A security guard named Don came to the bar and rushed out to search the companionway, but Weldon was gone.
BAD GRRLZ’ GUIDE TO PHYSICS
CONSIDERING THE COLLAPSE OF THE WAVE FUNCTION AND THAT DAMN CAT
If you’ve been following me so far, you know that quantum physics describes a world of many simultaneously existing and sometimes contradictory possibilities. An electron orbiting an atom can be, simultaneously, in more than one place.
It really can. Trust me on this. Experiments have shown that the same electron is in two places at once. However—and here’s the tricky part—the minute you try to measure the electron’s whereabouts, all those potentialities collapse into a single actuality.
The easiest way to describe all this is to use Schrodinger’s cat, a beast I find annoying but impossible to avoid.
Schrodinger’s cat is a thought experiment. Let’s get that straight at the start so that I don’t get nasty letters from cat lovers. No one has actually performed this experiment with a cat. This is a theoretical cat—the brainchild of one Erwin Schrodinger, winner of the 1933 Nobel Prize for Physics.
So here’s the imaginary experiment. Suppose you have a cat—let’s call her Fluffy. You put her in a sealed, soundproof box. You plan to keep Fluffy in this box for exactly one hour. There’s plenty of oxygen in the box; Fluffy won’t run out of air. But you have also placed in the box a Geiger counter and chunk of radium that emits gamma rays. Over the course of an hour, the radium has a probability of exactly 50% of tossing out a subatomic particle (a process known as radioactive decay).
Considered from the quantum mechanical point of view, the radium atom is in a superposition of decaying and not decaying with a 50% likelihood of doing either. Considered quantum mechanically, two realities exist: in one, the radium atom has decayed; in the other, it has not.
In the reality where the radium decays, the Geiger counter clicks. When this happens, a device breaks a flask that releases a poisonous gas that kills poor Fluffy.
In the reality where the radium does not decay, the Geiger counter doesn’t click, and everything is OK. In that reality, Fluffy is fine.
Here’s the part that tweaks the physicists. The radium atom is in a quantum mechanical state of superposition. It is simultaneously occupying two realities: decaying and not decaying. Since Fluffy’s survival is linked to the state of the radium atom, the cat is also simultaneously occupying two realities: alive and dead. It is not that the cat is definitely alive or definitely dead and you just don’t know which is true. It’s weirder than that. Until you open the box and observe the system, the atom and the cat are in both states at the same time the cat is oscillating between life and death.
Weird, huh? This is what makes my fellow physicists get twitchy. Strange behavior on the part of an electron or an atom is annoying enough. But Schrodinger’s cat allows the weirdness of an electron to manifest itself on the macroscopic scale. You’ve got a cat that is simultaneously alive and dead—until you sneak a peek.
When you take a look, all the potentialities collapse to a single actuality. Physicists call this “the collapse of the wave function.”
We know that the wave function collapses whenever we physicists try to measure or observe a system. The act of looking influences the system we are observing and causes all those lovely potentialities to become a single actuality. Open the box to look at the cat, and bingo—the cat is alive or the cat is dead.
Why should observation change a system? No one knows. Theoretical physicists call this the “measurement problem,” and the whole thing has made lots of physicists terribly uncomfortable.
People have come up with some lovely theories to explain the measurement problem. The most popular among physicists is the theory proposed by Niels Bohr, one of Schrodinger’s contemporaries. Bohr said that you can’t describe a system unless you measure it, so you can’t even talk about what it looks like between measurements.
As far as I’m concerned, Bohr’s interpretation avoids all the interesting questions. It’s sort of like he threw up his hands in disgust at the whole mess and just decided not to deal with it.
Then we have the Wigner Interpretation, proposed by physicist Eugene Wigner. Most physicists don’t like this one much, but I love it. Wigner suggests that when someone looks at a system, their consciousness influences the system. The mind of the observer attempting to measure or observe the system triggers the collapse of the wave function.
Another theory I rather like is the Many Worlds Interpretation, first suggested by H. Everett in his Ph.D. thesis at Princeton and later developed further by physicist B. de Witt. This one ducks the question of what triggers the collapse by saying that there really isn’t a collapse when someone makes a measurement. All the potentialities are realized as actualities, Everett said, but they exist in different universes, all branching out from the original point. There’s a separate universe for every possible outcome.
