During his internship at the Kuffner observatory, one of the binary stars of the Auriga constellation, just off the shoulder of Orion, went nova. For several days, it was the brightest object in the sky. The white dwarf in this dyad, which had remained dormant for aeons after having exhausted its fuel, began to draw on the gases of its red giant companion star and returned to life with a colossal explosion. Schwarzschild spent three days and nights awake, observing it; to understand the catastrophic death of stars seemed to him essential for the future survival of our species; if one of them exploded near the earth, it would burn up our atmosphere and extinguish all forms of life.
The day after he turned twenty-eight, he became the youngest university professor in Germany. He was appointed director of the observatory at the University of Göttingen, despite his refusal to undergo the Christian baptism required to take the position.
In 1905, he travelled to Algeria to observe a total eclipse, but he failed to heed the maximum exposure time and damaged the cornea of his left eye. When they removed the patch he had been forced to wear for weeks, he noticed a shadow the size of a two-mark coin in his visual field, which was apparent even when his eyes were closed. The doctors told him the damage was irreversible. To his friends, who worried about the effects eventual blindness might have on an astronomer’s career, he said—only partly in jest—that he, like Odin, had sacrificed one eye to be able to see further with the other.
As though to prove that the accident had in no way diminished his faculties, that year Schwarzschild worked like a man possessed, publishing article after article. He analysed the transport of energy through stars by means of radiation, carried out studies of the equilibrium in the atmosphere of the sun, described the distribution of astral velocities and proposed a mechanism for modelling radiative transfer. Arthur Eddington compared him to a guerrilla leader, as “his attacks fell where they were least expected and his joy was to range unrestricted over the pastures of knowledge.” Alarmed by the manic fervour of his academic output, his colleagues advised him to slow down, fearing that his inner fire would consume him. Schwarzschild paid them no attention. Physics was not enough for him. He aspired to the type of knowledge the alchemists had pursued, and laboured beneath the sway of a strange urgency that not even he could fully explain: “Often I have been unfaithful to the heavens. My interest has never been limited to things situated in space, beyond the moon, but has rather followed those threads woven between them and the darkest zones of the human soul, as it is there that the new light of science must be shone.”
In all that he did, Schwarzschild would take things to the limit; during an expedition to the Alps, at the invitation of his brother Alfred, he ordered their guides to loosen the ropes at the most dangerous part of a glacier crossing, putting the entire expedition at risk, merely so that he could get closer to two of his colleagues and solve a problem that they had been working on together, by scraping equations into the permafrost with their pickaxes. His recklessness so angered his brother that the two of them never climbed together again, although they had spent nearly every weekend in their university days exploring the mountains of the Black Forest. Alfred was aware of the extent of his brother’s obsessiveness: the year of his graduation, a snowstorm had stranded them on one of the ledges of the Brocken, the highest peak of the Harz mountain range. To keep from freezing to death, they had had to build a shelter and sleep holding one another, as they had when they were children. They survived on a bag of walnuts, but when they ran out of water and matches to melt the snow, they had to brave the descent in the middle of the night, their way brightened solely by the light of the stars. Alfred was terrified and kept tripping, though he arrived unharmed. His brother Karl did not misstep a single time, as if he were somehow capable of seeing the trail in the dark, but was left with nerve damage in his right hand from the cold; in the shelter, he had repeatedly removed his gloves to revise his calculations concerning a series of elliptical curves.
When he conducted experiments he was no less impulsive: he would remove pieces from one instrument to use them for another, without leaving any record of what he had done. If he needed a diaphragm in a hurry, he would simply drill a hole in the lens cap. When he left Göttingen to oversee the observatory in Potsdam, his replacement nearly quit before his appointment had begun: upon taking an inventory, in order to determine how badly the facilities had suffered under Schwarzschild, he found a transparency of the Venus di Milo inside the focal plane of the largest telescope, arranged in such a way that the stars of the Cassiopeia constellation outlined the goddess’s arms.
He was extraordinarily awkward around women. Although his female students pursued him, and referred to him as “the professor with the shining eyes”, he did not dare to kiss his future wife, Else Rosenbach, until the second time he had asked her to marry him. Else had rejected his first proposal out of fear that his interest in her was purely intellectual; Schwarzschild was so timid that he had only touched her once during their long courtship, and, even then, it had been by mistake: he had laid a hand on her breast while helping her focus on the star Polaris through the lens of a small, homemade telescope. They married in 1909, had a daughter, Agatha, and two sons, Martin and Alfred. The girl studied classics and became an expert in Greek philology; the older brother became a professor of astrophysics at Princeton, while the younger, born with an irregular heartbeat and perpetually dilated pupils, suffered multiple nervous breakdowns throughout his life, and committed suicide on finding himself unable to escape from Germany after the persecution of the Jews began.
