Singularity

by Bill DeSmedt

  “That unit’s going to be cycling on and off day and night just keeping the SQUID cold enough to operate,” Jack said. “And getting a good night’s sleep out here isn’t all that easy as it is, what with the skeeters and such. No sense my adding noise pollution to the problem.”

  Luciano opened his mouth to respond. A cough came out instead. Understandable, since he was directly downwind of the smoky fire. At first Jack had wondered why they were sitting around the campfire at all. It sure wasn’t for warmth; Siberian summers might be short but they made up for it with extra helpings of heat and humidity. Turned out, though, that the woodsmoke kept the ravenous Siberian mosquitoes—“flying alligators,” the Russians called them—at bay. It was the one deterrent that worked. Conventional bug-spray only served to encourage the insects.

  “Sorry, Jack, sorry,”—cough, cough—“what I wanted to say: perhaps the real reason our esteemed Academician has isolated you from the rest of the party is for fear of infection.”

  “Quarantining my contagious ideas, eh?” Jack smiled again. He liked this rotund, genial little man with his cherubic face and sly Machiavellian wit. “Don’t worry, Luciano; from what I can tell, my ‘discredited fantasies’ aren’t catching.”

  “Because you do not trouble to explain them.” Luciano stifled another cough. “Your theories, I mean, not your fantasies. I have read the abstract of your research proposal twice, but I confess this business about the very little black holes still remains a mystery to me.”

  “Didn’t seem much point going into detail, seeing how our friends from Tomsk were going to take the money and run, regardless.” As the premier center for studies of the Tunguska phenomenon and the host institution for the expedition, Tomsk University had final say on what research might be conducted at the site.

  Jack swiped at the air with his Stetson, beating back another insectile assault wave. “And close their ears to what I had to say in the process,” he added.

  “Not all of them, perhaps.” Luciano flicked his eyes off to Jack’s left.

  Jack turned to see a young blond Russian standing five feet away, listening to them. And looking at the Stetson. What was the real attraction here: Jack’s theories or his cowboy hat?

  Caught eavesdropping, the young man blushed and pushed thick bifocals back up his nose. “Excuse, please . . . Zaleskii, Igor Andreyevich, aspirant in molecular biology at Tomsk University. I could not help but to overhear . . .”

  “No harm done.” Jack said. “Sit down, Igor, pull up a stump and join the party.”

  The newcomer gave a grateful nod and joined them at the fire. He squatted down, looked both ways, then reached into his hip pocket and pulled out a metal flask. “Russian mosquito repellent,” he said, handing it to Jack with a grin. “For internal use only.”

  Jack unscrewed the lid and took a sniff. Vodka—what a surprise. He glanced at his watch: if he’d managed to keep pace with all the time-zone changes, it was past ten in the evening. At any reasonable latitude, the sun would’ve been over the yardarm hours ago. Even here the sky was beginning to stain with sunset. Close enough.

  “Thanks.” He took a swig and passed the flask back to Igor. “So, what’s a biology grad student doing on this junket?”

  “I assist Professor Nakoryakova with her studies of trace radioactive isotopes in local soils and flora.” Igor sipped at the flask and handed it to Luciano. “Other than the physical evidence of treefall and the like, residual radiation is the most persistent signature of the Tunguska Event. But please, I did not wish to interrupt. I, too, am interested in what you say about your little black holes. Are they very different from the big ones?”

  Jack shrugged. “Depends. What do you know about the big ones?”

  It was Luciano who finally replied. “They are said to form when a star grows so heavy that it collapses under its own weight.”

  “That’s good, but it’s not the whole story. Maybe it’s better if we back up a bit, begin at the beginning. And, for a black hole, the beginning is gravity.”

  Jack downed another slug from the passing flask. The vodka did seem to be keeping the mosquitoes at bay. Or maybe he was just noticing them less.

  “The thing of it is,” he went on, “gravity’s just not very powerful, as forces of nature go. Compared to the strong nuclear force, it’s the next best thing to nonexistent. Even plain old electromagnetism’s got it beat hands down. You ever pick up a three-penny nail with a toy magnet? Then you know how even a teensy bit of electromagnetic force can overcome the gravitational pull of the whole Earth.”

