Nebula Awards Showcase 2008

by Ben Bova

  “Thanks,” Amy said. “Do you like waffles? Or pancakes? Or eggs? Or cornflakes? Or what?”

  “The tables you took to the flea market—,” he began.

  “Were really amateurish,” Amy said. “I made them when I was still a student at Contemporary Arts—a school you never heard of—and I was keeping them for sentimental reasons. But I’ve run out of space.”

  “Pancakes would be nice,” said John.

  They ate in the kitchen. John set the table, sliced a cantaloupe and read newspaper bulletins to Amy while she whipped the batter and poured it onto the griddle. Over the pancakes he asked her why she hadn’t told him she was an artist.

  “Full-time waitress, part-time artist,” she explained. “I’ve had a few shows in some Bay Area galleries and a couple down in Santa Cruz. I love what I’m doing, I just wish I could do it all the time.”

  They talked through brunch, talked while Amy washed the dishes and John wiped them, talked and talked and suddenly decided to drive off in Amy’s car, drive anywhere, and while they drove John told her about his dissertation, about the equations he had concocted from a gedanken experiment. “What’s a gedanken experiment?” she asked him. “It’s where you just think an experiment, but you don’t actually do it, you just think it through,” he told her. “But now I’m beginning to wonder if the equations have anything at all to do with reality, real physical reality.”

  And after they had parked the car and were walking among the redwood trees, Amy told him, “I began as a painter and I still like painting, other people’s paintings, but for me—you’ll think I’m crazy—for me paint is too soft and squishy, too abstract. What I like about mosaic tesserae, the little pieces, whether they’re glass or ceramic or beach pebbles or whatever, what I like is that I can hold the color in my hand. It’s a piece of color. It has shape and size and weight. I love that. I love the idea of a solid piece of color. I know it sounds crazy.”

  “It doesn’t sound crazy to me,” John said.

  What sounded crazy to John came later, after they had driven all over the place and it was getting late—Amy had to waitress at the Capri and John had to get to his dissertation—and they had arrived back at their stucco apartment house. “You remember the Schrödinger wave equations we talked about?” said Amy. “Remember how we decided that by looking into those equations you could find out who the woman was that Schrödinger made love to and that she—”

  John interrupted, saying, “Not me. I mean, I couldn’t figure that out, couldn’t find out—”

  “She had a child nine months after that, and Schrödinger was the father,” Amy continued.

  “That’s in the book? In the biography?” He was quite surprised.

  “No. But that’s what I think. I’m sure of it.”

  “Ah,” John said, drawing it out slowly and, he hoped, thoughtfully. He thanked Amy for brunch and told her he had had a good time, a really good time, and Amy said she had had a really good time too.

  “You said you were hoping I’d drop by. Was it anything in particular?” he asked.

  “No. I was just hoping you’d drop by, that’s all.”

  Then Amy went off to work at the Capri and John went off to work on his equations.

  7

  John spent more and more of every day working on his equations, neglecting the rest of his life—sometimes even forgetting to eat, which had never happened before. On Friday he didn’t remember to drive up to Heidi Egret’s until it was already the moment when he should have been walking into her studio. He telephoned her, knowing from experience how irritated she would be at his tardiness, and as her phone rang and rang he phrased and rephrased how he would tell her he was going to be a little late. Her voice on the answering machine said to leave a message. John announced that he was not driving up there, was going to spend the weekend on his equations, good-bye. As a matter of fact, he did spend the rest of Friday and all the next day on his thesis, but late on Saturday he phoned Amy and asked did she want to have breakfast or brunch on Sunday. “Of course I do. Knock on my door tomorrow morning and I’ll make pancakes,” she said.

  The next morning John took a long hot shower, sang while he toweled himself dry, stepped into the crisp white cotton trousers which he almost never wore, pulled on a sky blue shirt and trotted downstairs, carrying CDs of Bach, Miles Davis, Olivia Newton-John, and Greek folk songs, and a big fresh pineapple, all of which he had bought right after phoning her. He knocked on Amy’s door.

