He did not notice the passing hours until midnight, when the cold obliged him to take refuge in the only place still open at that time, a bar where Copenhagen’s bohemians gathered, and artists, poets, criminals and prostitutes bought their doses of cocaine and hashish. Heisenberg’s sobriety bordered on the puritanical, and though he passed by there every day, and many of his colleagues were regulars, he had never entered before. The stench when he opened the door struck him like a blow to the face. Had it not been for the cold, he would have returned to his quarters. He headed to the back and sat at the only empty table. He raised a hand to call over a man dressed in black who he assumed to be a waiter, but instead of taking his order, the man sat at the other end of the table and looked at him with burning eyes. “What can I offer you tonight, Professor?” he said, removing a tiny bottle from the interior of his jacket. He looked back, positioning himself so the owner of the bar would not see Heisenberg’s attempts to get his attention. “Don’t worry about him, Professor, everyone is welcome here, even people like you,” he said, winking at him and placing the bottle on the table. Heisenberg felt immediate contempt for the stranger. Why did this man at least ten years his senior insist on addressing him so formally? Heisenberg continued trying to summon the barman, but the shoulders of the stranger, slumped over the table like a giant drunken bear, blocked his view almost entirely. “You won’t believe me when I say this, Professor, but not long ago a seven-year-old child was sitting in the same chair you are in now, crying nonstop. The saddest child in the world, I promise you, I can still hear him sobbing. And who can concentrate on their writing with such a racket? Have you tried hashish, sir? No, of course you haven’t. Today, no one has time for eternity. Only children, children and drunks, not serious people like you, Professor, those on the verge of changing the world. Or am I wrong?” Heisenberg did not answer. He had decided he would not play along, and was about to stand when he saw something metallic flash in the man’s hand. “There’s no hurry, Professor, we have the entire night before us. Relax, let me buy you a drink. Though, truth be told, I’d say you could use something stronger, no?” He spilled the contents of the bottle into what was left of his beer and pushed the glass towards Heisenberg. “You look tired, Professor. You should take better care of yourself. Did you know the first symptom of a psychological disturbance is the inability to contend with the future? If you consider that, you will realize how implausible it is that we are able to exert control over even an hour of our lives. How hard it is to control our thoughts! You, for example—it is obvious you are possessed. That you are in thrall to your intellect as a degenerate is in thrall to a woman’s cunt. You are bewitched, Professor, you’ve been sucked inside your own head. Come on, drink. Don’t make me ask you twice.” The physicist pushed himself away, but the stranger grabbed his shoulder and brought the glass to Heisenberg’s lips. Panicked, he looked around to ask for help and saw that the entire bar was staring at him impassively, as though present at a ritual each of them had been obliged to undergo. He opened his mouth and drank the green liquid in a single swig. The man smiled, leant back in his seat, and laced his fingers together behind his head. “Now, Professor, you and I can talk like two civilized people. Believe me, I know about these things. We must let space and time be woven together like a single fibre, we must always remain in motion. Who could bear to stay in a single place his whole life? That’s fine for a stone, but not for a man like yourself, Professor. Have you listened to the wireless recently? I have a programme that might interest you. It’s conceived for children, but curious children, brave children like yourself. I tell them about all the great catastrophes of our era. The tragedies, the massacres, the horrors. Did you know five hundred people died in a flood in Mississippi last month? The water flowed with such force that the levees broke and the people drowned in their sleep. There are those who think children shouldn’t know these things, but that doesn’t worry me. The horrible thing isn’t the bodies floating in the water, their swollen flesh falling off their bones. No. The truly grotesque thing is that I found out about all of this almost instantaneously. From the other side of the planet, word reached me that my adored Uncle Willy, that old bastard, and my beloved Aunt Clara, the old bitch, had saved themselves from the water by climbing up on the roof of their candy store. Candy! If that isn’t black magic, you tell me what is. It doesn’t matter how many people have died or how many have been saved, Professor—today, all of us are victims. You are too intelligent not to realize that. I still remember the first time I received a telephone call. I was in my grandfather’s house and my mother called me from the hotel where she liked to spend the holidays to get away from me. As soon as I heard the ring, I picked up the receiver and pressed my head against the speaker, giving myself over to the voice emerging from it, and there was nothing that could mitigate that violence. Impotent, I suffered as I saw how my consciousness of time was destroyed, my resolve, my sense of duty and proportion! And to whom do we owe this magnificent inferno if not to you, to people like you? Tell me, Professor, when did all this madness begin? When did we cease to understand the world?” The man held his face in his hands, stretching his skin out to both sides until he was utterly deformed, and then let himself collapse over the table, as though no longer capable of supporting his prodigious weight. Heisenberg used this moment to escape.
He ran without knowing where to, lost in the fog with his arms outstretched in front of him, groping at the air like a blind man. When his legs cramped, he collapsed on top of the roots of a gigantic oak and felt as if his heart would explode. He had made his way far into the park and could no longer see the light of the street lamps. What had that bastard drugged him with? He was shivering from the cold, his tongue was dry, his vision blurred, adrenalin was rushing through his body, and he could barely contain his longing to weep. All he wanted was to return to his attic, but he was too nauseated to stand. When he tried, the landscape began to spin around him, so quickly he had to hug the tree trunk and close his eyes.