Most physicists don’t like this theory much—it smacks too much of science fiction. But Everett’s approach offers some real advantages. Mathematically, it’s solid—I can show you how Schrodinger’s wave equation (developed by the same Schrodinger who came up with the cat conundrum) correctly describes the quantum mechanical state of the universe as a whole, including all of its branches.
As I mentioned before, my Ph.D. thesis deals with a mathematical model that connects Wigner’s theory and the Many Worlds theory, showing that consciousness is what determines how and when the universe branches.
Maybe you’re wondering what all this has to do with the Odyssey and Max Merriwell and my friend Susan. Could it be that Max has generated a mess of branching potentialities? If so, are we headed for the collapse of the wave function, where all these potentialities col lapse into a single reality? If that’s the case, will the reality when they collapse be our own? Or will the world as we know it cease to exist?
Or is the Everett-De Witt Many Worlds theory right? Do all these branching realities coexist, parallel realities that occasionally overlap?
I confess: I’m very curious about the answers to these questions. I think it’s time to work out the math.
NINETEEN
“You never know what’s going to be on the other side of the door,” Gitana said. “But you know you have to open it. Or you would wonder for the rest of your days.”
—from The Twisted Band
by Max Merriwell
The next morning, Susan woke early. Leaving Pat sleeping soundly, she went to Circe’s Kitchen, on the chance she might find Max having breakfast. Luck was with her and he was there. His notebook was on the table in front of him, but it was closed. He waved when he saw her.
“Good morning, Max,” she said. “Do you mind if I join you?”
“I’d be delighted to have your company. Please—sit down.”
An overhead lamp cast a warm golden glow over the table; the air was scented with coffee. Though the restaurant was warm, Susan felt cold. Outside the window, the sky was overcast; the ocean waves were the color of lead—gray and impenetrable. Hard to believe that this dark water was connected to the sparkling, turquoise blue seas off Bermuda.
She ordered breakfast—bacon and eggs, coffee, toast—while trying to figure out how to broach the subject of Weldon Merrimax. But before she could, Max started talking.
“I found another note under my door this morning,” he said. He took a piece of ship’s stationery from his notebook and offered it to Susan.
She unfolded it. Another hexagram: five broken lines, topped by a solid line. Printed under the hexagram in the same angular handwriting as the first note was one sentence: “The dark lines are about to mount upward and overthrow the last light line.”
“That sounds ominous,” she said.
Max frowned. “Not necessarily. Considering darkness to be evil is a very Occidental perspective. Darkness isn’t necessarily evil. There is always fluctuation between the dark and the light. The moon waxes and w
anes; the sun rises and sets. The bright and the dark; the firm and the yielding; the yang and the yin.”
Susan found herself remembering Mary Maxwell’s discussion of dragons. “I met Mary Maxwell night before last,” she said. “After drinking Rum Monkeys.”
“Really?” Max didn’t seem surprised. “I quite like Mary. She’s a wonderful person.”
Susan stared at him. “She’s a real person then?”
Max shrugged, looking uncomfortable. “It’s best not to examine these things too closely. It’s all part of the creative process. Tricky stuff, that.”
Susan shook her head. “I met Weldon Merrimax last night.”
Max frowned. “Oh, that’s too bad.”
“He’s real, isn’t he?” she asked.
Max sighed. “That’s a very difficult question, Susan.”
“Seems simple enough to me.”
“Might as well ask whether light is a particle or a wave,” he said. “It’s both, you know. Though not at the same time.”
“What is going on, Max?”
Max stared down at his coffee for a moment, then said, “You have to consider the power of names. To summon a demon, one needs to know its name. To activate a golem, one writes the name of God on its forehead. Names are very powerful.”
He looked up and met her eyes. “Mary Maxwell—the name came to me so easily, almost an echo of my own name. I dreamed of her and she told me stories. It was quite lovely.”
He sipped his coffee and frowned. “I should have stopped there. That would have been best. But that fall, my agent suggested I write a crime thriller. It was a dreary autumn and the garbage men were on strike. All Manhattan stank like a Dumpster. I was in a bleak mood and I thought of Weldon Merrimax. Another echo of my name; a joke, really. I told my agent and he laughed. That night, I dreamed of Weldon Merrimax, an angry man obsessed with money and power. We talked, and he told me about crimes he had committed, about cons and swindles and frauds. He seemed to like talking to me. I listened and I wrote the first Weldon Merrimax book.”