  “Oh, wow, you look—,” John began. Amy was in a blue-and-white striped dress; her hair was swept back and little blue trinkets dangled from her ears. She looked beautiful but also unfamiliar. “I like the way you look,” he said.

  “You’ve begun a beard!” she said, rubbing her palms against the stubble on his cheeks. “And I like it,” she added.

  “What beard?”

  John had forgotten to shave for the past five days. As he told Amy while slicing up the pineapple, he had been working steadily and had been forgetting everything else. “I haven’t spoken to anyone for a week,” he said. He made up for it by talking all through brunch, talking while he washed the dishes and Amy wiped, was talking when they got into his car and drove all over and he didn’t fall silent until they stepped barefoot onto the beach at Half Moon Bay to watch the surfers. “I used to know somebody who surfed,” Amy said, looking away at the blurred horizon, squinting. “He’s a real estate agent now, beachfront property, and he’s rich. I met him at a gallery show last year. He drives a red Alfa Romeo. Maybe you saw it in our parking space.”

  John said no, he hadn’t seen it.

  “He got so drunk I didn’t dare let him drive back to Berkeley. He fell asleep on the floor,” she said, turning to John. “I don’t see how you missed his car, a red Alfa Romeo. It was parked out back all night.”

  “Maybe I was away,” John said, looking off down the shoreline. “I used to go away on weekends.”

  They walked along the beach and swapped stories about everything under the sun. When the sky turned gray they got into his car and headed back home, arriving in Menlo Park as it began to rain. Amy said she had been rereading parts of Schrödinger: Life and Thought, especially the part where Schrödinger works out his equations on quantum mechanics. “The woman he was making love to is in those equations,” Amy said. “Because this other physicist, Werner Heisenberg, had already figured out how to solve those problems in quantum mechanics. Heisenberg had a way of arranging the numbers into boxes, an array, a big matrix, so that when you work the matrix you get the right answers. Then Schrödinger, our Erwin Schrödinger, created his wave equations and solved the same problems. Schrödinger used a more tactile approach. He was that kind of man, tactile. He called Heisenberg’s math repellent and ugly. Everybody calls Schrödinger’s equations beautiful.”

  “Well—,” John began.

  “It’s true, isn’t it?”

  “The part about Heisenberg and Schrödinger and the equations is true, but about the woman—”

  They had turned the corner into the flooded parking area in back of the apartment house and come to a stop. The rain was beating on the car, streaming down the windshield.

  “Yes, she had Schrödinger’s baby, a girl. And that girl grew up and had a daughter. And that daughter—”

  “Wow! How did you arrive at that?”

  She laughed. “I’ve been doing what you might call a gedanken experiment. I’ve just been thinking things through.”

  John had turned to Amy and now he put his hand tentatively, gently to her cheek, his fingers moving into her hair. “I’ve been thinking too,” he told her hesitantly. “About other things. Us.”

  “Good. Schrödinger loved the things of this world, women especially,” Amy said. She was slightly flushed and her speech was beginning to race a bit. “He liked to see things and touch them, smell them, taste them. He was that kind of man. But there are a lot of other people like Heisenberg who don’t care about the physical side of
things. They think the world is really, finally, when you get right down to it, an abstraction.” She turned her face to meet John’s kiss, and afterward said, “Heisenberg thought the world could be reduced to a box full of numbers. In those days everybody was taking sides about this.”

  “I hope we’re on the same side,” he said, his hand moving beneath her arm.

  “God, yes,” she said, sliding her arm around his neck. “There was this other physicist, Max Born, who argued with Schrödinger, said the wave functions were only—Oh, God,” she said, speeding up. “Probabilities of what might be there, said you could never picture what was actually going on,” she finished in a rush.

  “I’m going crazy, Amy.”

  “Me too.”

  The windows were getting foggy and it was cramped and uncomfortable in the car, so they dashed through the rain to the house.

