated in spectroscopy and worked on the intensities in the 
Zeeman effect for which we found the exact expressions [2]. Of course,
 it was quite different from today; there was no quantum mechanics at 
the time, don't forget that this did not yet exist! One had to guess 
these little formulae; one developed a feeling for them. It is just 
as with veterinary and human medicine. People can tell one where it 
hurts, but a veterinary doctor has to guess where it hurts. A horse 
or a cow cannot tell that. And so it is with these little formulae. 
It is really curious ...... it was a kind of numerology, and it is a 
miracle that we arrived at the correct expressions which later could 
be derived by quantum mechanics. Now, when it is derived it becomes 
quite simple. If one knows some mathematics, then one can derive all 
those things. We had to guess at them; I had a feeling for that. And 
that is the way Kronig and I did those things.

The Pauli principle was published early in 1925 [3]. I am convinced 
that although it is one of the most important publications in physics,
 who reads it now, of the younger generation, will find it hard to 
understand. Even that one will not understand it all. And I wrote a 
note in May [4] that the Pauli principle became easier to understand 
when introducing different quantum numbers. The quantum numbers I 
used for Pauli's principle were mL and ms; ms being always the same, 
plus or minus 1/2. (In those days it was slightly different, one used 
1 and 0, but that does not really matter.) And if you used these for 
the Pauli principle, then it became much simpler ......., as one does 
today of course. You people don't know that such a change was 
necessary but Pauli had introduced different quantum numbers. As a 
mathematician said, the change amounted to a simple linear 
transformation - which is trivial, mathematically trivial of course, 
but not so for the understanding and in teaching.

Well, I had introduced those quantum numbers, but if I had been a 
good physicist, then I would have noticed already in May 1925 that 
this implied that the electron possessed spin. But I was no good 
physicist, I am no good physicist and thus I did not realize this.

I sent my note to Copenhagen to get an opinion from Kramers and   
Kronig. I received a long letter from Kronig about other things but 
he did not say anything about my note. That did not interest him, 
apparently. This is another important point, besides Paschen's 
forbidden line, the forbidden fine-structure component. That was all 
in the spring of 1925. Then Uhlenbeck appears on the scene.


George Uhlenbeck knew nothing about the new physics, but yet he did an 
important thing for the modern physics that was to come. Ehrenfest 
had written him a letter in which he said: "I have read an article by 
a 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 George 
Uhlenbeck went to see that young man; the young man just came back 
from Germany and was totally discouraged. He had spent a semester in
 Goettingen and there they had given him a treatment: "Well that man 
cannot know anything, besides being too small he never studied 
anyplace worthwhile". So the young man really got discouraged and 
meant to give up physics. But Uhlenbeck said: "Don't do that before 
you first talk to Ehrenfest; come and see Ehrenfest." And the man 
came to Leiden and stayed for two or three months with Ehrenfest, of 
which I can show a picture. A well-known picture that you may have 
seen before: there is that young man, Enrico Fermi. And under 
Ehrenfest's encouragement it dawned on him that he really was a 
competent physicist. And if you look at Fermi's career ....... 
those are the days in which he really became a great physicist.

In any case, Uhlenbeck came to the Hague - where I lived and he lived 
there too. I had promised to write a short article for "Physica", 
then in Dutch, and I did it together with him, which was really 
great. Because he knew nothing, but was so good; he asked all those 
questions I had never asked, and from that collaboration to make 
things clear emerged a few, as we now know, important results. One of 
the first results that came out was a new interpretation of the 
spectrum of hydrogen. We had Sommerfeld's hydrogen spectrum, and for 
formal reasons and because I had investigated all those things, we 
obtained a new interpretation of the hydrogen spectrum. The new term 
scheme. I have a picture of it, but you know it because that is what 
you learn today. On the left is the old Sommerfeld scheme, on the 
right the real one ........... And the curious thing is that I, 
because I knew all these intensity rules and so forth, had already 
guessed the correct formulae. That was my contribution; that I knew 
which formulae one had to take. One took the classical expressions 
and instead of integral quantum numbers one put in half integral 
quantum numbers and did a few other things, it was like magic, but it 
nevertheless precisely fitted, and what I found so delightful - if 
you really believed it - then the "forbidden" line which Paschen had 
seen was not forbidden but a real spectral line which ought to be 
present and that gave me a lot of fun.