When he opened them, tiny orbs of light floated in the air around him, glimmering like a parade of fireflies. He no longer felt the cold, his legs no longer shivered. He was lucid and disoriented at the same time, just as if he had awakened from a dream. The forest was now unrecognizable; the roots were throbbing like veins, the branches swayed even though he could not feel the wind, and the earth seemed to breathe beneath his feet, but still he was unafraid. A feeling of great peace had come over him, and Heisenberg found it so unusual, given the circumstances, that he feared his tranquillity might turn to panic at any moment. To avoid this, he devoted himself to observing the play of the lights, which covered the entirety of space, falling from treetops or blossoming amid the leaves covering the ground. Most of them disappeared immediately, but some lasted long enough to leave a small trail. With his pupils dilated, Heisenberg noticed that these traces were not continuous lines, but a series of individual points that seemed to be leaping from place to place instantaneously, without passing through the intermediate space. Hypnotized by these hallucinations, he sensed his mind merging with the things he observed: every point of these traces appeared without cause, and the complete trajectory existed in his mind alone, which wove the distinct instances together. Heisenberg concentrated on one of them, but the more he tried to fix it, the more diffuse it became. He dragged himself over the ground on all fours, trying to catch one of the sparks in his hand, laughing like a child chasing after a butterfly, and had nearly caught one when he saw he had been surrounded by a legion of shadows.
Countless men and women with slanted eyes, their bodies sculpted of soot and ash, were stretching out their arms to try and touch him. They thronged around him without managing to advance, humming like a cluster of bees caught in the threads of an invisible web. Heisenberg tried to take the hand of a baby that had broken through the net and was crawling towards him, but an explosion pulverized the figures and brought him to his knees, rummaging in the dirt to try and salvage some
trace, some vestige of those phantoms. All he could find was one of the minuscule lights, the single one that had survived. He picked it up with infinite care, hugged it to his chest, and took the path home, fighting against a gale that blew his hair into his eyes and whipped the folds of his jacket, convinced he must do anything to prevent it from going out. He found the exit of the park and headed towards the university building. When he saw the window of his room, he felt something huge looming at his back. He looked over his shoulder and saw a black spectre that darkened everything behind him. He ran in dread, tripped over the cobblestones, and realized it was his own shadow chasing him, cast backward by the light he was holding in his hands. He turned to face his ghost, reached out his arms, and opened his palms. The light and shadow were extinguished in unison.
When Bohr returned from his holiday, Heisenberg told him there was an absolute limit to what we could know about the world.
No sooner had his superior entered the door of the university than Heisenberg grabbed his elbow and led him back out into the park, giving him time neither to leave his baggage nor shake the snow from his overcoat. Combining his own ideas with those of Schrödinger—Heisenberg told Bohr as he dragged his suitcases between the trees, ignoring all his mentor’s complaints—he had realized that quantum objects had no fixed identity, but instead dwelt in a space of possibilities. An electron, Heisenberg explained, did not exist in a single place, but in many, and had not one velocity, but several. The wave function showed all those possibilities superimposed. Heisenberg had forgotten the entire accursed debate about particles and waves, and had once more clung to numbers to find his path. Analysing Schrödinger’s mathematics and his own, he had discovered that certain properties of a quantum object, such as its position and quantity of motion, were coupled, and the relationship between them evinced strange properties. The more precisely the one was identified, the more uncertain the other became. If, for example, the exact location of an electron was established with certainty, arresting that particle in its orbit like an insect impaled on a pin, then its velocity became utterly undefined; it might be immobile or moving at the speed of light, and there was no way of knowing which. The opposite was true as well. If the electron was endowed with a set quantity of motion, its position was so indeterminate that it might be in the palm of your hand or at the other end of the universe. These two variables were mathematically complementary: establishing the one dissolved the other.
Heisenberg paused to catch his breath. He had been speaking frantically, without stopping, and was soaked with sweat from the effort of lugging Bohr’s suitcases through the snow. He had been so lost in his own head that he had not noticed Bohr was now several metres behind him, looking at the ground in extreme concentration. Heisenberg could almost hear the clicking of the gears in his master’s mind, which could grind ideas down until he had extracted their marrow; when he approached, Bohr asked if these paired properties were limited to the two variables mentioned, and Heisenberg, panting, said no: they reigned over many aspects of quantum reality, such as the time an electron remained in a state and the energy it possessed in that state. Bohr asked if these relations existed at all levels of matter, or only in the subatomic realm; Heisenberg assured him that they were as true for an electron as for the two of them, but the effects on macroscopic objects were imperceptible, while for a single particle they were vast.
