This edition What has changed since 1999

This web edition takes up the text of the 1999 thesis. Three things have changed, however, and are worth declaring: the order in which the cards are read, the fact that some of them have been split, and the new content, written today, that was not there in 1999.

The order

In the original, the path opened with the two Stern-Gerlach experiments, and from them drew the principles on which everything else is built. That was Feynman’s route, and I had followed it.

Today it no longer convinces me. The cascaded Stern-Gerlach experiments are thought experiments: at the time they were not feasible, and when they were finally carried out — around 2019, on an atom chip — it was by methods that require already knowing the theory they are supposed to ground. The premises they rest on, such as the fact that the beams can be recombined leaving no trace of the path taken, are not experimental data: they are a theoretical requirement. Founding the theory on them seems to me to ask the reader for a trust disguised as proof.

Electron diffraction, on the other hand, I actually performed, with the tube and the power supplies described in its card. So the path now starts from the electrons and builds the theory on an experiment that was done. The four principles stay where they are, in the introduction, but declared for what they are: premises. The two Stern-Gerlach cards are at the end, where the reader has the means to judge them and where a thought experiment is in its right place — because nobody is using it as proof any more.

The splits

In the original, the fourth and fifth cards held together the experiment and the theory that follows from it, and the result was two very long chapters. I have split them so that each card does one thing only: the fourth became three cards, the fifth two. Nothing in the text has been moved or rewritten: boundaries have been placed where the reasoning already paused.

In the same way two blocks of pure calculation — the proofs of the commutator formulas and the two appendices to the scattering calculation — have moved into notes, as had already been done for the hydrogen levels. They remain readable in full, but no longer interrupt the thread.

The new content

Not everything one reads here comes from the thesis. Some pages are written today: they serve to take weight off the cards, to recall what is needed before it is used, or to make repeatable what in 1999 could only be described. Where they take up the 1999 text, they take it up without rewriting it.

The original 1999 order

Anyone who prefers to read the work as it was written can follow this sequence. The pages are the same: only the order changes.

1. The Stern–Gerlach Experiment
2. Cascaded Stern–Gerlach Experiments
3. Experiments with Electrons
4. Electron Diffraction then the form of the equation and the Hamiltonian
5. The Rutherford Experiment then the scattering formula
6. Further Developments of the Theory
7. The Franck–Hertz Experiment
8. The Photoelectric Effect
9. Atomic Emission Spectra

What has not changed

The text of the cards that come from the thesis is the 1999 text, apart from minimal corrections and the cross-references between cards, which now go by name instead of by number: that way they do not break if the order should change again one day.