Heisenberg’s breakthrough

From In Search of Schrödinger’s Cat: Quantum Physics and Reality -by John Gribbin – we’re talking about atoms now. Other excerpts here and here and here. The following excerpt is about Werner Heisenberg, and honestly:

I barely know WHAT is going on here, really, but I can tell that it is FASCINATING. Actually, I’m exaggerating. I know what is going on here, it’s just that I could never summarize it or try to talk about it without sounding like a blundering idiot. All I can do is just follow along, try to keep up. I love this stuff.

Werner Heisenberg was born in Wurzburg on 5 December 1901. In 1920 he entered the University of Munich, where he studied physics under Arnold Sommerfeld, one of the leading physicists of the time who had been closely involved with the development of the Bohr model of the atom. Heisenberg was plunged straight into research on quantum theory, and set the task of finding quantum numbers that could explain some of the splitting of spectral lines into pairs, or doublets. He found the answer in a couple of weeks — the whole pattern could be explained in terms of half-integer quantum numbers. [Uhm … okay. I THINK I get that.] The young, unprejudiced student had found the simplest solution to the problem, but his colleagues and his supervisor Sommerfeld were horrified. To Sommerfeld, steeped in the Bohr model, integral quantum numbers were established doctrine, and the young student’s speculations were quickly quashed. The fear among the experts was that by introducing half integers into the equations they would open the door to quarter integers, then eighths and sixteenths, destroying the fundamental basis of quantum theory. But they were wrong.

Within a few months, the older and more senior physicist Alfred Lande came up with the same idea and published it; it later turned out that half-integer quantum numbers are crucially important in the full quantum theory, [Uhm, okay, if you say so …], and play a key role in describing the property of electrons called spin. Objects that have integer or zero spin, like photons, obey the Bose-Einstein statistics, while those that have half-integer spin (1/2 or 3/2, and so on) obey the Fermi-Dirac statistics … [Then follows a bunch of math, which I don’t feel up to typing.]

So Heisenberg missed a chance for credit for a new idea in quantum theory; but the point of the story is that just as it took young men in the previous generation to develop the first quantum theory, so in the 1920s it was time again for young minds unencumbered by ideas that “everyone knows” must be right to take the next step forward. Heisenberg certainly made up for missing out on one minor scientific “first” with his work over the next few years.

After a team working in Gottingen under Born, where he had attended the famous “Bohr festival”, Heisenberg returned to Munich and completed his PhD in 1923 — still not quite 22 years old. At that time, Wolfgang Pauli, a close friend of Heisenberg’s, equally precocious and another former student of Sommerfeld’s, was just moving on from a spell as Born’s assistant in Gottingen, and Heisenberg took over the post in 1924. It was a job that gave him the opportunity to work for several months with Bohr in Copenhagen, and by 1925 the precocious mathematical physicist was better equipped than anyone to find the logical quantum theory that every physicist expected to be found eventually, but no one expected to find so soon.

Heisenberg’s breakthrough was founded on an idea he picked up from the Gottingen group — nobody now is quite sure who suggested it first — that a physical theory should only be concerned with things that can actually be observed by experiments. This sounds trite, but it is actually a very deep insight. An experiment that “observes” electrons in atoms, for example, doesn’t show us a picture of little hard balls orbiting around the nucleus — there is no way to observe the orbit, and the evidence from spectral lines tell sus what happens to electrons when they move from one energy state (or orbit, in Bohr’s language) to another. All of the observable features of electrons and atoms deal with two states, and the concept of an orbit is something tacked on to the observations by analogy with the way things move in our everyday world … Heisenberg stripped away the clutter of the everyday analogies, and worked intensively on the mathematics that described not one “state” of an atom or electron, but the associations between pairs of states.