by Mark Alpert
“Just bear with me for a second. I’m talking about his attempts to derive a field equation that incorporated gravity and electromagnetism. You know, his work on five-dimensional manifolds, post-Riemannian geometry. How familiar are you with those papers?”
She shrugged. “Not very. That stuff is only of historical interest. It doesn’t have any relevance to string theory.”
David frowned. He’d hoped, perhaps unrealistically, that Monique would know the subject backward and forward, so she could help him examine the possibilities. “How can you say that? There’s definitely a connection with string theory. What about Einstein’s work with Kaluza? They were the first to postulate the existence of a fifth dimension. And you’ve spent your whole career studying extra dimensions!”
She shook her head. The expression on her face was that of a long-suffering professor explaining the basics to an ignorant freshman. “Einstein was trying to come up with a classical theory. A theory with strict cause and effect and no weird quantum uncertainties. But string theory derives from quantum mechanics. It’s a quantum theory that includes gravity, and that’s completely different from what Einstein was working on.”
“But in his later papers, he took a new approach,” David argued. “He was trying to integrate quantum mechanics into a more general theory. Quantum theory would be a special case in a larger classical framework.”
Monique waved her hand dismissively. “I know, I know. But in the end, what came of it? None of his solutions held up. His last papers were total nonsense.”
David’s face warmed. He hated her tone. Maybe he wasn’t a mathematical genius like Monique, but this time he knew he was right. “Einstein discovered a working solution. He just didn’t publish it.”
She cocked her head and gave him a quizzical look. The corners of her lips turned up ever so slightly. “Oh, really? Did someone send you a long-lost manuscript?”
“No, that’s what Kleinman told me before he died. He said, ‘Herr Doktor succeeded,’ those were his exact words. And that’s why he was killed tonight, that’s why all of them were killed.”
Monique heard the urgency in his voice and her face turned serious. “Look, David, I understand you’re upset, but what you’re suggesting is impossible. There’s no way Einstein could’ve formulated a unified theory. All he knew about was gravity and electromagnetism. Physicists didn’t understand the weak nuclear force until the sixties and they didn’t figure out the strong force until ten years later. So how could Einstein come up with a Theory of Everything if he didn’t understand two of the four fundamental forces? It’s like building a jigsaw puzzle without half the pieces.”
David thought about it for a moment. “But he wouldn’t have to know all the details to construct a general theory. It’s more like a crossword puzzle than a jigsaw. As long as you have enough clues, you can figure out the pattern, and then you can fill in the blank spaces later.”
Monique was unconvinced. David could see from the look on her face that she thought the idea was absurd. “Well, if he came up with a valid theory, why didn’t he publish it? Wasn’t that his lifelong dream?”
He nodded. “Yes, it was. But all this was happening just a few years after Hiroshima. And even though Einstein had nothing to do with actually building the atom bomb, he knew that his equations had pointed the way. E = mc2, huge amounts of energy from tiny bits of uranium. It was agonizing for him. He once said, ‘If I knew they were going to do this, I would have become a shoemaker.’”
“Yes, yes, I’ve heard all this before.”
“Well, think about it for a minute. If Einstein did find a unified theory, wouldn’t he worry that the same thing might happen again? He knew he had to figure out the implications of the discovery, all the possible consequences. And I think he foresaw that the theory could be used for military purposes. Maybe to create something even worse than a nuclear bomb.”
“What do you mean? What could be worse?”
David shook his head. This was the weakest link in his argument. He had no idea what the Einheitliche Feldtheorie was, let alone what it could unleash. “I don’t know, but it must’ve been something terrible. Bad enough that Einstein decided he couldn’t publish the theory. But he couldn’t abandon it either. He believed physics was a revelation of God’s handiwork. He couldn’t just erase the theory and pretend it never existed. So he entrusted it to his assistants. He probably gave each one a little piece of the theory and told them to keep it safe.”
“What good would that do? If the theory was so terrible, his assistants couldn’t publish it either.”