  Jack shook his head. “When you get right down to it, the only thing gravity’s got going for it is, it just keeps on adding up.”

  “But is this not true of the other forces as well?” Luciano asked.

  “Not really. The nuclear forces are too short-range to amount to much over the long run. Electromagnetism’s got the reach, all right, but it comes in opposing flavors: positive and negative charges, north and south poles. That puts a natural upper limit on how strong an electromagnetic field can get before it attracts enough opposite charges to neutralize itself.”

  “And gravity, you are saying, only works one way?”

  “Uh-huh. Never lets go, never cancels out. That’s unique for a long-range force, and ultimately it’s decisive. Pack enough mass into one place—like in a planet ten times the size of Jupiter—and the field-strength at the core exceeds anything electromagnetism can stand up to. The electron shells that give things their structural strength, why, they just up and buckle. What started out as nice, solid matter—like this,” Jack rapped his knuckles on the log he was sitting on, “dissolves into a soup of dissociated electrons and free nuclei.”

  “And so this is how you make black holes?” Igor said.

  “Not quite. No, what I just described—” Jack pointed up through the branches to where the first faint pinpricks of light were just beginning to appear in the darkening sky, “—is how you make stars.”

  Knox had been at his desk and sitting on his hands half the morning, waiting for normal business hours—or Mycroft’s peculiar definition of them—to begin.

  The country of the night is the coder’s true homeland, and Mycroft, a loyal native son. In the fresh, clean hours after midnight, with the petty interruptions and annoyances of the day fading like dreams at dawn, he essayed prodigies of system design, assembling soaring fairytale architectures of logic, elegance, and power from the dry dust of global variables and reserved keywords. But it did make him a devout late sleeper.

  Knox flicked his gaze to the timestamp in the corner of his widescreen: 10:25. Give it another five minutes.

  His speakerphone emitted a muted chirp.

  “Mycroft?” Calling in early? That would be a first.

  “Front desk,” the voice of Archon Office Manager Suzanne Ledbetter corrected. “Were you expecting a visitor, Jon?”

  “Unh-uh. My calendar’s clear far as I know.”

  “Well, you’ve got one. Take a look.”

  A small conferencing window popped up on Knox’s screen, offering a real-time view of a young woman in casual dress. She was standing at the reception desk, communing with her wristtop. Knox zoomed the window to full-screen mode. Did he know her? She didn’t look like someone he would soon forget. She looked . . . striking, the way that dark hair complemented her ivory complexion.

  “I don’t know her,” he said finally. “Not that I wouldn’t like to. Did she say what she wants?”

  “What who wants, Jonathan?” A second voice broke in, issuing from the new conferencing window now staking out its own piece of screen real estate.

  “Oh, good morning, Mycroft.”

  Knox didn’t need to ask how the night’s researches had gone. If Mycroft’s sly grin weren’t enough, his computer-enhanced imagery—the black eyepatch and rakish red bandana, the Jolly Roger fluttering against a backdrop of sky and sea—all betokened a successful hack.

  “Jon?” Suzanne again. �
�What should I tell her?”

  Oh, right—his unscheduled visitor. “Uh, I could be tied up with this for a while. See if she wants to hang out, or maybe come back after lunch, okay?”

  “Okay.” The reception window irised shut.

  Knox turned back to Mycroft. “Took you long enough.”

  “I trust you will find it well worth the wait, Jonathan.”

  “The wait got old an hour ago.”

  “Yes, well, I’m afraid it must get a little older. There are a few preliminaries to cover first.”

  “Can ’em.” Knox pulled his chair in and leaned forward. “Get to the good stuff.”

  Half a world away, Jack Adler was getting to some good stuff of his own. He peered through the smoke of the campfire at the expectant faces of his listeners, thinking how best to put it across.

  “Stars are really just controlled gravitational implosions,” he began. “Take that super-Jupiter we were talking about. Once gravity overcomes its structural integrity, it starts to shrink. It’d go right on shrinking, too, except compression generates heat, and enough compression’ll heat the planet’s core to upwards of ten million degrees Kelvin. That’s the flashpoint: at that temperature, the free atomic nuclei are moving fast enough to start slamming into each other. The strong nuclear force takes over and thermonuclear fusion kicks in.”