Like many sensitive people, Schwarzschild felt overcome by a sense of imminent disaster as the First World War approached. In him, this took the peculiar form of a fear that physics would be incapable of explaining the movement of the stars, or of finding an order in the universe. “Is there anything that is truly at rest, something stationary around which the universe revolves, or is there nothing at all to hold on to amid this endless chain of movements in which every single thing seems bound? Just imagine how far we have fallen into uncertainty if the human imagination cannot find a single place to lay its anchor, if not a single stone in the world has the right to be considered immobile!” Schwarzschild dreamt of the coming of a new Copernicus, someone who could model the intricacies of celestial mechanics and reveal the pattern dictating the complex orbits the stars trace out in the firmament. The alternative was unbearable: that there was nothing more than lifeless spheres in the throes of random chance, “like the molecules of a gas that float from one place to the other in a completely irregular manner, so much so that their very chaos is being enthroned as principle.” In Potsdam, he created an enormous network of colleagues to follow and register, with the maximum possible precision, the movements of more than two million stars. His hope was not only to understand the logic of their orbits, but to decipher where they would lead us. Because while the movement of two bodies bound by gravitation can be known with precision according to the laws of Newton, the addition of a third renders it unforeseeable. Schwarzschild believed that our own planetary system was completely unstable in the long term. Its present order might be vouchsafed for a million or even a billion years, but, with time, the planets would escape from their orbits, the gaseous giants would engulf their neighbours, and Earth itself would be expelled from the solar system to roam, like a wandering star, until the end of time, unless the form of space were not planar. Anticipating Einstein, Schwarzschild had considered the hypothesis that the geometry of the universe was less like a three-dimensional box than something that could be twisted and deformed. In his article “On the Admissible Curvature of Space” he analysed the possibility that we inhabited a semi-spherical universe, yielding a world that would turn in on itself like an ouroboros: “We would be faced with a fairyland geometry, a hall of mirrors whose horrifying perspectives would be more than the civilized mind could bear, as it abhors and flees from all it cannot comprehend.” In 1910, he discovered that the stars
had different colours, and he was the first to analyse them, using a special camera he had built with the assistance of the Potsdam observatory’s porter—the only other Jew who worked there, with whom he often drank till dawn. Attaching this camera to the porter’s broom and swinging it in circles, he took photographs from a number of angles to confirm the existence of red giants, monstrous stars hundreds of times larger than our sun. His favourite—Antares—was the colour of a ruby. The Arabs called it Kalb al-Akrab, the heart of the scorpion; the Greeks considered it the only rival of Ares. In April, Schwarzschild organized a journey to Tenerife to photograph the return of Halley’s Comet, which had always been considered an ill omen: in the year 66, the historian Flavius Josephus had described it as “a star that resembles a sword”, come to warn of the destruction of Jerusalem by the Romans, while in 1222 its appearance in the sky had inspired Genghis Khan to invade Europe. It struck Schwarzschild as fascinating that the long wake of its tail—which the earth crossed, on this occasion, over the course of six hours—always lay in the direction opposite to that of the sun. “What wind drags it off with the fury of an angel cast out from Heaven, falling and falling and falling?”
When war broke out four years later, Schwarzschild was among the first to volunteer.
He was assigned to the battalion that laid siege to Namur, in Belgium, to reinforce the German bombardment, trying to break the ring of fortresses surrounding the thousand-year-old city. As Schwarzschild had trained at a meteorological station, he was posted to lead the charge. The Germans’ advance was impeded by a mist that rose up without warning, so thick it turned midday to night. Both sides were shrouded in darkness and unable to attack for fear of shooting their own men. “What is it about the strange, chaotic climate of this country that it so doggedly resists our knowledge and control?” he wrote to his wife after a week of work to counteract the effects of the mist or, at least, predict the moment when it might occur. When he failed to do so, his superior chose to withdraw the troops to a safe distance and engaged in massive, indiscriminate bombings, firing without care for wasted munitions or civilian casualties, using 42-centimetre ordnance shot from a gigantic howitzer the troops nicknamed “Big Bertha”, until the citadel, which had stood fast from the time of the Roman Empire, was nothing more than a mountain of rubble.
From there, Schwarzschild was transferred to the 5th Army artillery regiment, entrenched in the forest of Argonne on the French front. When he presented himself to the officers in charge, they ordered him to calculate the trajectories of twenty-five thousand shells loaded with mustard gas, which would fall on the French troops in the middle of the night. “They ask me to predict the winds and storms, when we ourselves are the ones stoking the fires that rage behind them. They want to know the ideal trajectory that will lead our projectiles to the enemy, and don’t see the ellipse that will drag all of us down. I am tired of hearing the officers say that we are ever closer to victory, and that the end of the war is in reach. Don’t they understand that we are rising up only to fall?”
Not even in the midst of the butchery of war did he abandon his research. He carried his notebook beneath his uniform, close to his chest. When he was promoted to lieutenant, he took advantage of his newfound privileges to ask that the most recent publications in physics be sent to him from Germany. In November 1915, he read the equations of general relativity published in Annalen der Physik no. 39 and began working out the solution he would send Einstein one month later. From that moment onwards, he underwent a change that would even affect his manner of note-taking. His handwriting became smaller, to the point of becoming practically illegible. In his diary, and in the letters he sent to his wife, his patriotic zeal gives way to bitter complaints about the meaninglessness of the war and a growing contempt for the stupidity of his fellow officers that would only increase as his calculations came closer to the singularity. When he finally reached it, he could think of nothing more: he became so immersed that he failed to take cover during an enemy attack, and a mortar exploded a few metres away from his head. No one understood how he had survived.