“He was thinking of the future. Einstein was a hopeless optimist. He really thought that in a few years the Americans and Russians would lay down their arms and form a world government. Then war would be outlawed and everyone would be at peace. And his assistants just had to wait until that day before revealing the theory.” Unexpectedly, David’s eyes began to sting. “They waited their whole lives.”
Monique gave him a sympathetic look, but she clearly didn’t believe a word of what he said. “It’s an extraordinary hypothesis, David. And extraordinary claims require extraordinary proof.”
David steeled himself. “Kleinman told me a series of numbers when I saw him in the hospital tonight. He said it was a key that Einstein had given him, and now he was giving it to me.”
“Well, that’s hardly—”
“No, that’s not the proof. The proof is what happened afterward.”
Then he told her about his interrogation at the FBI complex and the massacre that followed. At first she just stared at him, incredulous, but as he described how the lights went out and the gunfire echoed down the corridors, she unconsciously gripped the hem of her nightshirt and bunched it in her fist. By the time he finished, Monique seemed just as shell-shocked as he’d been when he emerged from the parking garage on Liberty Street. She grabbed his shoulder. “My God,” she whispered. “Who attacked the place? Were they terrorists?”
“I don’t know, I never saw them. I just saw the dead FBI agents. But I bet they’re the same people who killed Kleinman and Bouchet and MacDonald.”
“How do you know? Maybe the FBI killed them. It sounds like the government and the terrorists are after the same thing.”
He shook his head. “No, the FBI would’ve taken them in for questioning. What I think happened is that the terrorists found out about the unified theory first. Maybe Kleinman or Bouchet or MacDonald let something slip. So the terrorists went after them, torturing each one for information. But after they started turning up dead, the American intelligence agencies must’ve figured out that something was going on. That’s why the FBI agents showed up so quickly at the hospital. They probably had Kleinman under surveillance.”
David’s voice had risen as he outlined the scenario, and his last words rang against the walls of the kitchen. Catching himself, he looked at Monique to see her reaction. Her face was no longer quite so skeptical, but she still wasn’t convinced. She let go of his shoulder and stared again at her laptop, which had by now reverted to its screen saver, an animation of a rotating Calabi-Yau manifold. “It doesn’t make sense,” she said. “I mean, maybe you’re right about the killings, maybe the terrorists were going after Kleinman and the others because of some secret project they were all working on. But I can’t believe the project was a unified field theory that Einstein’s assistants had been hiding for fifty years. It’s just too implausible.”
He nodded again. He could understand her disbelief. It wasn’t simply a preference for quantum over classical theories. Her whole life’s work was at stake here. David was suggesting that all the accomplishments that she and her fellow string theorists had achieved over the past two decades, all the painstaking advances and hard-won insights and brilliant reformulations, were irrelevant. A scientist who’d died before most of them were born had already captured their ultimate prize, the Theory of Everything. And this possibility was, to put it mildly, a little hard to accept.
He turned away from Monique, wondering how to convince her. He had an extraordinary claim but no extraordinary proof. He didn’t even have much in the way of ordinary proof. As he stared at the blank walls of the kitchen, though, a new thought occurred to him. It wasn’t a pleasant thought; in fact, it was so abhorrent that his heart started knocking against his breastbone. But it was evidence.
“Look around,” he said, turning back to Monique and pointing at the walls and cabinets. “Look at this kitchen. There’s no damage here, no graffiti. Not a single swastika.”
She gazed at him, uncomprehending. “Yeah? So?”
“Why would a bunch of New Jersey skinheads trash every room in this house except the kitchen? Doesn’t that seem a little odd?”
“What does this have to do with—”
“There weren’t any skinheads, Monique. Somebody tore this place apart to look for Einstein’s notebooks. They searched under the floorboards and dug holes in the backyard and poked through the plaster to check the spaces between the walls. And they put swastikas everywhere to make it look like vandalism. They didn’t touch the kitchen because it was added to the house long after Einstein died, so he couldn’t have hidden anything there. And they didn’t touch your furniture for the same reason.”
