Why Beauty is Truth (46 page)

Erwin was born in Vienna in 1886, the offspring of a mixed marriage. His father, Rudolf Schrödinger, manufactured cerecloth, a waxy cloth used to make shrouds for the dead; he was also a botanist. Rudolf was a Catholic, while Erwin's mother, Georgine Emilia Brenda, was a Lutheran. From 1906 to 1910 Erwin studied physics in Vienna under Franz Exner and Friedrich Hasenöhrl, becoming Exner's assistant in 1911. He gained his habilitation in 1914, at the start of World War I, and spent the war as an officer in the Austrian artillery. Two years after the war ended, he married Annemarie Bertel. In 1920 he became the equivalent of an associate professor in Stuttgart, and by 1921 he was a full professor in Breslau, now the city Wrocław, in Poland.

He published the equation that is now named after him in 1926, in a paper showing that it gives the correct energy levels for the spectrum of the hydrogen atom. This was quickly followed by three other major papers on quantum theory. In 1927, he joined Planck in Berlin, but in 1933, upset by the anti-Semitism of the Nazis, he left Germany for Oxford, where he was made a fellow of Magdalen College. Not long after he arrived, he and Paul Dirac were awarded the Nobel Prize in physics.

Schrödinger maintained a scandalously unorthodox lifestyle, living with two women, and this offended the tender sensibilities of the Oxford dons. Within a year he had moved again, this time to Princeton, where he was offered a permanent position, but he decided not to accept—possibly because his attachment to both wife and mistress in the same household didn't go down any better in Princeton than it did in Oxford. Eventually, he settled in Graz, Austria, in 1936, and ignored the opinions of straitlaced Austrians.

Hitler's occupation of Austria caused severe difficulties for Schrödinger, a known Nazi opponent. He publicly rejected his earlier views (and much later apologized to Einstein for doing so). The ploy didn't work: he lost his job because he was politically unreliable, and had to flee to Italy.

Schrödinger finally settled in Dublin. The year 1944 saw the publication of
What Is Life?
an intriguing but flawed attempt to apply quantum physics to the problem of living creatures. He based his ideas on the concept
of “negentropy,” the tendency of life to disobey—or somehow subvert—the second law of thermodynamics. Schrödinger emphasized that the genes of living creatures must be some kind of complicated molecule, containing coded instructions. We now call this molecule DNA, but its structure was discovered only in 1953, by Francis Crick and James Watson—inspired, in part, by Schrödinger.

In Ireland, Schrödinger retained his relaxed attitude to sexuality, getting involved with students and fathering two children by different mothers. He died of tuberculosis in Vienna in 1961.

Schrödinger is best known for his cat. Not a real cat, but one that appeared in a thought experiment. It is generally interpreted as a reason for not considering Schrödinger's waves to be real physical things. Instead, they are thought of as a behind-the-scenes description that can never be verified experimentally but that has the right consequences. However, this interpretation is controversial—if the waves do not exist, why do their consequences all work out so nicely?

Anyway, back to the cat. According to quantum mechanics, wavicles can interfere with each other, piling up on top of each other and reinforcing when peak meets peak, and canceling each other out when peak meets trough. This type of behavior is called “superposition,” so quantum wavicles can superpose—implying that they can contain a variety of potential states without fully existing in any of them. Indeed, according to Bohr and the famous “Copenhagen interpretation” of quantum theory, that is the natural state of affairs. Only when we observe some physical quantity do we force it out of some quantum superposition and into a single “pure” state.

This interpretation works well for electrons, but Schrödinger wondered what it would imply for a cat. In his thought experiment, a cat locked in a box can be in a superposition of the states alive and dead. When you open the box, you observe the cat and force it into either one state or the other. As Pratchett noticed in
Maskerade
, cats aren't like that. Greebo, a hypermacho cat, emerges from a box in a third state: absolutely bloody furious.

Schrödinger also knew that cats aren't like that, though for different reasons. An electron is a submicroscopic entity, and it behaves like something on the quantum level. It possesses (when we measure it) a particular position or velocity or spin that can be described relatively simply. A cat is
macroscopic, and it doesn't. You can superpose electron states, but not cats. My wife and I have two cats, and when they try to superpose, the result is flying fur and two highly indignant cats. The jargon term here is “decoherence,” which explains why large quantum systems like cats look like the familiar “classical” systems in our daily lives. Decoherence tells us that the cat contains so many wavicles that they all get tangled up together and ruin the superposition in less time than light can travel the diameter of an electron. So cats, being macroscopic systems composed of an absolutely gigantic number of quantum particles,
behave
like cats. They can be alive, or dead, but not both at once.

Nonetheless, on suitably small scales—and we are talking very small stuff here, not anything you can see in a normal microscope—the universe behaves just as quantum physics says it does, and it can do two different things at the same time. And that changes everything.