  No matter how many times Jack told this story, he was always struck anew by the wonder of it. “Fusing hydrogen into helium releases energy. Colossal amounts of energy. Enough energy to push back against the pull of gravity. Enough to light the heavens. Enough to warm the worlds and spark the chemical processes that lead to life, to us.

  “Enough to make stars,” he breathed. He paused again, looking up. This sense of awe was as close as he got to what, he supposed, other people felt in the presence of the sacred.

  A hush fell over the little group. No sound stirred the still, warm evening air, save for an occasional pop from the fire.

  Jack shook himself. “Of course, things can’t go on like that forever. It takes fuel to keep those fires burning—hydrogen, in particular. The average star holds enough to chug along for billions of years, converting hydrogen to helium. But sooner or later it’s got to run out. And, when it does, the squeeze starts all over again.”

  Once it resumed, gravitational contraction would raise the core temperature back up to where the fire rekindled. Only now the helium “ash” itself became the fuel, fusing into heavier and heavier elements: carbon, lithium, oxygen, neon, silicon, finally bottoming out with iron. Then, nucleosynthesis having reached the point of diminishing returns, the stage was set for the final act.

  “At the very end there, gravity can grip hard enough that the core of the star just . . . collapses.” Jack stared into the campfire, seeing instead the cataclysmic last moments of a dying sun. “Collapses so fast it rebounds. You get a gigantic explosion, a nova or supernova. The star puts out more energy in that single instant than it did in a lifetime of steady shining. The shockwave is powerful enough to transmute elements wholesale.” In its spectacular death throes the star would seed the universe with the building blocks of new worlds, new life.

  “In the aftermath,” he went on, “the key thing is how much of the star’s original mass the explosion leaves behind. If it’s only around a sun’s worth, no problem: atomic nuclei have got more than enough structural strength to hold up under that much weight. You wind up with a brown dwarf star the size of the Earth.

  “But go upwards of that, and things start to get interesting.”

  Jack looked up. Three more expedition members, two middle-aged men and a younger woman, had come trooping in from the twilight forest and were walking purposefully toward the firepit. They gave Jack a perfunctory nod but continued talking quietly among themselves. Not here for the soapbox seminar, then—just more refugees from the gnats.

  “Please go on, Jack,” Luciano said. “You were saying?”

  “Oh, right. Well, if the leftovers weigh much more than the sun, things start to happen. The pressure in the interior of the “cinder” is enough to mash electrons and protons together, so you get neutrons. That triggers another collapse, into a neutron star only a few miles across. Bizarre enough in its own way, I suppose. But the point where us relativity theorists really sit up and take notice is when the supernova remnant is more than three times the mass of the sun. Not even neutrons can hold back that much gravity; they just up and cave. And neutrons are the last line of defense. Once they go, the whole mass collapses to what we call a singularity—a dimensionless point of infinite density, infinite space-time curvature, infinite you-name-it.”

  “Now you go too far, Adler,” a rumbling bass broke in.

  Jack turned and saw Medvedev’s great bulk looming just beyond the circle of firelight. “Oh, good evening, Academician,” he said. “I didn’t see you standing there. I’m sorry, what did you mean, ‘go too far’ ?”

  Medvedev sighed in seeming exasperation. “As everyone knows, the infinite is purely a mathematical construct. It can exist nowhere in nature.”

  “Maybe not for material objects and such. But gravity’s different. When you get right down to it, gravity is mathematics—geometry to be exact.”

  Medvedev said nothing, just stood there glaring at him.

  “Look,” Jack went on, “imagine that our three-dimensional space is a two-dimensional sheet of rubber. Then gravity’d just be a measure of how much that rubber sheet stretches when you drop a mass on it—a little for a marble, a lot more for a bowling ball. Drop a planet-sized mass onto that rubber sheet and the nearby surface’ll dip down to form a gravity well, one so steep it can curve the path of a moon into orbit around it. Drop in a sun, and you’ve got a deformation deep enough to trap a whole family of planets.”

