He gave himself over to the routines of the ill.
He floated around the swimming pools, slept out in the open beneath a layer of animal pelts, and burned his lungs with the glacial air of the mountains and the searing heat of the saunas; he let his back be massaged with oils, his body tortured with cupping glasses, dragging himself from room to room with the rest of the inmates, enjoying the consolation of a person whose entire life has been reduced to the inflexible repetition of therapy. The only real benefit he noticed from all of this was an almost miraculous recovery in his ankle. Soon he could walk without need of a cane, which permitted him to spend as little time as possible in his room; a considerable relief, as from there he could hear the sobs and groans of his neighbour as clearly as if they were sharing a bed. He spent his nights with a girl who worked as a lifeguard at the clinic’s pool and slept with Schrödinger and his fellow patients in exchange for money—an arrangement which Doctor Herwig tolerated. During the day, when he had no treatments, Schrödinger would stroll through the clinic like a sleepwalker, crossing the endless hallways and trying not to think of Miss Herwig, his equation or his wife, who would certainly have spent the previous weeks fucking incessantly while he was fantasizing about an adolescent. He thought of the classes he would have to resume as soon as he had recovered, of the tedium of repetition, the blank stares of his students and the texture of chalk as it crumbled between his fingers, and suddenly he seemed to see his entire future life as though it were composed of parallel and simultaneous scenes opening like a fan and leading off in all possible directions; in one, he and Miss Herwig ran away to start their lives together; in another, his health took a sudden turn and he died there in the clinic, drowning in his own blood; in a third, his wife left him, but he flourished, professionally; in most of these scenarios, Schrödinger continued down the same path he had taken up until then, remaining married to Anny and working as a professor until death overtook him at some unknown European university. Laid low by depression, he walked down to the first floor and out onto the terrace to take some fresh air. He was unready for the desolation he would see outside. It seemed as though someone had erased the entire world. Where the lake had once been, surrounded by trees and cradled by the distant profile of the mountains, there was now only an immense burial shroud, a layer of snow so even and dense that it obscured every last detail of the landscape. All the roads would be blocked. Schrödinger could not leave the clinic even if he wished. He went back inside with a sensation of seclusion, of claustrophobia, that he could hardly bear.
His health worsened as the new year approached. When he was overcome with fever, he had to give up his walks and submit to bed rest. His skin felt raw, and even the touch of his sheets bothered him. If he closed his eyes, he could hear the clicking of the spoons in the canteen, the movement of the chess pieces in the recreation room, the shriek of the steam in the laundry. Rather than ignore them, he concentrated on them, trying to drown out the sound of Miss Herwig’s breath, that thin thread of air that could barely enter through her swollen throat and was incapable of filling her lungs. Schrödinger had to restrain his desire to break down the door between them and hold the sick girl in his arms; at the same time, he could not even gather the energy to put a title to the article in which he had formalized his equation. He had decided to publish it as it was and let others unravel its significance, if there was any. Truthfully, it no longer mattered to him: every time Miss Herwig coughed, he was shaken by uncontrollable spasms. This same relapse seemed to have affected everyone at the sanatorium. The cleaning staff had not come to his room in two days, and when he called reception to complain, they told him everyone was busy with more urgent cases than his own. That same morning, two boys had died: the twins Schrödinger had seen in the dining room hanging on Miss Herwig’s neck. Schrödinger could give no expression to his rage, and simply asked them to advise him when the roads were once again clear. He wanted to leave as soon as possible.