  8

  Amy was right about Schrödinger’s equations and Heisenberg’s matrix. Schrödinger himself wrote a paper (1926, Annalen der Physik 79, 734–56) about the relationship between his wave equations and Heisenberg’s matrix, showing that they produced the same results. But he believed theories should be visualizable (Anschaulichkeit) and he loathed Heisenberg’s quantum mechanics. In 1926, a few days after Schrödinger had published his fourth and final paper on wave mechanics, Max Born published a paper asserting the statistical nature of Schrödinger’s waves—the waves, he said, were unimaginable clouds of probabilities. Of course, Schrödinger rejected that idea. For Erwin Schrödinger, everything he knew and loved was graspable in this world, our world of space and time, our living world, as he demonstrated during his years in Ireland.

  As for John’s thesis, it consisted of three papers on gravity, of which the first two were complete. In the third paper he had arrived at a bothersome equation or, as his dissertation director pointed out, many bothersome equations, and he was having a hard time figuring out what the equations implied. Unlike the European physicists of 1926, John had not read much in the way of philosophy and had not speculated on the relationship of mathematics to the physical world that it might, or might not, represent. Now all sorts of questions distracted and fascinated him, and though they were old questions to Schrödinger and Born, they were new to John Artopoulos. Indeed, these questions appeared to be at the opaque heart of his dissertation and they seemed unanswerable. To put it another way, in the previous six months he used up three reams of paper and hadn’t completed a single page. Of course, the past two weeks had been different because now his brain, his body, everything was on fire.

  9

  We don’t know the details of what they did, Erwin Schrödinger and the woman he was with, during the winter of 1925/26. The important thing is that he came out from that snow-covered chalet with his wave equations. And we shouldn’t pry into what John and Amy did after they had dashed through the downpour and into her flat. John probably spent most of his waking hours on his equations, some of his time with Amy, and a couple of hours playing handball with his colleague Gino. As for Amy, most likely she waitressed at the Capri and spent her free time on a new mosaic. What’s important is that on Sunday, April 18, 2004, Amy stepped out of a hot shower, wrapped herself in a towel and—Hey!—there stood John in the open doorway, wisps of the steam cloud floating away to reveal a bottle of wine in one hand and two glasses in the other. “I finished it!” he announced.

  “Wonderful! Fantastic!” said Amy.

  In the kitchen John set to work uncorking the bottle while Amy toweled her hair. Then they sat at the table and he poured a glass for her, a glass for himself. “Greek wine,” he told her, smiling. He was more unshaven than ever, his eyes puffy and red rimmed from lack of sleep, but he was happy. “Greeks have been producing wine for thousands of years,” he said, lifting his glass.

  “Producing mathematicians and physicists, too,” Amy said, smiling a little, touching her glass to his. They drank.

  They talked about this and that, trivial things like John’s having enough time now to get his car radio fixed. Actually, Amy wasn’t paying attention to the conversation because up to now she had been able to avoid thinking about where John might disappear to when he had finished his graduate studies. Now she was thinking about it. John asked her how her new mosaic was coming along. Amy said she’d show him later. He said it felt good to be through being a student and that it would feel even better to go to a real job someplace. Amy felt her heart contract at the thought of his leaving. She hesitated a long moment. “Now what do you do?” she asked him.

  “I take a shower. Like you,” he said, standing up, laughing. “A long, hot shower.” He pulled off his T-shirt and padded barefoot down the hall toward the bathroom, tossing his shirt in the air, catching it, singing. By the time John returned to the kitchen Amy had pulled on her cutoffs and a frayed jersey that said Xanadu, and was refilling their glasses. John lifted his glass to hers, saying, “Tell me about Schrödinger’s woman and show me your new mosaic.”

  “I’ll show you the mosaic,” Amy said, touching her glass to his.

  “What about the anonymous woman and her daughter and so on?”

  “I’m sorry I ever said anything,” Amy told him. She hurriedly drained her glass and nearly choked, then coughed. “Now you think I’m crazy or silly or just strange.” She coughed again, wiped her eyes and looked at John hopelessly.

