Frankfurt, 8 February 1922
The Postcard With Two Silver Roads
A neutral silver beam crossed an inhomogeneous magnetic field. The field-on plate carried two deflected deposits and no detected central component. Choose the rule the atoms obey, then make its detector trace.
Computing the force integral.
The answer outlived its explanation
The 1921 prediction and the later spin account land on the same two ideal positions in this approximation. The marks settled continuous versus discrete projection. They did not, by themselves, tell the experimenters what carried the moment.
Every position below is recomputed as z = K g m with the current apparatus. No row is scaled to fit its own separation.
| model | allowed quantum values | moment projections | ideal detector positions |
|---|
The 1921 rule excluded m = 0. It predicted a doublet, not a triplet.
Ground-state silver has L = 0. Its unpaired electron supplies the doublet.
Computing old-rule versus ideal-spin residual.
Change the instrument, not the verdict
These are model choices, not a reconstruction of the 1922 apparatus. The field gradient can rise or fall along the magnet. Faster atoms spend less time in it. The slit, velocity spread, and detector resolution blur every hypothesis by the same rules.
Fz = μz ∂Bz/∂z
zdet = μz / (M v²) × ∫0L (L + D - x) (∂Bz/∂z) dx
The check
Published anchors
The browser uses the 2022 CODATA Bohr magneton μB = 9.2740100657 × 10-24 J/T, the 2022 CODATA atomic mass constant u = 1.66053906892 × 10-27 kg, and 107.8682 u as a rounded standard-atomic-weight proxy for natural silver. These are published inputs, not derived from the postcard. The verifier independently derives μB from eℏ/(2me) and reproduces the published value at its stated precision before checking this page.
Gerlach and Stern's 1922 report says the field produced two discrete beams and that they found no evidence for undeflected atoms. “No evidence” is a detection statement, not an exact zero. Stern's 1921 proposal gives the old rule's two values, m = -1 and +1. Modern ground-state silver has L = 0 and an unpaired-electron spin s = 1/2 with ms = -1/2 or +1/2. Here gs = 2 is the published one-significant-figure explanatory approximation. It is not the exact free-electron or bound-atom factor. The explicit electron-spin hypothesis was published in 1925.
Free choices and uncertainty
- The eight controls, the linear gradient profile, equal populations of allowed states, the 41-point Gaussian velocity proxy truncated at ±3σ, the top-hat slit, the Gaussian detector kernel, the fixed 16 mm window, the 240-dot burst, and its deterministic seed 19220208 are choices made here.
- The density is a probability density with total area one before the fixed detector window clips it. It is never rescaled by a model's separation. The canvas scales each curve's vertical peak to the available height, while the horizontal millimetre axis and the printed density stay fixed. The dots are a seeded sample from that density, not experimental data.
- This is a one-dimensional, adiabatic, small-deflection model. It omits transverse fields, field zeros, hyperfine and isotope substructure, collisions, detailed pole geometry, glass chemistry, and the original trace's curved asymmetry.
- The classical band tests one stated model: equal fixed dipoles with isotropically continuous orientations. The 1922 trace does not rule out every later classical account.
- Zero gradient, zero magnet length, or zero moment would make every model coincide at the center. Those vacuous settings are not reachable here. A blur wider than a split makes it unresolved; it does not make the models agree.
Independent check: node research/stern-gerlach/verify-stern-gerlach.mjs.
Sources and the historical boundary
- Walther Gerlach and Otto Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld”, Zeitschrift für Physik 9, 349-352 (1922). Primary experimental report.
- Otto Stern, “Ein Weg zur experimentellen Prüfung der Richtungsquantelung im Magnetfeld”, Zeitschrift für Physik 7, 249-253 (1921). Primary proposal and two-component prediction.
- Martin Bauer, “The Stern-Gerlach Experiment, Translation of: ‘Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld’” (2023), arXiv:2301.11343v1. Close English translation, one version, submitted 26 January 2023.
- Walther Gerlach and Otto Stern, “Über die Richtungsquantelung im Magnetfeld”, Annalen der Physik 379, 673-699 (1924). Primary quantitative account.
- George E. Uhlenbeck and Samuel Goudsmit, “Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons”, Die Naturwissenschaften 13, 953-954 (1925). Primary electron-spin note.
- Bretislav Friedrich and Dudley Herschbach, “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics”, Physics Today 56(12), 53-59 (2003). Postcard, later interpretation, and the reenactment showing smoke darkened silver while sulfurous breath alone did not.
- Horst Schmidt-Böcking, Lothar Schmidt, Hans Jürgen Lüdde, Wolfgang Trageser, Alan Templeton, and Tilman Sauer, “The Stern-Gerlach experiment revisited”, European Physical Journal H 41, 327-364 (2016). Modern physical and historical review.
- NIST, 2022 CODATA recommended values, web version 9.0 (2024). Fundamental constants used by the simulator.