The next day there was a blizzard. Schrödinger spent the entire morning in bed, watching how the snowflakes accumulated on his window ledge until at last he fell back to sleep. Two knocks on his door woke him. He got up, his hair in disarray, food stains on his pyjamas, but the man he saw when he opened the door looked infinitely worse; Doctor Herwig resembled one of those soldiers Schrödinger had seen return from the trenches, eyes filmy from clouds of chlorine gas. His host begged his pardon for the pitiful state of Schrödinger’s room. The clinic was going through a crisis. At reception, he had been told Schrödinger was planning to depart, and he had come to convey a message from his daughter: might a final lesson be possible before he left? The doctor looked at the ground as he spoke, as though he were asking for something unpardonable. Schrödinger could hardly conceal his enthusiasm. While the doctor went on to say that he didn’t wish to trouble him and that he understood perfectly if the request was out of line, Schrödinger dressed clumsily, explaining he was not inconvenienced in the least, quite the contrary, it would be a pleasure, he could do it right then, right away, he just needed five minutes to comb his hair, or not even that, if he could just find his goddamned shoes, where the hell had he left them! The doctor watched him stomping from one end of the room to the other with the bewildered expression of a man who has lost what matters most to him in the world—an expression Schrödinger could not fathom until he saw Miss Herwig’s state.
Pale and skeletal, she was submerged in piles of cushions that closed in on her like the petals of a monstrous flower. She was so thin that Schrödinger began to wonder whether time had passed differently for each of them: it was impossible that a human being should undergo a change so drastic in a matter of days. The skin on her neck had turned transparent and the veins were so clearly marked that Schrödinger could have measured her pulse just by looking at her. Sweat pearled on her forehead, her hands shook from fever, and her body seemed to have shrunk to that of a nine-year-old girl. Schrödinger did not dare enter the room. He stayed standing there in the doorway, with Doctor Herwig waiting behind him, until she opened her eyes, looking at him with the same expression of reproach that had greeted him during their first lesson. The girl asked her father to leave the two of them alone, and told Schrödinger to sit down.
Schrödinger walked towards a chair, but she patted the mattress beside her, inviting him over to the bed. Schrödinger did not know where to look: he could not reconcile the image of the woman he had dreamt of with the one he now saw. He felt immense relief when she asked him to examine her notebook; she had completed her final test. Schrödinger looked at the exercises, and, at first, the numbers seemed to him unintelligible; he was so shaken that he could not solve the basic equations he himself had devised for her. Playing for time, he asked her to explain to him how she had arrived at a certain result, the only one that evinced a certain degree of difficulty. Miss Herwig told him she could not: her mind had presented her with the results, and she had had to work backwards to write out her calculations. Schrödinger confessed to a similar affliction, but said he had abandoned that intuitive approach to mathematics when he entered the university, in order to satisfy his professors. Only now had he begun to give his intuition free rein, and he had gone so far he had no idea how to find the way back. Miss Herwig asked him if he had made progress on his equation. Schrödinger stood up and began pacing from side to side while he spoke of the strangest aspect of his formula.
In appearance, he said, it was very simple: applied to any physical system, it allowed one to describe its future evolution. If used for a particle, such as an electron, it revealed all its possible states. The problem lay in its central term—the soul of the equation—which Schrödinger had represented with the Greek letter ψ and had baptized as the “wave function”. All the information one could wish to have about a quantum system was contained in the wave function. But Schrödinger did not know what it was. It had the form of a wave, but could not be a real physical phenomenon, because it moved outside this world, in multidime
nsional space. Perhaps it was only a mathematical chimera. The only certain thing was its power, which seemed unlimited. In theory, Schrödinger could apply his equation to the entire universe: the result would be a wave function that would encapsulate the future evolution of all things. But how would he convince others that such a thing could exist? ψ was undetectable: it would leave no trace on any type of instrument. Neither the most advanced apparatus nor the most ingenious experiments could capture it. It was something new, of a nature totally distinct from that of the world it described with unsettling precision. Schrödinger knew it was the discovery he had longed for his entire life, but he had no way of defending it. He had not derived his equation from pre-existing principles. His thinking had not departed from any known basis. The equation itself was a principle, and his mind had pulled it from nothing. When he turned to see whether Miss Herwig had been able to follow his long disquisition, he found her sound asleep.