And this, of course, is something I want to say again; people don't 
believe it. In the beginning when you do something you never know 
whether it is important or not, and we absolutely had no idea that a 
new interpretation of the hydrogen spectrum was important. Therefore, 
this was published in "Physica", in Dutch [5]. We also had an article 
about those quantum vectors L and S, the coupling of quantum vectors, 
all that tommy rot, I don't know how you call it, and that was sent 
off to the "Zeitschrift fur Physik". Do you note the difference? We 
did not know what was important. Everyone worked on those quantum 
vectors and that was published in the "Zeitschrift fur Physik". The 
hydrogen spectrum was published in "Physica", but you note, this 
spectrum pointed in the right direction.

The old and the new term scheme of hydrogen [5]. 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 of 1926. 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 used for 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 Pauli principle - 
of course using my own quantum numbers - then he said to me: "But 
don't you see what this implies? It means that there is a fourth 
degree of freedom for the electron. It means that the electron has a 
spin, that it rotates". Now, I can also exactly tell you the 
difference between Uhlenbeck and me as physicists. In those days, all 
through the summer when I told Uhlenbeck about Landé and Heisenberg, 
for instance, or about Paschen, then he asked: "Who is that?" He had 
never heard of them, strange. And when he said: "That means a fourth 
degree of freedom", then I asked him: "What is a degree of freedom?" 
In any case, when he made his remark, it was luck that I knew all 
these things about the spectra, and I then said: "That fits precisely 
in our hydrogen scheme which we wrote about four weeks ago. And if 
one now allows the electron to be magnetic with the appropriate 
magnetic moment, then one can understand all those complicated 
Zeeman-effects. They come out naturally, as well as the Landé 
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 I went 
again to Amsterdam and various episodes followed. Naturally, I found 
it wonderful, because in the formalism which I knew it fitted 
perfectly. And the rigorous physics behind it I did not fathom. But 
Uhlenbeck, being a good physicist, started to think about it. ...... 
"A charge that rotates"......? He claims that he then went to Lorentz 
and that Lorentz replied: "Yes, that is very difficult because it 
causes the self energy of the electron to be wrong".

And Uhlenbeck also tells you that ........ We had just written a 
short article in German and given to Ehrenfest, who wanted to send it 
to "Naturwissenschaften". Now it is being told that Uhlenbeck got 
frightened, went to Ehrenfest and said: "Don't send it off, because 
it probably is wrong; it is impossible, one cannot have an electron 
that rotates at such high speed and has the right moment". And 
Ehrenfest replied: "It is too late, I have sent it off already". But 
I do not remember the event, I never had the idea that is was wrong 
because I did not know enough. The one thing I remember is that 
Ehrenfest said to me: "Well, that is a nice idea, though it may be 
wrong. But you don't yet have a reputation, so you have nothing to 
lose". That is the only thing I remember.

Well the note was submitted and published [6]. Directly, the next day,
 I received a letter from Heisenberg and he refers to our "mutige 
Note" (courageous note). I did not even know we needed courage to 
publish that. I wasn't courageous at all. I think I still have 
Heisenberg's letter. In it he writes a formula ......... I did not 
understand a bit of it. And then he says somewhere: "What have you 
done with the factor 2?" Which factor? Not the slightest notion, and 
the formula given without derivation.

Bohr was highly optimistic, in particular when he saw that I had 
already all the formulae for the fine structure. And he thought 
perhaps, that it [i.e. the factor 2] is something trivial; probably 
something relativistic. I have never understood the argument 
precisely. When Bohr and Einstein were talking together at the 
Ehrenfests', I did not understand a bit of it.

Anyway, Bohr made one mistake. Instead of Uhlenbeck he invited me to 
Copenhagen, to see if I might learn something there. That did not 
work, of course, and after six weeks he presented me with a 
first-class railway ticket, to go back to the Hague. But in 
Copenhagen there was a young man, Thomas, who was thoroughly 
acquainted with the theory of relativity. While I was there he worked 
out that Heisenberg's factor of two - which seemed lost - actually 
represented the relativistic factor and everything was in order [7].


I told you, the spin fitted nicely into the whole formalism. But, of 
course, we also ought to have made a quantitative calculation of the 
size of the splittings. If one believed in the spin, then the spin 
can be "up" or "down", and what is the difference in energy - does it 
come out correctly? We had the formulae already, but was it possible 
to derive these formulae? We did not do that because we imagined it 
would be very difficult. Now every beginning student does it; 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 would have 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 does not.

Well, we were discouraged but, again, it was a matter of luck. Just 
in those days Lorentz celebrated the fiftieth anniversary of his 
doctorate. And Bohr and Einstein and many other great scientists came 
to Leiden. And Bohr had seen our note and was quite interested. Every 
day we had a meeting, a get together with Bohr, Einstein and 
Ehrenfest about the problem of the spin and all those things, at 
Ehrenfest's home. There we learned a lot.