The Physical Tourist in Frankfurt (1)

I can imagine some of our readers have been in Frankfurt am Main at least once - albeit in most cases only at the airport. If you have some time to kill, for example because of flight delays, or if you just want to see a bit of the town: the city centre of Frankfurt is easy to reach by a 10-minute ride with the S-Bahn from the airport, either to "Hauptbahnhof" (the main train station), or to "Hauptwache" (near the city centre) [1].

Besides the standard "places to see", the scientifically minded tourist might definitely want to have a look at the Senckenberg Museum, one of the largest museums of natural history in Europe. It is run by the Senckenbergische Naturforschende Gesellschaft and named after Johann Christian Senckenberg, a Frankfurt physician whose 300th birthday is celebrated this year. On display in the museum are for example the unique, 50 million year old fossils from the nearby Messel pit, but kids will probably be most fascinated by the skeletons of dinosaurs and mastodons - and by the true-to-life replicas of a Tyrannosaurus and a Diplodocus in the front yard of the museum.

The Senckenberg Museum with the replica of a Tyrannosaurus. The building on the left with the green dome covering a small astronomical observatory is the home of the Physikalischer Verein.

If you're standing in front of the museum [2], you will notice to the left a building with a small astronomical observatory on the roof - this is the home of the Physikalischer Verein, the "Physical Association". Both the Senckenbergische Naturforschende Gesellschaft and the Physikalischer Verein have quite an interesting history: They have been founded in 1817 and 1824, respectively, following a suggestion by Johann Wolfgang von Goethe at a visit to his hometown Frankfurt, as institutions of research and public outreach in the natural sciences. Foundation was not by the local ruler or government, but by private persons - Frankfurt citizens who until today operate and generously finance these science institutions out of personal memberships and private donations.

The building of the Physikalischer Verein at the corner Senckenberganlage - Robert-Mayer-Straße. It was constructed in 1907 and harboured the Physics Institute of the Frankfurt University between 1914 and 2005.

Since the time of its foundation, the Physikalischer Verein had been engaged in a lot of scientific activities: It organised astronomical observations to establish time for the City of Frankfurt, lectures on science for students and the Frankfurt citizens, and it sponsored research in physics, chemistry, and technology. To this end, the Verein paid lecturers and scientists and provided office and laboratory space for them. Early research at the Physikalischer Verein included, for example, the development of an electric telegraph by Samuel Soemmering, and the demonstration of the telephone by Philipp Reis. When the Frankfurt University was founded in 1914, all these activities were integrated into the physics institute of the new university, and hosted in a large building next to the Senckenberg Museum, which the Physikalischer Verein had built in 1907.

In the meantime, the physics institute has moved on to a new campus on the outskirts of Frankfurt, and the building is mostly empty, used only for public lectures on astronomy and observations at the telescope on Friday nights. There are plans to establish a Science Centre and a Planetarium on the premises, but currently, the building is dreaming of its exciting days in the past - for example, when in the early 1920s, Otto Stern and Walther Gerlach had been conducting here the famous experiment demonstrating space quantisation of magnetic moments for the first time.

The entrance door to the - now mostly empty and unused - building of the Physikalischer Verein. On the left is the plaque commemorating ...
... the Stern-Gerlach experiment, conducted here in 1921/22. The plaque shows schematically the apparatus of the experiment, and Stern and Gerlach to the left and right, respectively. The text says: "In February 1922, the fundamental discovery of the space quantisation of the magnetic moments in atoms was made in this building of the Physikalischer Verein, Frankfurt am Main, by Otto Stern and Walther Gerlach. The Stern-Gerlach experiment is the foundation of important physical and technical developments of the 20th century, such as the nuclear resonance method, the atomic clock, or the laser. Otto Stern was awarded the Noble prize for this discovery in 1943."

In the early Bohr-Sommerfeld theory for the quantisation of the motion of electrons in atoms, orbiting electrons could have only discrete values of angular momentum, and thus, only discrete magnetic moments. Moreover, in an external magnetic field, these magnetic moments were supposed to have only specific, discrete orientations with respect to the direction of the field. For example in silver atoms, which have one "hydrogen-like" valence electron, there should be only two possible orientations of the magnetic moment in an external field.

