HEISENBERG, Werner. Three autograph letters to Samuel Goudsmit in German (1902-1978) comprising: Autograph letter signed ("Werner Heisenberg") Göttingen 21 November [1925]. 2 pages on a single sheet, slightly worn, two punch holes to left margin, not affecting text. - Autograph letter signed ("Werner Heisenberg") Göttingen, 9 December 1925. 2 pages on stationery of the "Institut für theoretische Physik der Universität," folded, few marginal tears, one with tape repair, two punch holes to left margin, not affecting text.. -- Autograph letter signed ("W. Heisenberg") Göttingen, 19 February 1926. 2 pages on a single sheet, two punch holes to left margin, affecting two letters.
Historic, very detailed scientific letters reacting to the discovery of electron spin, showing how Heisenberg grappled with the difficulties presented by a basic new discovery in quantum physics. The three autograph letters document the progress of Heisenberg's and Wolfgang Pauli's efforts to solve the problem up to the actual day before H. L. Thomas provided the missing solution.
{1} Having studied in Goettingen under Arnold Sommerfeld and Max Born, Heisenberg was at this time teaching at the University of Goettingen. A few months after our last letter, in May of 1926, Heisenberg would move to Copenhagen to work with Neils Bohr. Heisenberg's first autograph letter to Goudsmit was written only days after the November 16 submission of Max Born, Heisenberg, and Pascual Jordan's famous paper on the foundations of quantum mechanics. [See lot 31]. This autograph letter written by the 24 year old Heisenberg to his 23 year old contemporary, Goudsmid, raises Heisenberg's objection that the doublet separation predicted by Goudsmit's and Uhlenbeck's formulation was too large by a factor of two. So promptly did Heisenberg react to Goudsmit's discovery that Goudsmit apparently received this letter one day after the day his paper was published:
Your courageous article published in Naturwissenschaften is of such great interest to me that I would like to address a number of questions to you. You are entirely correct in stating that one can never extinguish all of the principal difficulties of the muliplet structure like waving a magician's wand, if one presumes the magnetic momentum of an electron; and I am convinced that all of the formular difficulties (as the appearance of about j (j+1) instead of j2 etc.) could be eliminated by means of quantum mechanics. But I have some reservations, which are perhaps the result of my own shortcomings, about the thinking regarding the selective separation. If one determines more clearly (according to your model) the reciprocal action , one arrives, as far as I can see, at
FIX FORMULAS ON SCREEN
(1) D r 7 h = K 7 h 7 Z2 a2 Z2 7 2 7 Dm
n3k2
where Dm denotes the change of the projection from r, that is of mechanical movement to K. If, for instance, Factor 2, which originates in the double magnetism of an electron, did not exist, it would be most like that (1) is the realistic formula; only instead of1
k (h-1)
one would get1/k - 1
which most probably would result according to the considerations of quantum mechanics. It is certainly true that now you can determine the Z4 law through magnetism. My question to you is, how you eliminated Factor 2. I also would like to hear your opinion about the the prohibition of the equivalent paths as advanced by Pauli, as well as about your theory of the hydrogen spectrum. After all, with hydrogen there has got to be some relativity, if one doesn't think of the relativity theory as somehow wrong."
{2}. Heisenberg continued his correspondence in a slightly more philosophical vein two weeks later on December 9, showing that he was continuing to work on the matter. The fact that during two weeks' time Goudsmit had already responded twice to Heisenberg's letter of November 21, and that Heisenberg was apologetic in his slow response, reminds us how prompt and intense written correspondence could be before telephone, fax and e-mail:
"Many thanks for the two letters. Forgive me that I didn't answer you early. In the meantime I have often thought about your theory and I am convinced that you have brought to light a new and important facet of the phenomenon about multiple structures. Of course I also believe that the ultimate result lies even deeper and that is really related to a multi-dimensional-in-variations formulation of quantum mechanics. I think that some segments speak against the literal use of your hypothesis. First of all, there is this Factor 2 which really denies a direct agreement with experience. Then you must also think of the triplet spectras. The distance between a singlet to a triplet system for a given value of C would have to be produced, and only through different orientations of the two electrons against each other. But classically seen, such a reciprocal action energy would be much smaller than the distance between singlet--triplet. It seems to me that in this case one suddently correctly gets the order of magnitude.