Just how strange the quantum world must be emerged from the research of Werner Heisenberg. Heisenberg was a brilliant theoretical physicist, but his grasp of experiments was so poor that during his examination for the doctorate he couldn't answer simple questions about telescopes and microscopes. He didn't even know how a battery worked.

August Heisenberg married Anna Wecklein in 1899. He was a Lutheran, she a Catholic, and she converted to his religion to make the marriage possible. They had much in common: he was a teacher and an expert classicist specializing in ancient Greek, while she was a head teacher's daughter and an expert on the Greek tragedies. Their first son, Erwin, was born in 1900 and became a chemist. Their second, Werner, was born in 1901 and changed the world.

Germany was still a monarchy at this time, and the teaching profession carried high social status, so the Heisenbergs were financially comfortable and could send their sons to good schools. In 1910, August was made professor of medieval and modern Greek at the University of Munich, to which city the family moved. In 1911, Werner started at the King Maximilian School in Munich, where Planck had also studied. Werner's grandfather, Nikolaus Wecklein, was the school principal. The boy was bright and quick, partly because his father encouraged him to compete with his elder brother, and showed remarkable abilities in math and science. He had musical
talent too, and learned the piano so well that by the age of 12 he was performing in school concerts.

Heisenberg later wrote that “both my interests in languages and in mathematics were awakened rather early.” He earned top grades in Greek and Latin and did well in mathematics, physics, and religion. His worst subjects were athletics and German. His mathematics teacher, Christoph Wolff, was excellent, and stretched Werner's abilities by setting him special problems to solve. Soon the pupil had outclassed the teacher, and Heisenberg's school report stated, “With his independent work in the mathematical-physical field he has come far beyond the demands of the school.” He taught himself relativity, preferring its mathematical content to its physical implications. When his parents asked him to tutor a local college student for her exams, he taught himself calculus, a subject not included in the school curriculum. He developed an interest in number theory, saying that “it's clear, everything is so that you can understand it to the bottom.”

To help Werner improve his Latin, his father brought him some old papers on mathematics, written in that language. Among them was Kronecker's dissertation on a topic (“complex units”) in algebraic number theory. Kronecker, a world-class number theorist, famously believed that “God created the integers—all else is the work of Man.” Heisenberg was inspired to have a go at proving Fermat's Last Theorem. After nine years in the school he graduated at the top of his class and attended the University of Munich.

When World War I broke out, the Allies blockaded Germany. Food and fuel were in very short supply; the school had to be closed because it could not be heated, and on one occasion Werner was so weak from starvation that he fell off his bike into a ditch. His father and his teachers were fighting in the army; the young men who remained behind received military training and nationalistic indoctrination. The end of the war brought the end of the German monarchy as well, and Bavaria briefly had a socialist government along Soviet lines, but in 1919 German troops from Berlin kicked out the socialists and restored a more moderate social democracy.

Like most of his generation, Werner was disillusioned by Germany's defeat and blamed his elders for their military failure. He became the leader of a group associated with the New Boy Scouts, an extremist right-wing organization that aimed to restore the monarchy and dreamed of a Third Reich. Many branches of the New Boy Scouts were anti-Semitic,
but Werner's group included a number of Jewish boys. He spent a lot of time with his boys, camping and hiking and generally trying to recapture a romantic vision of Germany as it once had been, but these activities ended in 1933 when Hitler banned all youth organizations other than those he had set up himself.

In 1920, Werner went to the University of Munich, intending to become a pure mathematician until an interview with one of the pure math professors put him off the idea. He decided instead to study physics under Arnold Sommerfeld. Immediately recognizing Werner's abilities, Sommerfeld allowed him to attend advanced classes. Soon Werner had done some original research on the quantum approach to atomic structure. His doctorate was awarded in 1923, breaking the university's record for speed. In the same year, Hitler tried to overthrow the Bavarian government in the “beer hall putsch,” intended as a prelude to a march on Berlin, but the attempt failed. Hyperinflation was rampant; Germany was coming to pieces.

Werner continued working. He collaborated with many leading physicists, all of whom were thinking about quantum theory because that was where the action was. He worked with Max Born to devise a better theory of the atom. It occurred to Heisenberg to represent the state of an atom in terms of the frequencies observed in its spectrum—the kinds of light that it emitted. He boiled this idea down to a peculiar kind of mathematics involving lists of numbers. Born eventually realized that this kind of list was actually quite respectable: mathematicians called it a matrix. Happy that the ideas made sense, Born sent the paper off for publication. As the ideas developed, they matured into a new, systematic mathematics of quantum theory: matrix mechanics. It was seen as a competitor to Schrödinger's wave mechanics.