Otto Stern, who had been as a postdoc with Einstein in Prague and Zurich and had become an assistant to Max Born in Frankfurt in 1919, had the idea that one might check space quantisation of magnetic moments using atomic beams - a technique quite new at that time: atoms are evaporated from an oven into a vacuum, and with systems of apertures and screens, one can obtain well-defined, sharp beams. Stern and Born had successfully used this method to study the thermal velocity distribution and the mean free path of atoms, and Stern thought it should be possible to test if space quantisation is real:

If a beam of atoms with a magnetic moment passes through a magnetic field with a strong gradient, the gradient of the field causes a deflection of the atoms according to the orientation of their magnetic moments. Now, if the magnetic moments can have any orientation in the magnetic field (as in the classical theories of the atom of Lorentz and Zeeman), the deflection would have any value, and the beam would be smeared out. If, however, the magnetic moments could only have some discrete orientations in the magnetic field (two, for silver atoms), deflection would also be discrete, and the beam should split (in two beams, for silver atoms). Stern was confident that this splitting could be measured (Otto Stern: Ein Weg zur experimentellen Prüfung der Richtungsquantelung im Magnetfeld. Zeitschrift für Physik 7 (1921) 249; English translation in Zeitschrift für Physik D: Atoms, Molecules and Clusters, 10 (1988) 114), but he also knew that the experiment was tricky.

Fortunately, he had a colleague who was an expert in atomic and molecular beams: Walther Gerlach, assistant to the professor of experimental physics in Frankfurt since 1920. Stern had no trouble to convince him that they collaborate on this problem.

They had to cope with many technical and organisational problems: The experiment was quite delicate, requiring adjustments of the beam and magnets to within 0.01 millimetre, maintaining a vacuum for the beam, and detection of tiny amounts of silver atoms deposited by the beam. Moreover, funding was difficult because of the consequences of the war and the beginning inflation. They could get money for the experiment from grants of Einstein at the Kaiser-Wilhelm-Institut in Berlin, from Henry Goldman of Goldman and Sachs, and from entrance fees Max Born had charged for a series of public lectures on relativity [3].

But finally, in February 1922 - Stern had already left Frankfurt and moved on to another position in Rostock - Walther Gerlach succeeded in measuring the splitting, in quantitative agreement with the calculations of Stern.

The postcard Walther Gerlach sent to Niels Bohr on 8 February 1922 to tell him about the discovery of space quantisation. It shows a photograph of the beam splitting (actually, the width of the splitting is only 0.2 millimetre), with the note: "Attached the continuation of our work (Zeitschrift für Physik 8 (1921) 110): The experimental proof of directional quantisation. Silver without magnetic field / with magnetic field. We congratulate on the confirmation of your theory." (Source: Physics Today, Courtesy AIP Emilio Segrè Visual Archives). The same photos are also shown in the short discovery paper by Otto Stern and Walther Gerlach: Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld, Zeitschrift für Physik 9 (1922) 349.

It's ironic, in a sense, that the theory Stern had used to calculate the splitting of the beams of silver atoms was wrong: as we know today, the splitting Gerlach eventually managed to observe is not caused by an electron orbital angular momentum taking on projections along the axis of the magnetic field of ±h/2π, but by the electron spin, which is only have as large and has projections ±h/4π. However, thanks to the electron g factor of 2, the value of the splitting coincides, again, with the calculation of Stern.

These subtleties notwithstanding, the Stern-Gerlach experiment is now one of the prototypical experiments showing quantum physics at work - and in case you have time to kill in Frankfurt, you can have a look at the place where all this has happened some 85 years ago.

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[1] To check out connections using public transport, the website of the local transport authority, rmv.de, is very helpful - useful connections are Airport-Hauptbahnhof, Airport-Hauptwache (city centre), or Airport-Bockenheimer Warte (Senckenberg Museum and Physikalischer Verein).

[2] For a first orientation, maps.google.com is as usual helpful. The dinosaurs in the yard aren't yet there in the aerial photo.

[3] A full account of the very interesting circumstances around the discovery of the Stern-Gerlach splitting can be found in Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics, by Bretislav Friedrich and Dudley Herschbach, Physics Today, December 2003, pages 53-59 (PDF), and Space quantization: Otto Stern's lucky star, also by Friedrich and Herschbach, Daedalus, Winter 1998.

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TAGS: physics, Stern-Gerlach experiment, Frankfurt