For Schrödinger, she was no less beautiful than ever. He pushed aside the cushions surrounding her to pull back a lock of hair that had covered her face, and he could not resist touching her further. He caressed her neck, her shoulders, her collarbones, followed the strap of her nightgown to the soft curvature of her breasts and circled the place where he imagined her nipples lay. He continued on towards her navel and stopped a few millimetres from her pubis, too timid to go further. He closed his eyes and held his breath, listening to Miss Herwig’s clipped respiration, and when he opened them, she threw off the sheet that covered her and he saw her transformed into the goddess of his dreams, a black-skinned corpse covered in suppurating wounds and scabs, her tongue lolling from her smiling skull while her hands pulled open the shrivelled lips of her vagina, where the legs of a massive beetle flailed, trapped in a tangle of snow-white hairs. The vision lasted a fraction of a second, then the sheet once more covered Miss Herwig, who was sleeping as though she had never awakened. Still, Schrödinger ran out in dread. He gathered his papers and fled the centre without paying his bill, dragging his suitcases against the stormy wind and trying to reach the train station, not knowing if the roads would be closed from the snow.
IV
THE KINGDOM OF UNCERTAINTY
In Zurich, Schrödinger not only recovered his health but gave the impression of a man possessed by genius.
He built on his equation until it comprised a complete mechanics developed over five articles written in only six months, each of them more brilliant than its predecessor. Max Planck, who had been the first to postulate the existence of energy quanta, wrote to tell him he had read them “with the pleasure of a child hearing the solution to a riddle that has troubled him for years”. Paul Dirac went even further: the eccentric English genius, whose mathematical abilities were legendary, said that the Austrian’s equation contained practically all physics known up to that moment and—at least in principle—all of chemistry as well. Schrödinger had touched glory.
No one dared deny the importance of this new wave mechanics, but pretty soon some began to ask themselves the same questions that had troubled Schrödinger in the Villa Herwig. “It is a truly beautiful theory. One of the most perfect, precise and elegant man has discovered. But there is something strange in it. It’s as if it were warning us: don’t take me seriously. The world I reveal is not the one you are thinking of when you employ me,” wrote Robert Oppenheimer, one of the first to question what wave functions actually had to say about reality. Schrödinger devoted himself to travelling through Europe expounding his ideas, and applause met him wherever he went, until he came across Werner Heisenberg.
In the Munich auditorium, the Austrian was unable to finish his presentation before his young rival leapt to the stage and began erasing his calculations from the blackboard, replacing them with his horrible matrices. For Heisenberg, what Schrödinger proposed was an indefensible step backward. Methods from classical physics could not be used to explain the quantum world. Atoms were not simply marbles! Electrons were not water droplets! Schrödinger’s equation might be exquisite and even useful, but it erred in what was most essential when it ignored the radical strangeness of matter at the smallest scale. What enraged Heisenberg was not the wave function—though who the hell knew what that thing was?—but a matter of principles: however much the Austrian’s contrivance had bewitched all who encountered it, he knew it was a dead end, a blind alley leading them away from true comprehension. Because none of them would dare to do what he had achieved in the midst of his torments in Heligoland: not merely to calculate but to think in a quantum manner. Heisenberg shouted louder, trying and failing to make himself heard over the public’s scorn, while Schrödinger remained perfectly calm; for the first time in his life, he felt in complete control of his faculties. Convinced of the undeniable value of his work, he was unmoved by the young German’s tantrum. Before the host of the event threw Heisenberg out on his ear, egged on by all those present, Schrödinger told him there surely existed things in the world which were immune to analysis through common sense metaphors—but the internal structure of the atom was not one of them.
Heisenberg returned home broken, but unwilling to accept defeat. For two years, he attacked Schrödinger’s ideas in publications and seminars of all sorts, but fate seemed to smile on his opponent; in what seemed to be the coup de grâce in their quarrel, Schrödinger published an article showing that his procedure and Heisenberg’s were mathematically equivalent. Applied to a problem, they gave the exact same results. They were merely two ways of approaching an object, but his had the immense advantage of being intuitively comprehensible. There was no need to tear out one’s eyes to look at subatomic particles, as young Heisenberg liked to say: all you had to do was close them and imagine. “When discussing subatomic theories,” Schrödinger wrote at the end of his article, “we may perfectly well speak in the singular.”
