# What is the origin of the terminology 'spin up/down'?

In my research area one seminal reference is H. Bethe, ''Zur Theorie der Metalle'', Z. Phys. 71 205 (1931), see also the English translation by T. C. Dorlas (2009). On page 206 of the original reference we read

Solange von der Wechselwirkung abgesehen wird, gibt es für jedes Atom zwei Zustände mit gleicher Energie: Der Spin des Leuchtelektrons kann nach rechts oder nach links zeigen.

Thus it seems that at the time, at least in the German-speaking scientific community, the terminology spin 'left' and 'right', rather than 'up' and 'down, was used for the two basis vectors of the spin-1/2 irrep of $su(2)$. Was this indeed common practice? If so, was this the original terminology used? And why and by whom was it changed to 'up' and 'down'?

NB. I can speculate that the following happened. 'Left' and 'right' may originate from the Stern--Gerlach experiment, of course depending on the direction of the external magnetic field in the original experiment. Later on, '$\leftarrow$' and '$\rightarrow$' might then have been replaced by the more compact '$\uparrow$' and '$\downarrow$' for typographical reasons.

• You may have already seen this, but this paper on arXiv titled "A Short History of Spin" may be of some help. Please see : arxiv.org/abs/1311.5016 . The paper states that Stern-Gerlach observed deflection as either up or down and there is no reference to the left/right terminology. – Nick May 5 '17 at 16:35
• @NickR Thanks, I did not know that. It only makes Bethe's terminology more surprising, then. – Jules Lamers May 6 '17 at 8:46
• Note that Bethe’s paper has an “official” translation in his Selected works (1997). Unlike Dorlas, it renders “Linksspin” and “Rechtsspin” as “left-handed” and “right-handed”. – Francois Ziegler Oct 16 '17 at 17:29

Bethe is quoting and following Felix Bloch, who said left/right in (1929; 1930, p. 207). But I don’t think this was ever “common practice”. Stern, in his original Stern–Gerlach paper, drew the magnetic field $\mathfrak H$ and quantized angular momentum component $\mathfrak m_z$ vertically (1921, p. 251):

$\hspace{11em}$

In doing so, he followed (and quoted) Sommerfeld’s Atombau und Spektrallinien (2nd ed., 1921, pp. 408-411) and ultimately Sommerfeld’s original “spatial quantization” paper (1916, pp. 29-32):

(If Fig. 6 looks like a horizontal component is being quantized, it’s only because the lines represent the orbital plane, not the angular momentum vector perpendicular to it; Sommerfeld didn’t switch to picturing the latter until Atombau’s 5th edition (1931; 1934 translation, p. 123):

$\hspace{50em}$.)

It’s true that the Stern–Gerlach experimental magnetic field was apparently horizontal (1922, 1924). But they didn’t call it left/right any more than front/back or up/down; and the subsequent theories of Heisenberg–Jordan (1926, p. 266), Pauli (1927, p. 605), Dirac (1928, p. 620) and expositions by Weyl (1928, p. 65), Dirac (1930, p. 152), Wigner (1931, p. 238) or Bethe himself (1933, p. 276) all quantized in the $z$ direction!

Edit:
As to the title question, my guess is that the standard terms were “positive spin” and “negative spin” from around the time of Sommerfeld–Bethe (1933) and until maybe the early 1950s, when “spin up” and “spin down” began to appear, with and then without quotes, in references like Blatt–Weisskopf (1952), Kittel (1953), Bethe–Maximon (1954), Bethe–Salpeter (1957).