  “Tell me anyway,” he said. “Please.”

  “I calculated that Erwin’s woman gave birth to a baby girl on September 9, 1926. I figure that about twenty-five years later this daughter gave birth to a daughter, too, probably in England. That would be Erwin’s granddaughter, like Olivia Newton-John is Max Born’s granddaughter, also born in England.”

  “Olivia Newton-John, the singer? The singer in Xanadu? She’s Max Born’s granddaughter?”

  “I thought everybody knew that.”

  “Please go on,” said John.

  “That woman, the granddaughter, probably gave birth about twenty-five years later to a daughter, probably here in the United States,” she said, fearing that every word would drive him away.

  “In California?”

  “In California, yes,” she said firmly. “Probably.”

  “And you are?”

  Amy laughed. “Amy Bellacqua, daughter of Vincent and Catherine Bellacqua, who is the daughter of Cosima Ferraro from Morano, Italy, and no relation to Erwin Schrödinger.”

  “How would we know if we found Schrödinger’s great-granddaughter amid all these probabilities?”

  “She’d be twenty-eight years old and have the Schrödinger equation tattooed on her butt,” she said briskly. “Now let me show you the mosaic.”

  They went into the front room, the one John loved to linger in, the air full of green leaves and tendrils, the floor carpeted with trays of moss, uncurling ferns, pale celery-colored sprouts, the mosaic tables bearing potted plants, the pots themselves composed of shards from broken mosaics, the walls blazing with mosaic designs. “Here,” she said, handing him a tray-like tablet where a dark background had imbedded in it a formula in white stones, like chalk on a blackboard. It was one of Schrödinger’s wave equations. “I copied it from Schrödinger: Life and Thought. I chose one I liked the shape of. As a kid I used to look at the symbols in my dad’s math books. I loved the sigmas, the deltas, the stately integration signs,” she told him. John gazed at the equation, murmuring “Yes,” and “Yes,” and “Yes,” all the while frowning. “But this first big symbol,” he said at last. “The wave function.”

  “The Greek letter psi,” said Amy. “What’s wrong with it?”

  “You’ve made it look like—it looks like—”

  “Like a pitchfork, or a trident like the old man of the sea carries. It’s psi, but I made the tale a bit longer. It’s more elegant,” she said.

  “What are the chances that Schrödinger’s unknown great-granddaughter has it tattooed on her shoulder?” he asked.

  10

  The third part of John�
�s dissertation was published by the American Physical Society (2004, Phys. Rev. Lett. 09, 18 65–88) and was cited with sufficient frequency to be included in an online list of most important papers. Amy’s mosaics were exhibited by the Stern-Whitehall gallery in San Francisco, a show that was favorably reviewed in California Spectrum. Fred Marsh, hitherto unnamed, who drove the red Alfa Romeo sports car and who was already rich at thirty-five (beachfront property), was introduced to Heidi Egret at a gallery reception in Berkeley and two weeks later they were living together at his place.

  The tattoo on Heidi’s shoulder did—and still does—look like the Greek letter psi, y, the symbol for the wave function in Schrödinger’s equations. The tattoo also looks like a pitchfork and like Poseidon’s trident because, in fact, they all look alike. So much for the tattoo. As for Heidi’s great-grandmother and whether she was the woman who spent fifteen or twenty days with Schrödinger in that snow-covered chalet, that’s far less clear. It’s as if nature had rigged the game so that the more precisely we get to know one part, the tattoo, the less certain we will be about the other, the great-grandmother. Indeed, in 1927 Heisenberg published a paper (Zeitschrift für Physik 43, 172–98) neatly defining this problem which has since become known as Heisenberg’s uncertainty principle.

  We know all we need to know about the tattoo. “It means I’m a follower of Neptune, you know, the sea god,” Heidi explained. “I used to do a lot of surfing—Wadell Creek, Santa Cruz, places like that.”