Who was the first to make a Stern-Gerlach experiment with two magnets?

[Frigorifico9]

TL;DR Summary

I want to find who was the first person to make a Stern-Gerlach experiment with two static magnets

I'm trying to fill a conceptual gap I have in the history of physics

In 1922 Stern and Gerlach make their experiment, proving that electrons have intrinsic angular momentum, however it takes a while for people to understand this. At first they think this is somehow caused by quantization of orbital angular momentum, but as the months go by they realize this is not possible

At some point someone does experiments with two magnets, realizing that the beam doesn't split again after identical measurements, but always splits in two after measurements at different angles **<- This is the hole I want to fill**

Based on the results of these consecutive measurements, Pauli, Sommerfeld, and a few others start proposing a new quantum number that can only take two values

Then in 1925 Ralph Kronig, as well as Uhlenbeck and Goudsmith, independently come up with the idea that this new quantum number is intrinsic angular momentum

Pauli is initially skeptic about this, dismissing Kronig when he brings up the idea to him, but eventually ends up embracing this concept and in 1927 publishes a paper containing the Pauli matrices we know and love today

 

[Haborix]

I didn't verify any of the citations, but this paper suggests the experiment you're looking for didn't occur until the early or mid 1930s. What gave you the impression this experiment was what inspired the work of the late 1920s you refer to?

 

[vanhees71]

I don't think that the SGE was the key driver to discover spin as a generic quantum-mechanical angular momentum but that was the puzzle about the "anomaloud Zeeman effect", and the main confusion was that on the one hand there was the idea of half-integer quantum numbers around rather early. AFAIK this was an idea by Heisenberg just analyzing experimental data, and his picture was completely within the old Bohr-Sommerfeld QT, i.e., no idea about any kind of "non-classical angular momentum" but the idea was that part of an orbital angular momentum was carried by the valence electron and the rest by the rest of the atom. What was then a puzzle was the observation that the magnetic moment associated with this half-integer piece of angular momentum of the valence electron was 1 Bohr magneton and not 1/2 Bohr magneton.

It took a while to realize that there was indeed intrinsic angular momentum which could be half-integer valued but that there was a Lande/gyro factor of (about) 2. One should also be aware that Pauli already knew that from the angular-momentum algebra alone, i.e., only using $[\hat{J}_a,\hat{J}_b]=\mathrm{i} \hbar \epsilon_{abc} \hat{J}_c$ one can derive the possibility of half-integer angular momentum, i.e., eigenvalues $\hbar^2 j(j+1)$ for $\hat{\vec{J}}^2$ with $j$ half of an integer and then the eigenvalues of $\hat{J}_3$ also half-integer $m \hbar$ with $m \in \{-j,-j+1,\ldots,j-1,j \}$. On the other hand he also carefully derived that for the orbital angular momentum $\hat{\vec{L}}=\hat{\vec{x}} \times \hat{\vec{p}}$ the half-integer eigenfunctions go out of the domain of the definition of $\hat{\vec{L}}$ as self-adjoint operators, i.e., that orbital angular momenta must have integer quantum numbers.

The idea of an electron spin with $s=1/2$ together with Lande's rules for the gyro factor (2 for the spin and 1 for the orbital angular momentum), which solved the puzzle about the "anomalous Zeeman effect" then was also consilidated by Pauli's idea of the exclusion principle, leading to the correct "closed shells" of multi-electron atoms, due to the two additional spin states of the electron, i.e., in the lowest orbital there was space for 2 (not only 1) in the next for 8 (not only 4) electrons.

A very nice book about this is Enz's Pauli biography:

https://www.amazon.de/dp/0199588155/

or Eckert's Sommerfeld biography:

https://www.amazon.de/dp/1461474604/

For sure there's also a lot of details in Mehra and Rechenberg's comprehensive history of quantum mechanics.

 

[WernerQH]

TL;DR Summary: I want to find who was the first person to make a Stern-Gerlach experiment with two static magnets

At some point someone does experiments with two magnets, realizing that the beam doesn't split again after identical measurements, but always splits in two after measurements at different angles **<- This is the hole I want to fill**

It may have been Isidor Rabi, inventor of the Rabi method, but the point was not to check that "the beam doesn't split again after identical measurements".

Probably you have fallen victim to the description of idealized experiments that you can find, for example, in the Feynman lectures. These are quite difficult to do in the real world. (Analogous experiments are much easier to do with light and polarization filters.)
In Rabi's method you have two Stern-Gerlach magnets (one as polarizer, the other as an analyzer, so to speak) plus an interaction zone in between. In the interaction zone you can immerse the particles with an RF-field causing transitions between different spin states while monitoring the count of particles that emerge from the second Stern-Gerlach magnet (the analyzer).

By the way, this is key to how atomic clocks work.

EDIT: After looking at @Haborix's post and the paper he quoted, it may well have been Frisch and Segré: https://scholar.google.com/scholar?...der+richtungsquantelung.+II+Z.+Phys.+80+610–6

 

[Meir Achuz]

I believe it was Pauli who kept Goudschmidt and Uhlenbeck from getting the Nobel Prize for deducing spin from atomic spectroscopy. They were just graduate students, Pauli didn't immediately accepted it, and then attributed it to Kramers. I remember Goudschmidt complaining that he often had to start a colloquium by relating that he wasn't a Nobel laureate, as had been stated in his introduction.

 

[vanhees71]

AFAIK Pauli dissuaded Kronig (not Kramers) from publishing his idea. I'm not aware, why Goudsmit and Uhlenbeck didn't get the Nobel Prize for their discovery of spin.

 

[Frigorifico9]

I didn't verify any of the citations, but this paper suggests the experiment you're looking for didn't occur until the early or mid 1930s. What gave you the impression this experiment was what inspired the work of the late 1920s you refer to?

The thing that made me assume this has happened was this: In real space, up and down spin are separated by 180 degrees, but in probability space they are separated by 90 degrees. Using only these observations it is possible to derive the math of spin from scratch, but this experiment hadn't been done, how could Pauli figure out how should these vectors work?

 

[PeterDonis]

how could Pauli figure out how should these vectors work?

Because they can't actually be vectors. Pauli knew from the original S-G experiment results that he was looking for a spin quantum number that was two-valued--since there were only two output beams in the S-G experiment. No integral spin number would work--the smallest nonzero integral spin, spin-1 (i.e., an ordinary vector spin), predicts three output beams, not two. So Pauli was forced to basically invent what are now called spinors, spin-1/2 objects, to get something that would give only two output beams, i.e., two possible values. (The general formula for the number of eigenvalues of spin $j$ is $2 j + 1$.)

 

[Haborix]

To add to @PeterDonis, I would also note that science doesn't always go in the order of (1) experiments with everything you need to know to put together the correct theory then (2) put together the theory. Often, experiments themselves are motivated by some earlier theoretical prediction. There may even be decades between the theoretical prediction and its verification in experiments, e.g., Higgs boson.

 

[vanhees71]

AFAIK the first direct experimental confirmation that a rotation by $2 \pi$ leads to a phase factor of $(-1)$ for a spin-1/2 wave function was done in an experiment with neutrons by Rauch, Zeilinger et al:

https://doi.org/10.1016/0375-9601(75)90798-7