Monique raised her hand to her mouth. Her long slender fingers touched her lips.
“If I had to guess,” David continued, “I’d say it was the FBI that did the search. The terrorists wouldn’t have bothered to wait until you’d left the house for the weekend. They would’ve just killed you in your sleep. And I’d also guess that the agents didn’t find any notebooks. Einstein was too clever for that. He wouldn’t have left anything in writing.”
Although Monique’s hand covered the lower half of her face, David could still observe the change in her expression. First her eyes widened in fear and surprise, but within seconds they narrowed and a deep vertical crease appeared between her eyebrows. She was livid, absolutely furious. Neo-Nazi skinheads were bad enough, but federal agents who would spray-paint swastikas on the wall to cover up a clandestine operation? That was another class of evil entirely.
She finally lowered her hand and grabbed David’s shoulder again. “What were the numbers Kleinman gave you?”
SIMON HAD NO TROUBLE GETTING across the Hudson River. There was a checkpoint at the entrance to the Lincoln Tunnel, where a pair of police officers ordered him to roll down his window and a bomb-sniffing dog poked its snout into the car, but Simon had changed his clothes at the Waldorf and showered every trace of C-4 off his skin, so the German shepherd just gazed dumbly at the steering wheel. Simon showed the officers his ID—an expertly forged New York State driver’s license—and they waved him through.
Five minutes later he was on the New Jersey Turnpike, racing along the causeway that spanned the dark, dank Meadowlands. He could drive as fast as he liked because the highway was nearly empty at four o’clock in the morning and all the state troopers were assisting the New York police at the bridges and tunnels. So he tore past Newark Airport at ninety miles per hour, then banked west toward the sprawling Exxon refinery.
It was the deadest part of night, the very bottom. Up ahead, the distillation towers of the refinery rose from the blackness. A gas fire streamed from one of the flare stacks, but the flames were thin and flickering, as weak as a pilot light. The road seemed to darken as Simon sped by the maze of pipes and petroleum tanks, and for a few seconds he felt like he was traveling underwater. On the blank screen of his mind he saw two faces, the faces of his children, but it wasn’t the comforting image he’d saved on his cell phone. In this picture, Sergei and Larissa weren’t smiling. Sergei’s eyes were closed as he lay in a muddy ditch, his arms streaked with long black burns and his hair caked with blood. But Larissa’s eyes were wide open as if she were still alive, as if she were still staring in horror at the fireball that had engulfed her.
Simon hit the accelerator and the Mercedes leaped forward. He soon reached Exit 9 and barreled onto Route 1 South. He’d be in Princeton in fifteen minutes.
4 0 2 6 3 6 7 9 5 6 4 4 7 8 0 0
DAVID WROTE THE NUMBERS IN PENCIL on a sheet of notebook paper. He passed it to Monique and immediately felt a powerful urge to snatch the paper back and tear it to shreds. He was afraid of those sixteen digits. He wanted to destroy them, bury them, erase them forever. But he knew he couldn’t. He had nothing else.
Monique held the paper in both hands and scrutinized the numbers. Her eyes darted from left to right, looking for patterns, progressions, geometric sequences. On her face was the same focused stare that David had seen when she delivered her paper on Calabi-Yau manifolds at the string theory conference. Like the face of the goddess Athena preparing for battle.
“The distribution looks nonrandom,” she noted. “There are three zeroes, three fours and three sixes, but only a single pair, the pair of sevens. In a numeric sequence of this size, it’s improbable to have more triplets than pairs.”
“Could it be a key for decrypting a computer file? Kleinman used the word key, so that would be logical.”
She kept her eyes on the numbers. “The size is about right. Sixteen digits, and each can be transformed to four bits of digital code. That would make sixty-four bits in all, which is the standard length for an encryption cipher. But the sequence has to be random for the technique to work.” She shook her head. “With a nonrandom sequence, you could break the code too easily. Why would Kleinman choose an imperfect key like that?”