Heisenberg’s matrix mechanics was doomed to oblivion. His epiphany in Heligoland would be nothing more than a postscript in the annals of science. With every day that passed, it seemed, someone published a new piece of work presenting results obtained with his matrices, but translated into the elegant wave language of Schrödinger. Heisenberg’s contempt reached fever pitch when he found himself incapable of deriving the spectrum of a hydrogen atom with his own theory and was forced to rely on his rival’s equations: he performed his calculus gnashing his teeth, as if trying to crack them one by one.
Even though he was still a very young man, his parents pestered him continually to stop wasting his talent and seek out a position as a full-blown professor in Germany. Heisenberg had travelled to Denmark, where he worked as an assistant to Niels Bohr, living in a tiny attic of the Bohr Institute for Theoretical Physics at the University of Copenhagen, beneath a sloping roof that forced him to move about with his head bowed, reminding him daily of what his father called his “subservience” to the Danish physicist.
Bohr and Heisenberg had a great deal in common: like his pupil, the Dane was famous for the almost deliberate obscurity of his arguments, and, though everyone respected him, many said that his ideas tended to stray closer to philosophy than to physics. Bohr was one of the first to accept Heisenberg’s new postulates, but he also proved a source of eternal frustration to his student, being inclined to tolerate both Schrödinger’s waves and Heisenberg’s matrices, unified through a principle he referred to as complementarity.
Rather than working to resolve the contradictions between the two approaches, Bohr embraced them. In his view, the attributes of elementary particles were only valid in a given context and arose from a relationship. No single frame of reference could encompass them. Measured in experiments of one type, they would exhibit the properties of a wave; in another, they would appear to be particles. These perspectives were mutually exclusive, antagonistic, and at the same time complementary: neither was a perfect reflection, and both were models of the world. Combined, they gave a more perfect notion of nature. Heisenberg detested complementarity. He was certain they needed
to develop a single conceptual system, not two contradictory ones. And he was ready to do anything to achieve this: if the price of understanding quantum mechanics was upsetting our very concept of reality, he, for one, was willing to pay it.
When he was not shut up in his room working, pacing from one end to the other with his head down and his shoulders hunched, he would argue with Bohr until dawn. Their dispute lasted for months and turned increasingly violent. When Heisenberg lost his voice screaming at Bohr, the Dane brought forward his winter vacation to take a break from his irritable pupil, whose stubbornness was only rivalled by his own, and whose character he had come to loathe. Without Bohr to provoke him, Heisenberg was left alone with his demons, and soon he had become his own worst enemy. He broke off into two people, giving long monologues that argued for his position and then Bohr’s, and his enthusiasm was such that he could soon imitate perfectly the insufferable pedantry of his teacher, as if he had developed a split personality. Betraying his own intuitions, he set aside his columns of numbers and matrices and tried to imagine the electron as a bundle of waves. What did Schrödinger’s equation actually describe when applied to an electron revolving around a nucleus? It was not a wave proper, that much was clear on account of its dimensionality. Perhaps it showed all the states the electron could inhabit—its energy levels, velocities and coordinates—but like hazy snapshots, superimposed, one atop the other. Some were in focus: these were the most probable states for the electron. Or was it a wave of probabilities? A statistical distribution? The French had translated the wave function as densité de probabilité de présence. That was all Schrödinger’s mechanics revealed: blurry images, a ghostly presence, diffuse and undefined. The vague outline of something not of this world. But what would happen if one considered that point of view and Heisenberg’s own at the same time? The result was absurd and intriguing: an electron that was both a particle confined to a given point and a wave extending through time and space. Overcome by all these paradoxes and seething at his incapacity to banish Schrödinger’s ideas, he left to walk through the park surrounding the university.
When We Cease to Understand the World Page 12
