Emboldened by his successes with nitrogen, Haber proposed to reconstitute the Weimar Republic and pay the war reparations that were strangling its economy through a process as wondrous as the one that had won him the Nobel Prize: harvesting gold from the waves of the sea. Travelling under a false identity to avoid raising suspicions, he gathered five thousand samples of water from assorted seas across the globe, including bits of ice from the North Pole and Antarctica. He was convinced he could mine the gold dissolved in the oceans, but after years of arduous labour had to accept that his original calculations had overestimated the quantities of this precious metal by several orders of magnitude. He returned to his country empty-handed.
In Germany, he found refuge in his work as director of the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry as anti-Semitism continued to flourish around him. Protected, for the moment, in his academic oasis, Haber and his team produced a number of new substances: one of them used cyanide in a pesticidal fumigant so destructive it was dubbed Zyklon, the German word for cyclone. The compound’s extraordinary effectiveness stunned the entomologists who used it for the first time to delouse a ship covering the Hamburg–New York route. They wrote directly to Haber to praise “the extreme elegance of the eradication process”. This new success led to Haber’s promotion to National Commissioner for Pest Control, from which post he organized the extermination of bedbugs and fleas on the navy’s submarines, and of rats and cockroaches in the army barracks. He fought against a veritable legion of moths that attacked the flour the government stored in a network of silos that stretched from Flensburg to Freiburg, which Haber described to his superiors as “a biblical plague that threatens the well-being of the German Lebensraum”, unaware that they had already begun the persecution of all those who shared his Jewish roots.
Haber had converted to Christianity at twenty-five years old. He identified so closely with his country and its customs that his sons knew nothing of their ancestry until he told them they would have to flee Germany. Haber escaped after them and sought asylum in England, but his British colleagues scorned him, aware of his instrumental role in chemical warfare. He had to leave the island not long after arriving. Thenceforth, he would travel from country to country in the hope of reaching Palestine, his chest gripped with pain, his arteries incapable of delivering sufficient blood to his heart. He died in Basle in 1934, clutching the canister of nitroglycerine he needed to dilate his coronary vessels, not knowing that, years later, the Nazis would use in their gas chambers the pesticide he had helped create to murder his half-sister, his brother-in-law, his nephews and countless other Jews who died hunkered down, muscles cramping, skin covered with red and green spots, bleeding from their ears, spitting foam from their mouths, the young ones crushing the children and the elderly as they attempted to scale the heap of naked bodies and breathe a few more minutes, a few more seconds, because Zyklon B tended to pool on the floor after being dropped through hatches in the roof. When ventilators had diffused the cloud of cyanide, the bodies were dragged to enormous ovens and incinerated. The ashes were buried in pit graves, dumped in rivers and ponds, or scattered as fertilizer in the surrounding fields.
Among the few possessions Fritz Haber had with him when he died was a letter written to his wife. In it, he confessed that he felt an unbearable guilt; not for the part he had played, directly or indirectly, in the death of untold human beings, but because his method of extracting nitrogen from the air had so altered the natural equilibrium of the planet that he feared the world’s future belonged not to mankind but to plants, as all that was needed was a drop in population to pre-modern levels for just a few decades to allow them to grow without limit, taking advantage of the excess nutrients humanity had bestowed upon them to spread out across the earth and cover it completely, suffocating all forms of life beneath a terrible verdure.
SCHWARZSCHILD’S SINGULARITY
On December 24, 1915, while drinking tea in his apartment in Berlin, Albert Einstein received an envelope sent from the trenches of the First World War.
The envelope had crossed a continent in flames; it was wrinkled, grubby and covered in mud, one corner was completely torn off, and the sender’s name was obscured by a large bloodstain. Einstein handled it with gloves and slit it open with a knife. Inside he found a letter bearing the last spark of a true genius: Karl Schwarzschild, astronomer, physicist, mathematician and lieutenant in the German army.
“As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas” were the final words of the letter Einstein read completely dumbfounded—not because one of the most respected scientists in Germany was commanding an artillery unit on the Russian front, nor because of his friend’s cryptic warnings about a coming catastrophe, but due to what was written on the back of the page: in a minuscule hand that Einstein could only decipher with a magnifying glass, Schwarzschild had sent him the first exact solution to the equations of general relativity.
Einstein had to reread it several times. When had he published his theory? A month ago? Less than a month? It was impossible for Schwarzschild to have solved such complex equations in so little time, if even he—who had created them!—had only been capable of finding approximate solutions. Schwarzschild’s solution was precise: it perfectly described the manner in which the mass of a star deforms the space and time surrounding it.