Heisenberg took out the paper on which he had worked out the mathematics behind his new idea, and Bohr sat in the snow to read it. He was silent as he checked the calculations for what seemed to Heisenberg like an eternity, and when he finished, he asked for help getting up. They started walking again to shake off the cold. Bohr asked if this might constitute an experimental limitation, something future generations with advanced technology might overcome. Heisenberg said no: it was something constitutive of matter itself, a principle that governed the way in which all things were created, and that seemed to exclude the possibility that a given phenomenon should possess certain perfectly defined attributes simultaneously. His original intuition had been correct: it was impossible to “see” a quantum entity for the simple reason that it did not have a single identity. Illuminating one of its properties necessarily obscured the other. The best description of a quantum system was neither an image nor a metaphor, but rather a set of numbers.
They left the park and plunged into the city streets while they discussed the consequences of Heisenberg’s discovery, which Bohr saw as the cornerstone upon which a truly new physics could be founded. In philosophical terms, he told him as he took his arm, this was the end of determinism. Heisenberg’s uncertainty principle shredded the hopes of all those who had put their faith in the clockwork universe Newtonian physics had promised. According to the determinists, if one could reveal the laws that governed matter, one could reach back to the most archaic past and predict the most distant future. If everything that occurred was the direct consequence of a prior state, then merely by looking at the present and running the equations it would be possible to achieve a godlike knowledge of the universe. Those hopes were shattered in light of Heisenberg’s discovery: what was beyond our grasp was neither the future nor the past, but the present itself. Not even the state of one miserable particle could be perfectly apprehended. However much we scrutinized the fundamentals, there would always be something vague, undetermined, uncertain, as if reality allowed us to perceive the world with crystalline clarity with one eye at a time, but never with both.
Drunk with enthusiasm, Heisenberg noticed that his route through the park was nearly the perfect converse of the one he had traced out the night of his epiphany. He told Bohr this, and the Dane immediately related it to what they were discussing: if we cannot know, at the same time, such basic things as where an electron is and how it moves, we also cannot predict the exact path it will follow between two points, only its multiple possible paths. That was the ingenious thing about Schrödinger’s equation: somehow it managed to thread together the infinite destinies of a particle, all its states, all its trajectories, in a single schema—the wave function—showing them all superimposed. A particle could cross space in many ways, but from among them it chose only one. How? Through pure chance. For Heisenberg, it was no longer possible to speak of any subatomic phenomenon with absolute certainty. Where before there had been a cause for every effect, now there was a spectrum of probabilities. In the deepest substrate of all things, physics had not found the solid, unassailable reality Schrödinger and Einstein had dreamt of, ruled over by a rational God pulling the threads of the world, but a domain of wonders and rarities, borne of the whims of a many-armed goddess toying with chance.
When they passed in front of the bar Heisenberg had escaped from, Bohr said all those things were deserving of a beer. The owner had just opened and the place was empty, but the suggestion turned Heisenberg’s stomach. He proposed a coffee instead, and perhaps something warm to eat. You don’t celebrate with coffee, the Dane replied, and pushed him in.
They sat at the same table Heisenberg had occupied that strange night. Bohr ordered two beers, which they sipped slowly, then two more that they drank down in one go. During the third, Heisenberg confessed all that had happened there: he spoke of the stranger who had drugged him, his fear, the bottle on the table, the man’s bearish hands and the glimmer of his knife blade; he described the bitterness of the green liquid, the stranger’s irrepressible outburst of emotion and his cowardly escape; he talked of the cold outside, the beauty of his hallucinations, the throbbing roots of the trees, the dance of the fireflies, the tiny ember of light he had caught in his hands and the giant shadow that had followed him to the university. He spoke of all that, and of his life in the weeks afterwards, the storm of ideas unleashed in his head and the unrestrained enthusiasm that had gripped him since that night; but for a strange reason he could explain neither to himself nor to Bohr, for it was one he would not understand until decades later, he was incapable of confessing his vision of the dead baby
at his feet, or the thousands of figures who had surrounded him in the forest, as if wishing to warn him of something, before they were carbonized in an instant by that flash of blind light.
V
GOD AND DICE
On the morning of Monday, October 24, 1927, beneath the grey sky of Brussels, twenty-nine physicists crossed the frost-caked lawn of Leopold Park and entered one of the lecture halls of the Physiology Institute, unaware that five days later they would shake the very foundations of science.
The institute had been built by the industrialist Ernest Solvay for the purpose of demonstrating, insofar as possible, that “the phenomenon of life should be explained by the physical laws that govern the universe, which we may know through observation and the objective study of the facts of the world.” Old masters and young revolutionaries had travelled from all over Europe to participate in the Fifth Solvay Conference, the most prestigious scientific gathering of the era. Never before or again were so many geniuses united beneath the same roof: seventeen of them had won, or would go on to win, the Nobel Prize, including Paul Dirac, Wolfgang Pauli, Max Planck and Marie Curie, who had won it twice and was overseeing the conference committee along with Hendrik Lorentz and Albert Einstein.
Although the theme of the conference was “Electrons and Photons”, all present knew the true purpose was to analyse quantum mechanics, which was casting doubt on the whole edifice upholding physics.
When We Cease to Understand the World Page 13