Die Brückenbauer

Leiden, late October 1927. Paul Ehrenfest has just come home from the Fifth Solvay Conference in Brussels and has not slept properly in four days. Tatiana, his wife, is waiting at Witte Rozenstraat 57 with tea, a pencil, and questions. He is Austrian. She is Russian. They met at the University of Goettingen because he argued with the administration to let her into the mathematics club -- women were barred. The argument became a friendship, the friendship became a marriage, and the marriage became a body of work that transformed statistical mechanics. Paula has visited them several times now. Paul has never stopped asking her questions. Tatiana has never stopped correcting her answers.

Bohr, in the previous episode, told Paula about the man who stood between him and Einstein at Solvay and tried to make them understand each other -- and pointed her toward Leiden. Today Paula goes there. The story usually told stops at the bridge-builder. The story has another half. Tatiana co-authored the Encyklopaedie article on the foundations of statistical mechanics, the one van der Waerden's generation grew up reading. She is rebuilding the axiomatics of thermodynamics from Caratheodory upward. Her name is on the title page and somehow vanishes from the citations. Paula has come for both halves.

Paul talks first, because he always talks first. The Solvay account pours out of him. Bohr towering completely over everybody. Einstein like a jack-in-the-box, jumping out fresh every morning with a new thought experiment, and Bohr awake all night to refute it. Paul standing in the middle, going to one and then the other, trying to translate. At the height of Einstein's resistance, Paul wrote on the blackboard the Tower of Babel verse from Genesis: "The Lord did there confound the languages of all the earth." The conference is the moment classical physics realises it is being asked to die, and Paul is the one trying to organise the funeral with kindness.

The conversation moves to the theorem that carries his name. The Ehrenfest theorem, 1927: the expectation values of position and momentum in quantum mechanics obey the classical equations of motion. The bridge between two languages is not metaphorical. It is a statement about averages. It is also exactly the kind of result Paul cannot stop asking awkward questions about, because averages do not tell you what one electron is doing, and what one electron is doing is what students keep asking him, and he has no answer he believes.

Tatiana intervenes. She always intervenes when Paul gets too excited. She tells Paula that progress in axiomatics is slow, and that, unlike Paul, she does not measure progress by the number of exclamation marks she produces per hour. She wants to know precisely what Paula means by a "branch" of the multiverse, what the topology of Paula's access is, whether her measurements respect the second law. She does not soften her questions. Einstein once described her as "such a sturdy and steadfast personality as one seldom encounters" and as "possessed somewhat by a logical polishing devil." Paula meets that devil tonight, and the polishing is not gentle.

The episode closes on the question Paul puts to Paula at the door. Einstein once called him the best teacher in our profession he had ever known. Paul does not believe that. He thinks he is a man who never finished his own physics because the formal apparatus -- what he called the infinite Heisenberg-Born-Dirac-Schroedinger Wurst-machine -- was not the kind of physics he could love. He asks Paula whether, in 2127, anyone still loves physics in the way he means it. Or whether by then it has all become formalism. Paula's answer is honest, and not consoling. They part agreeing that the night was useful and that Tatiana was right about most things.