Although he was holding the solution in his hands, Einstein could scarcely believe it. He knew these results would be fundamental to generating greater interest in his theory among the scientific community, which until then had viewed it with little enthusiasm, largely because of its complexity. He had already resigned himself to the possibility that no one would find a precise solution to his equations—at least not during his lifetime. That Schwarzschild had done so among mortar explosions and clouds of poison gas was a proper miracle. “I had not expected that one could formulate the exact solution of the problem in such a simple way!” he responded to Schwarzschild as soon as he had composed himself and promised to present his work to the Academy, unaware that he was writing to a dead man.
The trick Schwarzschild had used was simple: he analysed an ideal, perfectly spherical star, without rotation or electric charge, then employed Einstein’s equations to calculate how that mass would alter the form of space, analogous to the way a cannonball placed on a bed would deform the mattress.
His measurements were so precise that even today they are used to trace out the paths of the stars, the orbits of planets and the distortions undergone by rays of light as they pass near a body that exerts a significant gravitational pull.
Yet there was something deeply strange about Schwarzschild’s results.
They worked flawlessly for an ordinary star, around which space curved softly, just as Einstein predicted, and the body of the star remained suspended in the centre of a depression, like a pair of children resting inside a cloth hammock. The problem arose when too much mass was concentrated in a very small area, as occurs when a giant star exhausts its fuel and begins to collapse. According to Schwarzschild’s calculations, in such a case, space-time would not simply bend; it would tear apart. The star would go on compressing and its density would increase till the force of gravity became so powerful that space would become infinitely curved, closing in on itself. The result would be an inescapable abyss permanently cut off from the rest of the universe.
They called this the Schwarzschild singularity.
Initially, even Schwarzschild cast this result aside as a mathematical anomaly. After all, physics is rife with infinities that are nothing more than numbers on paper, abstractions that do not represent real-world objects, or that simply indicate calculating errors. The singularity in his metrics was undoubtedly one of these: a mistake, an oddity, a metaphysical delirium.
Because the alternative was unthinkable. At a certain distance from Schwarzschild’s idealized star, the
equations of general relativity went mad: time froze, space coiled around itself like a serpent. At the centre of that dying star, all mass became concentrated in a single point of infinite density. For Schwarzschild, that such a thing could exist in the universe was inconceivable. Not only did it defy common sense and cast doubts on general relativity, it threatened the very foundations of physics, as, within the singularity, the notions of space and time themselves became meaningless. Schwarzschild attempted to find a logical solution to the paradox he had created. Did the fault lie in his conceit? Had he simply been too clever for his own good? Because in the real world, there was no such thing as a perfectly spherical, completely immobile star, with no electric charge. Surely the anomaly arose from the ideal conditions he had tried to impose on the world, impossible to replicate in reality. His singularity, he told himself, was nothing but an imaginary monster. A paper tiger, a Chinese dragon.
And yet, he could not get it out of his head. Even immersed in the chaos of war, the singularity spread across his mind like a stain, superimposed over the hellscape of the trenches; he saw it in the eyes of the dead horses buried in the muck, in the bullet wounds of his fellow soldiers, in the shadowy lenses of their hideous gas masks. His imagination had fallen prey to the pull of his discovery: with alarm, he realized that if his singularity were ever to exist, it would endure until the end of the universe. Its ideal conditions made it an eternal object that would neither grow nor diminish, but remain eternally as it was. Unlike all other things, it was immune to becoming and doubly inescapable: in the strange spatial geometry it generated, the singularity was located at both ends of time: one could flee from it into the remotest past or escape to the furthest future only to encounter it once more. In the last letter he sent to his wife from Russia, written the same day he chose to share his discovery with Einstein, Schwarzschild complains of something strange that has begun to grow inside him: “I don’t know how to name or define it, but it has an irrepressible force and darkens all my thoughts. It is a void without form or dimension, a shadow I can’t see, but one that I can feel with the entirety of my soul.”
Soon afterwards, that shadow invaded his body.
His sickness began with two blisters at the corner of his mouth. Within a month, they covered his hands, feet, throat, lips, neck and genitals. After two, he was dead.
The military physicians diagnosed him with pemphigus, a disease in which the body fails to recognize its own cells and attacks them violently. Ashkenazi Jews show a particular susceptibility. The doctors who treated him told him it might have been triggered by a gas attack that had taken place months before, one that Schwarzschild described in his diaries: “The moon crossed the sky so quickly, it seemed time itself had sped up. My soldiers readied their arms and waited for the order to attack, but the phenomenon was so strange and unsettling, they thought it a bad omen, and I could see the fear in their eyes.” Schwarzschild tried to explain to them that the nature of the moon had not changed; it was an optical illusion, caused by a thin layer of clouds crossing in front of it, making it seem larger and faster than it was. He spoke to them with the same tenderness he would have used with his children, but he did not manage to convince them. Nor could he himself shake off the feeling that everything had begun to move more swiftly since the start of the war, as though the world was slipping off a precipice. When the clouds cleared, he saw two horsemen at full gallop, followed by a dense mist that advanced towards them like the waves of the sea. The fog spread across the whole of the horizon, as solid as the sheer walls of a cliff, and from a distance it appeared immobile, but soon it had enveloped the hooves of the horses, and the animals and their riders tumbled to the ground. Alarm echoed throughout the trenches and Schwarzschild managed to help two soldiers who were petrified with fear to adjust the rubber straps on their masks, but he had hardly managed to don his own before the cloud of gas settled over them.
