Manny’s Reviews > The Theory of Groups and Quantum Mechanics > Status Update

Having read two useful books of background material, I return to the fray. And they have indeed helped: I have no qualms about downgrading from "utterly incomprehensible" to "incomprehensible". Things are moving in a very positive direction.

According to Peter Woit in Not Even Wrong, which I'm rereading, Weyl's book is to the older generation of theoretical physicists as A Brief History of Time is to the general reading public. Virtually every physicist born before 1935 had a copy on their shelf, but it usually turned out that they hadn't got much further than opening it and reading the introduction.

The fundamental observation is that the number of elements in a set is the same irrespective of the order in which they are presented. A minor adaptation of the proof gives you the Jordan-Hölder theorem, then Noether's generalization of it, you apply that to representations of continuous groups, and then it's pretty obvious why spectral lines look the way they do.

At least, obvious if you're as smart as Weyl...

Bohr's original model of the atom seemed to give the right answer most of the time, but there was always a nagging feeling that something wasn't quite as it should be; you kept having to make little adjustments. Looking at it now [i.e. in 1930], the astonishing thing is that it worked as well as it did.

Not a bra in sight, and the translator has decided to call eigenvalues "characteristic values". I wonder why? Residual anti-German feeling after the Great War?

If in the following little is said concerning the experimental facts, it should not be attributed to the mathematical haughtiness of the author; to report on these things lies outside his field. Allow me to express now, once and for all, my deep respect for the work of the experimenter and for his fight to wring facts from an inflexible Nature, who says so distinctly "No" and so indistinctly "Yes" to our theories.