Before winter came, they shipped him off to the eastern front. The soldiers he came across shared rumours of horrible massacres of civilians, lootings, rapes and deportations. Whole towns decimated in the course of a single night. Cities with no strategic value that vanished from the map as though they had never existed. The atrocities committed obeyed no martial logic; often it was impossible to know which of the two sides was responsible. When Schwarzschild saw a group of his soldiers practising their aim on a scrawny dog quivering some way away, panicked and incapable of fleeing, something broke inside him. The drawings he was used to making of the daily life of his comrades or the splendours of the countryside—which grew colder and more forbidding the further they advanced—gave way to whole pages covered in thick lines of charcoal and black spirals that vanished past the edges of the page. At the end of November, his battalion joined the 10th Army on the outskirts of Kosava, in Belarus. From there, he sent a letter to Ejnar Hertzsprung, a colleague from the University of Potsdam, which included a draft of his singularity, a description of the blisters that had begun to appear on his skin, and a long digression on the insidious effects the war might have on Germany’s soul, a country Schwarzschild continued to love, but that he saw reeling on the edge of an abyss: “We have reached the highest point of civilization. All that is left for us is to decay and fall.”
Pemphigus, acute necrotizing ulcerative gingivitis. The blisters in his oesophagus prevented him from swallowing solid food. Those in his mouth and throat burned like hot coals whenever he tried to drink water. Schwarzschild was given a furlough by the doctors, but he continued to work on the equations of general relativity, unable to control the manic speeding of his mind, which accelerated as the illness consumed the rest of his body. He published 112 articles in total during his lifetime, more than virtually any other scientist in the twentieth century. The final ones he composed on sheets of paper laid out on the floor, his arms hanging over the edge of his bed, lying on his stomach, covered in scabs and abscesses left behind by his blisters when they burst, his body transformed, as it were, into a miniature model of war-torn Europe. To distract himself from the pain, he catalogued the shape and distribution of his wounds, the surface tension of the fluid building up in his blisters, and the average time they required to rupture, but still he could not tear his mind from the void his equations had opened up.
He filled three notebooks with calculations meant to explain away the singularity, in the hope of finding a pathway out or an error in his reasoning. In the last of these, Schwarzschild deduced that any object could generate a singularity if its matter were compressed into a sufficiently restricted space: for the sun, three kilometres, for the earth, eight millimetres, and 0.000000000000000000000001 centimetres for the mass of an average human body.
Inside the void his metrics predicted, the fundamental parameters of the universe switched properties: space flowed like time, time stretched out like space. This distortion altered the law of causality; Schwarzschild deduced that if a hypothetical traveller were capable of surviving a journey through this rarefied zone, he would receive light and information from the future, which would allow him to see events that had not yet occurred. If he could reach the centre of the abyss without gravity tearing him apart, he would distinguish two superimposed images projected at once in a small circle over his head, like those that are visible through a kaleidoscope: in one, he would perceive the entire future evolution of the universe at an inconceivable pace, in the other, the past frozen in a single instant.
The anomalies were not confined to the singularity’s interior. Around it, there existed a limit, a barrier that marked a point of no return. After crossing that line, any object—from a whole planet to a minuscule subatomic particle—would be trapped forever. It would disappear from the universe as though it had fallen into a bottomless pit.
Decades later, this limit was dubbed the Sc
hwarzschild radius.
Einstein wrote a eulogy for him after his death, and read it aloud during his funeral. “He fought against the problems from which others fled. He loved discovering the relations between multiple aspects of nature, but what drove his search was joy, the pleasure an artist feels, the vertigo of the visionary capable of discerning the threads that weave the fabric of the future,” he said to the small group of men gathered before his tomb. None of them suspected how much Schwarzschild had been tormented by his greatest discovery, as not even Einstein himself could understand what takes place when equations bleed into the singular and infinity appears as their only possible result.
The young mathematician Richard Courant was the last person to speak directly to Schwarzschild, and the only one who could attest to the effects the singularity wrought on the astrophysicist’s mind.
Courant had been wounded in Rava-Ruska; he met Schwarzschild in the military hospital. The young man had been assistant to David Hilbert, one of the most influential German mathematicians of his era, so he recognized Schwarzschild right away, despite the wounds that disfigured his face. He approached him timidly, not comprehending how a man of his prestige and intellectual standing had been sent to so dangerous a place. In his diary, Courant described how the eyes of Lieutenant Schwarzschild, darkened by battle, lit up as soon as he heard the ideas Hilbert was developing. The two men spoke throughout the night. Close to dawn, Schwarzschild spoke to him of the rupture he believed he had discovered.
When We Cease to Understand the World Page 4