In spite of all this I can clearly see the progress contained in your hypothesis. I have a vague idea that the conformity of yours and of the relativistic formula could not be an accident. At the moment I am researching here with [Pascual] Jordan a four-dimensional formulation of quantum mechanics and I am curious to find out what becomes of it. It is obvious that, so far, quantum mechanics has stood in conflict with the relativity theory; for instance, a hollow space, used as an oscillator [?], would have to result in point zero, but in spite of that one would not like to attribute the form of a mass to it.
Yet in reality I don't know how one can put the muliplets in order. The Copenhagen people [i.e. Bohr's laboratory staff] should have sent you some excerpts of my work, but they are so awfully slow there . . . .
According to Pais, both in Inward Bound and Niels Bohr's Times, Bohr accepted the validity of electron spin in December of 1925 and in meetings with Heisenberg, Jordan, and Pauli, converted them to the new theory. Mehra and Rechenberg (III, 202) precisely date Bohr's departure for Leiden and then Goettingen to December 9, which confirms that Bohr would have met with Heisenberg in Goettingen a few days after December 9, the date of the above letter to Goudsmit. From the content of the above letter it would certainly seem that Heisenberg's conversion occurred after December 9.
{3}. Heisenberg's third letter to Goudsmit dated February 19, 1926 seems to have fallen just before Llewellyn Thomas supplied the missing factor two, which has since been known as the Thomas factor. "Thomas noted that earlier calculations of the precession of the electron spin had been performed in the rest frame of the electron, without taking into account the precession of the electron orbit around its normal. Inclusion of this relativistic effect reduces the angular velocity of the electron (as seen by the nucleus) by the needed factor 1/2. Einstein was surprised. Pauli became converted." (Pais, Inward Bound, p. 279). In the third letter written before they knew of Thomas' successful resolution of the problem Heisenberg and Pauli are still grappling with the problem of the factor two:
First all of all many thanks for having had the corrections of your article sent to me; it is very good. But the main reason for this letter is something else: the calculations pertaining to your model according to quantum mechanics are now completed (the second part was done together with Pauli) and in every instance the results are as expected, that is, the Zeeman-effects appear to be correct as far as intensities and the splitting up of fissures are concerned. Especially in the D-line types for intensities and fissures the results are according to the formula of [Woldemar] Voigt's [1850-1919] theory:
H = Ho W = Wo + 2R2 h2 Z4 j(j+1) - h(h+1) - 1/2 7 3/2-1+ 3
mo 7 n3 k(k+1/2) (k+1)k+1/2 4n
In this formula k is taken as zero j = k 1 1/2. Above all one sees here that relativity does not result in the Sommerfeld formula; Sommerfeld established the final two links of the bracket as (- 1/k+1 + 3/4n). Obviously, therefore, the relativisitic explanation of the doublets does not apply. But, to continue, your theory yields exactly double the amount of the split fine structure, as observed, and because of this there is no separation within the screening doublet, and also not in the magnetic doublets. But there is a curious connection: if one erased Factor 2 from your electrons then, for one thing, the correct doublet size would appear, and for another, the correct division in the screening- and magnetic doublets could be seen, that is, one would have the Sommerfeld formula exactly.
For all of this I would like to deduce that an electron is not a point charge and that your theory regarding magnetism is about right; but that new research of the mechanical behavior of electrons will be necessary in order to understand the doublets logically. Here it might be useful to do some research about the distance existing between triplets and singlets . . . .
Mehra and Rechenberg III, pp. 269ff. discuss the correspondence between Heisenberg and Pauli in their attempts to resolve the exact problems mentioned in our third letter. They also date Bohr's learning of L. H. Thomas's resolution of the problem to exactly one day after Heisenberg wrote this letter; i.e. February 20, 1926. Thomas, a researcher from Cambridge, who happened to be visiting Bohr's laboratory at the time of his discovery, sent his note in to Nature on February 20. Bohr communicated the solution to Pauli in a letter dated the same day. Pauli initially objected strongly to this solution, but eventually accepted it, as our postcards document.
The best brief accounts of Goudsmit's and Uhlenbeck's discovery of electron spin are in the DSB article on Goudsmit (Vol. 17, Suppl. II, pp. 362-68.) and Pais, Inward Bound (1986), pp. 274-80. Both of those accounts refer specifically to the problems posed in these letters. An excellent, comprehensible summary of the background problems leading to the discovery of electron spin is in Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (1992), pp. 207-11. Pais (p. 280) suggests that Goudsmit and Uhlenbeck did not receive the Nobel prize for their discovery because their work may have been anticipated, without their knowledge, by Kronig. (3)