At the start of the war, Schwarzschild was more than forty years old, and director of the most prestigious observatory in Germany. Either of those would have sufficed to exempt him from active service. But Schwarzschild was a man of honour who loved his country, and, like thousands of other Jews, he was anxious to show his patriotism. He enlisted voluntarily, deaf to the counsel of his friends and the warnings of his wife.
Before witnessing the cruel reality of combat and suffering the horror of modern war in his own flesh, Schwarzschild had found the camaraderie of the army rejuvenating. When his unit was first deployed, he discovered a system for perfecting the sights on the tanks—without anyone having requested that he do so—tinkering with them in his free time with the same eagerness with which he had built his first telescope, as if the drills and simulations of his months of training had rekindled in him the boundless curiosity he had known during childhood.
He had grown up obsessed by light. At seven, he took apart his father’s glasses and placed the lenses inside a rolled-up newspaper to show his brother the rings of Saturn. He passed entire nights without sleep, peering up at the sky, even when it was completely cloudy. His father, unnerved to see his son spellbound by that darkened firmament, asked him what he was searching for. The boy told him there was a star hiding behind the clouds that he alone could see.
From the time he learnt to talk, he spoke of nothing but celestial bodies. He was the first scientist in a family of merchants and artists. At sixteen, he published a paper in the prestigious journal Astronomische Nachrichten about the orbits of binary stars. Before he had turned twenty, he had written about the evolution of stars, from their formation as clouds of gas to their catastrophic final explosion—and had invented a system of his own for measuring the intensity of their light.
He was convinced that mathematics, physics and astronomy constituted a single body of knowledge and believed that Germany was capable of exercising a civilizing force comparable to that of ancient Greece. To do so, however, its science must be raised to the heights already achieved by its philosophy and art, for “only a vision of the whole, like that of a saint, a madman or a mystic, will permit us to decipher the true organizing principles of the universe.”
As a child, he had close-set eyes, big ears, a button nose, thin lips and a pointy chin; as an adult, a broad forehead, sparse hair hinting at an eventual baldness that did not have time to develop, an intelligent gaze and a roguish smile hidden behind an imperial moustache as thick as Nietzsche’s.
He attended a Jewish primary school, where he tried the patience of the rabbis with questions to which they lacked answers: what was the true significance of that passage in the Book of Job which says that Yahweh stretcheth out the north over the empty place, and hangeth the earth upon nothing? In the margins of his notebooks, next to the arithmetic problems that so frustrated his classmates, Schwarzschild calculated the equilibrium of liquid bodies in rotation, desperately trying to prove the long-term stability of the rings of Saturn, which he saw coming apart over and over in a recurring nightmare. To lighten his obsessions, his father obliged him to take piano lessons. At the end of his second lesson, young Schwarzschild opened the lid of the instrument and unwound its strings to understand the underlying logic of its tones; he had read Johannes Kepler’s Harmonice Mundi, which expressed the view that each planet generated a melody in its transit around the sun, a music of the spheres that our ears were incapable of distinguishing but that the human mind was able to decipher.
He never lost the capacity for astonishment: when he was a student at university, he observed a total eclipse from the heights of the Jungfraujoch, and though he understood the mechanism responsible for the phenomenon, he struggled to believe that a mass as small as the moon could blanket all of Europe in the deepest darkness. “How strange space is, and how capricious the laws of optics and perspective, that they should permit even the smallest child to cover the sun with one of his fingers,” he wrote to his brother Alfred, a painter who lived in Hamburg.
For his doctoral thesis, he calculated the deformation unde
rgone by satellites subject to the gravitational pull of the planets they orbit. The mass of the earth, for example, generates a tide that crosses the surface of the moon, just as the moon itself gives rise to a tide in our oceans. In the former case, this is a wave of solid rock four metres high propagated over the moon’s crust. The attraction between the two bodies synchronizes their rotation periods perfectly: as the moon turns on its axis at the same speed as it rotates around our planet, one of its faces is eternally hidden from view. This dark side remained beyond the reach of our knowledge from the birth of the human race until 1959, when the Soviet probe Luna 3 photographed it for the first time.
When We Cease to Understand the World Page 3