# How did Stern-Gerlach experiment change the concept of space quantization and electron spin?

I got confused by a question which is : "How did Stern-Gerlach experiment change the concept of space quantization and electron spin?" Its the question asked in our previous year examination. And I cannot make sense of it. In almost all of books its written that Stern-Gerlach experiment proved the concept of space quantization and electron spin.

1. I have read about the experiment, and also about its history, and at that time Stern and Gerlach didn't know about the concept of spin.

The magnetic moment they measured of silver atoms was not due to orbital angular momentum but due to spin angular momentum.

So how can it change the concept of spin? Does the question want to ask how the stern-gerlach experiment would have changed the concept of spin if both experimenters knew something about the spin. Since Uhlenbeck and Goudsmit proposed somewhat classical concept of spin so if the experiment would have been performed after Uhlenbeck's hypothesis then the classical concept would have been changed to quantum one.

1. And also it proved the concept of space quantization which was proposed by Sommerfeld :

The plane in which the orbit could be located in a magnetic field could have only certain definite orientations in space.

It proved the concept so why its asked that it changed the concept of space quantization?, What the question actually means?

• What do you mean by "space quantization?" This is not standard terminology. – Ben Crowell Apr 1 '16 at 16:02
• I think this could potentially be a good question, but right now it's too unclear what exactly you're asking. – Danu Apr 1 '16 at 17:27
• @Danu l I edited the question, I hope it will clear somewhat what I want to ask. – shivani Apr 4 '16 at 8:23

## 1 Answer

Stern and Gerlach indeed did not know anything about the electron spoin when they conducted their experiments in 1921-22. Their experiments rather were originally misinterpreted to confirm the old quantum theory of Bohr-Sommerfeld, without spin, and eventually led to the emergence of the concept of spin proposed by Goudsmit and Uhlenbeck in 1925-26. Interestingly Goudsmit and Uhlenbeck did not even mention Stern-Gerlach results, their motivation was the anomalous Zeeman effect, two many spectral lines observed in a magnetic field.

Larmor’s classical theory predicted that the beam of silver atoms would show maximum intensity in the center, even in a magnetic field, whereas Sommerfeld's theory predicted spatial separation into two peaks (assuming silver atoms were in a state with angular momentum 1). Originally they did not detect any separation, but after 1922 refinements it was detected. This meant that angular momentum is quantized, hence the excitement, as Pauli put it:"Hopefully now even the incredulous Stern will be convinced about directional quantization". This is what "space quantization" refers to, quantization with respect to direction in space, but the name is highly misleading today when literal quantization of space at Planck length is being discussed.

As it turned out, while they were right that something directional was quantized in the experiment they were mistaken as to what it was. Contra Stern and Gerlach the silver atoms were actually in a state with angular momentum 0, not 1, and Sommerfeld's spinless theory predicted no separation, like Larmor's. So in fact their experiment disconfirmed both. See Right Experiment, Wrong Theory: The Stern-Gerlach Experiment by Franklin and Perovic.

This was not the first case of spin implicitly appearing in early experiments, which were misinterpreted to confirm a theory they did not in fact confirm. Einstein-de Haas and Barnett conducted a series of experiments in 1915-16 designed to measure the gyromagnetic effect due to Ampere's molecular currents. The effect they did measure was in fact due to spin, and only a measurement error prevented them from detecting the discrepancy, which got the name "gyromagnetic anomaly", see How did gyromagnetic ratio come up before quantum mechanics, and who introduced it? However, the discrepancy came to light by 1919, and went under the name "gyromagnetic anomaly", Beck and Barnett even discussed it with Einstein before the introduction of spin. The irony is that the spin origin of the anomaly meant that the gyromagnetic effect received no contribution from the orbital motion of electrons, the very "molecular currents" it was taken to detect.

• 1. According to Sommerfeld theory L = 1 and there was no spin. He had proposed three quantum numbers n,k,m. n=k=1 (for circular orbit n=k) so m = + and - 1 (two orientations, m=0 state was rejected) So the experiment was right but the theory was wrong. 2. According to new quantum theory L = 0 but without spin there should not be any splitting, again wrong theory or incomplete theory. 3. After Uhlenbeck's hypothesis L=0 and $S= + or - 1/2$ so it predicted the splitting. – shivani Apr 4 '16 at 8:50