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Quantum Mechanics & How Much Math

Faust in Copenhagen is an account of an extraordinary group of people who explored the mysteries of quantum mechanics in the 1920s and early 1930s. The author is Gino Faust in CopenhagenSegre, a physicist himself, and in the Acknowledgments of this finely written and carefully researched volume he says, “Writing this book has been a labor of love, allowing me to spend time in the company of many of the intellectual heroes of my youth.” Indeed, the figures he writes about were heroes to many of us who had a youthful interest in physics.

In Segre’s book, the lines of history converge on April,1932, in Copenhagen. There a group of physicists meets to review the advance they’ve made in understanding the baffling world of quantum mechanics. They’ve made amazing progress and 1932 was a “miracle year.” At the end of the meeting they’re entertained by a small theatrical production, a comic skit written by fellow-physicist Max Delbruck. It’s a light parody based on Goethe’s culturally heavy Faust, but with the names and personalities changed to resemble the physicists themselves. Of course, we know what they did not, that the political storm gathering in Europe would make their swift gain in knowledge look like a bargain with the devil, a Faustian bargain to be paid for with the horrific birth of the atomic bomb.

Faust in Copenhagen is written for the general reader. It focuses on the physicists, their friendships and conflicts with each other, their competing attempts to understand the structure of the atom, the twists and turns in their lives. For readers with an interest in physics and physicists, this is a fascinating stretch of history — those not interested in such things would probably not pick up the book. There are no equations in this volume, no mathematics at all.

I wonder if you can say much about quantum mechanics without saying at least a little about numbers. One of the people at the center of Segre’s story, Lise Meitner, was an experimentalists, but the others — Niels Bohr, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, Max Delbruck, Paul Ehrenfest — dealt primarily with numbers, the results of experiments which were expressed in numbers. What made quantum mechanics so baffling was that these physicists had to figure out what was happening when they couldn’t see what was happening – they couldn’t peer inside an atom. All they had were numbers and the relationship between certain numbers, and from that they had to work backward to guess at would produce those numbers. It took a while to figure things out because, as they discovered, the weird rules governing the sub-atomic world were nothing like the familiar laws of Isaac Newton that determine the world we experience.

Of course, the same set of experimentally derived numbers can mean different things to different people. Certain numbers might suggest that an electron makes elliptical orbits around the nucleus of an atom. But you can’t really trace the orbit and see it do that; maybe the electron does something else that merely produces the same effect as an elliptical orbit. Werner Heisenberg, very young and very bright, hoped to erase what he felt were false visualizations, and he came up with a way of handling the numbers that didn’t depend on a theory of orbital motion but did produced the right results.Thirty Years that Shook Physics

At the same time, another physicist who wasn’t part of the Copenhagen group, Erwin Schrodinger, did like to visualize the sub-atomic world and he came up with a completely different way of dealing with numbers and, like Heisenberg’s mathematics, his produced the right answers, too. The two men soon hated each other’s math. Of course it’s possible to discuss their conflicting ideas simply as ideas, but explaining a little bit about Heisenberg’s matrices and Schrodinger’s wave equations might allow the reader a better sense of how different those approaches were.

As it happens, one of the physicists not able to attend that meeting in 1932 was George Gamow, who was detained in Russia by the Soviets. He had had a couple of sojourns in Niels Bohr’s Copenhagen in the past and he eventually escaped Soviet Russia, rejoined the physics community in Europe and settled in the United States. Gamow, who was writing important papers in quantum mechanics when he was twenty-four, later wrote a series of books on physics for the general reader; one of those books, Thirty Years That Shook Physics, tells the story of the people who developed quantum theory, much the same tale that Gino Segre tells at greater length and with more detail fifty years later.

Thirty Years That Shook Physics is lighter in tone than Segre’s book and has anecdotes, illustrations, sketches and cartoonish drawings by Gamow himself. It also has some mathematics — not a lot, not blindingly difficult, but real and useful in giving the reader a sense of what the physicists were doing. Segre’s work, with its extended conceit of the Faust story, has more artistry to it, and happily Gamow’s book is still available as a follow-up for interested readers of Faust in Copenhagen. After all, if you don’t like the look of an equation you can always skip it, but if it isn’t there, you won’t know what you’re missing.

More Notes

Tim Carmody, in his excellent piece, "How Haiti Became Poor", notes that President Trump's racist policies and vulgar language have sullied the word "shithole" which used to be one of the all-time great swear words. He's right. It's another terrible power this careless President wields.