“Well, maybe it’s a different kind of key. Maybe it’s more like an identifying label. Something to help us find the file instead of decrypt it.”
Monique didn’t respond. Instead she brought the paper a little closer to her face, as if she were having some difficulty reading the numbers. “You wrote this sequence in an odd way.”
“What do you mean?”
She turned the sheet of paper around so he could see it. “The numbers are bunched up a bit. Slightly wider spaces after every second digit. Except at the end, where the spacing is even.”
He took the paper from her. She was right, the first twelve digits were arranged in two-digit blocks. He hadn’t consciously written it that way, but there it was. “Huh,” he grunted. “That is odd.”
“Did Kleinman specify this grouping when he gave you the sequence?”
“No, not exactly.” He closed his eyes for a moment and saw Professor Kleinman again, sitting up in his hospital bed as he choked out his last words. “His lungs were failing, so the numbers came out in gasps, two at a time. And that’s the way I see the sequence in my memory now. A half-dozen two-digit numbers and a four-digit number at the end.”
“But is it possible that the grouping was intentional? That Kleinman wanted you to organize the numbers that way?”
“Yeah, I suppose. But how does that change things?”
Monique grabbed the paper and placed it on the kitchen table. Then she found a pencil and drew lines between the two-digit blocks.
4 0 / 2 6 / 3 6 / 7 9 / 5 6 / 4 4 / 7 8 0 0
“If you order the sequence this way, it looks even less random,” she said. “Forget about the four-digit number for now and just look at the two-digit numbers. Five of the six are between twenty-five and sixty. Only the seventy-nine falls outside that range. That’s a fairly tight grouping.”
David stared at the numbers. They still looked pretty random to him. “I don’t know. It looks like you’re doing some picking and choosing to make a pattern.”
She frowned. “I know what I’m doing, David. I’ve spent a lot of time studying data points from particle-physics experiments, and I know a pattern when I see one. For some reason the numbers are clustered in a narrow band.”
He stared at the sequence again and tried to see it from Monique’s point of view. Okay, he thought, the numbers seem to be clustered below sixty. But couldn’t this simply be a chance arrangement? To David’s eye, the sequence looked just as random as the winning numbers f
or the New York Lotto, which he played from time to time despite the pitifully bad odds. The lottery numbers also tended to cluster below sixty, but that was only because the highest number you could pick was fifty-nine.
And then he saw it, clear as day. “Minutes and seconds,” he said.
Monique didn’t seem to hear. She stayed bent over the kitchen table, studying the sequence.
“You’re looking at minutes and seconds,” he said, a little louder this time. “That’s why the numbers are below sixty.”
She looked up at him. “What? You’re saying this is some kind of time measurement?”
“No, not time. These are spatial dimensions.” David gazed at the sequence once more and now its meaning opened up like a flower, with all six of its petals perfectly arranged. “They’re geographic coordinates, latitude and longitude. The first two-digit number is angular degrees, the second is arc minutes, and the third is arc seconds.”
Monique stared at him for a moment, then turned to look at the numbers. Her face broke into a smile, one of the loveliest smiles David had ever seen. “All right, Dr. Swift,” she said. “It’s worth a shot.”
She went to her laptop and started tapping the keyboard. “I’ll punch in the coordinates on Google Earth. Then we can get a look at the place.” She found the program and typed in the numbers. “I’m assuming the latitude is forty degrees north, not south. Otherwise you’d be somewhere in the Pacific Ocean. And for longitude, I’m assuming it’s seventy-nine degrees west, not east.”
David stood beside her so he could see the laptop’s screen. The first image that came up was a grainy satellite photo. At the top was a large building shaped like an H and at the bottom was a row of smaller buildings shaped like Ls and plus signs. The structures were too big to be houses but not tall enough to be office towers. And they weren’t arrayed in a street grid or located next to a highway; instead, most of the buildings were situated at the periphery of a long rectangular courtyard crisscrossed by walkways. A campus, David thought. It was a college campus. “Where is this place?”