  “This much I grant you,” Medvedev said. “Still, I hear in it nothing of your supposed infinities.”

  Jack held up a hand. “Hang on, I’m getting there. Turns out when a really massive star dies, it can form a sink-hole so deep that the well-walls wrap around and pinch shut, sealing off its remains from the rest of space-time. Remember Alice in Wonderland, where the Cheshire Cat vanishes, leaving only its smile behind? Well, here, all the matter disappears, collapses to a point, and only the mass is left. Enormous mass, taking up zero room. I don’t know about you, but that sure sounds like infinite density to me.”

  Jack glanced at Medvedev, but the big Russian was back to holding his peace, at least for the moment. That was okay; it would only take a moment to finish this up.

  “If there are no further questions,” Jack said, “then there’s only one more thing to add. Namely, that while all this is going on, the gravity gradient is getting steeper and steeper. Until it’s finally so steep that nothing, not even light, can escape . . .

  “. . . Which is why we call them black holes.”

  “Very nice, Adler.” Medvedev was smiling through his beard now. “A pretty story, but it has been told before. Two hundred years ago, the Frenchman LaPlace imagined ‘black stars’ with escape velocity greater than the speed of light. Why not be so good as to share with us the fruits of your own intellect instead.”

  “Well, these aren’t really my ideas, you understand,” Jack said. “But the fact is, supernovas aren’t the only way to make black holes. Every mass has its own cosmic point of no return—a lower limit on its size called the Schwarzschild radius. Beyond that, gravity takes over and collapses it down to a singularity. Shrink any mass small enough, and you get a black hole.”

  Medvedev smirked. “Even, perhaps, this?” He bent over abruptly. When he straightened again he was holding out a small lump of river-rounded rock.

  “Huh? Yeah, sure,” Jack said, eyeing the pebble. “Though it’d be easier to visualize if we start with something slightly larger. The Earth, say.

  “By all means, choose what example you will.” The Russian eased himself down opposite Jack, keeping the fire between them.

  “Okay, well,
Earth’s Schwarzschild radius is about one and a half centimeters. So, if you could put the whole planet into some humungous vise and crush it down to a one-inch sphere, it would become a miniature black hole.” Jack looked Medvedev in the eye. “With me so far? This is all just plain-vanilla relativity.”

  “No one disputes what you say, in theory,” Medvedev bristled. “But where is the actuality? Show me this fantastic vise, this ‘Schwarzschild machine’ of yours. Let me create a singularity myself, purely as an experiment. Then I, too, will believe.”

  “You know that’s impossible. The pressures needed are unimaginable, beyond anything we can even dream of today.”

  “Hah!” The Russian turned to his colleagues with a told-you-so grin.

  Jack sighed. “But that doesn’t mean it’s never been possible. There was more than enough radiation pressure in the first instants of the Big Bang to spawn PBHs—primordial black holes—of arbitrarily small size. And, as you know . . .”

  “Yes, yes,” Medvedev said, “I know only too well: it must therefore have been one of your famous PBHs that caused the Tunguska Event. All the generations of scientists who have struggled to understand this phenomenon of the Tunguska Cosmic Body are fools, fools or worse—futilely scouring the taiga for a meteorite that never existed. So claim the Three Wise Men from Texas University: Jackson and Ryan and Adler.

  “But, Adler,” Medvedev went on, “I say it is you who are the fool, coming all this way in pursuit of what was known to be folly when first published thirty years ago.”

  “Known? What do you mean known?”

  “Simply that if your compatriots Jackson and Ryan had troubled to acquaint themselves with the geophysical evidence—evidence gathered painstakingly over the years by serious researchers—they would never have put forward their preposterous idea in the first place.”

  “Believe me when I tell you,” Jack said, “that I’ve gone back and forth over your geophysical evidence, what little there is of it: seventy years of expeditions and you still haven’t got a clue what the thing was. Was it a comet? A meteor?” He shook his upraised hands in mock dismay. “We don’t know, we can’t tell. Let’s just call it a TCB, a ‘Tunguska Cosmic Body,’ and have done with it.”