Max looked out the window at the gray ocean waves. “There’s a question writers joke about. People always ask, ‘Where do you get your ideas?’ As if we had a clue. Oh, I can tell you bits and pieces of the process—someone mentioned this which led me to think about that and so I put these things together with a story from the New York Times and ended up over here. But where did Mary and Weldon come from? I don’t know. I made up the names and invented the characters—or did I? Maybe they were already out there, waiting to be found. Maybe I called them up by invoking their names.” Max shrugged. “Does it matter?”
“But what’s going on now?” Susan asked.
“Well, I’m working on a new book,” he said. “Writing a novel always involves a bit of turbulence.”
Susan stared at him. “A bit of turbulence?” she repeated.
Max shrugged. “It’s part of the creative process,” he said. “The subconscious isn’t a tidy place. I’ve been sleeping badly and I haven’t been dreaming.” He shrugged. “But I’m sure it will all work out.”
“Weldon Merrimax said he wanted to talk to you,” Susan said. “He said he was rearranging things so that they’d be more to his liking. He talked about God and Lucifer and said it’s a question of who is going to be the Creator. He said to tell you he wants to talk to you.”
“And so you have.” Max did not seem perturbed. “That was the right thing to do.”
“But what are you going to do?” Susan asked. “I think you need to talk to Weldon.”
“Do I? I have nothing to say to him.” Max shook his head. “If Weldon wants to sneak around leaving cryptic notes, that’s his business. I’ll just ignore him.”
Max reached out and tapped a finger on the note in her hand. “The lower trigram is K’un, representing receptivity and the earth. The upper trigram is the mountain, which keeps very still. The superior man will wait quietly, avoiding action.” Max folded his hands in front of him, smiling. “I believe that’s the course the I Ching recommends.”
“But he’s very angry,” Susan said.
Max did not reply. He glanced at his watch. “You know, we’d better hurry or we’ll be late to class.” He smiled at her. “Just relax. There’s nothing to worry about.”
Somehow Susan didn’t believe him.
Susan returned to her stateroom before workshop, figuring she would wake up Pat. But when she got there, Pat was already in the shower. The dressing table was covered with sheets of notebook paper and the notebook paper was covered with equations.
As Susan closed the stateroom door, the sound of running water stopped. A moment later, Pat stepped from the bathroom. She was wearing one of the white terry cloth robes and toweling off her hair. “What have you been up to?” Susan asked her, waving a hand at the drift of notebook pages.
“I ran into Ian last night, after the show. We got to talking about the weird stuff that’s been going on. I came up with a theory to explain it, and I’ve been working out the math.”
“The math?” Susan said, baffled.
“It’s Everett’s Many Worlds Interpretation with a few extra spins suggested by Roger Penrose’s work. The influence of the conscious mind on the quantum state, that is. I can show you the math, if you like.”
“That’s okay,” Susan said quickly. “Maybe you could just give me the overview.”
“I figured I’d tell Max about it after workshop,” Pat said. “Maybe we could all have lunch. I bet Ian would be up for it.”
Though they hurried, they arrived at workshop late. Max was already lecturing.
“An important aspect of a story that beginning writers often forget is point of view. Who is telling the story? Whose eyes are you seeing the world through, whose perceptions are filtering the information you provide? You can tell the same story from two different points of view and get two very different stories.”
He talked for a while about possible points of view. Susan didn’t take very good notes. She was distracted. Every time a jogger ran past the window, she glanced in that direction, thinking it might be Weldon Merrimax.
“Now let’s try an exercise,” Max said. “Earlier on, you wrote about monsters. I asked you to write a scene where your monster was just out of sight. Today, we are going to try something a little different. I mentioned that writers have to get to know their monsters. One way to learn about something is to observe it from the outside. But as a writer, that’s not enough. You need to know your characters inside and out.
“So here’s what I want you to do. Imagine yourself standing by a closed door. It can be any kind of door you like: a spaceship airlock, a garden gate, the front door of your own home. You hear something at the door and you know that there’s a monster on the other side. The monster wants to come in.”
“I want you to write a scene from the point of view of that monster. You have to be the monster. Think about what the monster wants, what the monster needs.” Max was silent, giving them all a chance to think. “Now I want you to write a scene from the monster’s point of view.”
Max waited while everyone got out notebooks and pens. As usual, Alberta had a question: “Does it have to be the same monster I wrote about before?”
“That’s up to you. It could be a little different. You’re getting to know your monster, and the version of it that you see today may be a little different from the version you knew a few days back.”
Susan stared at the page. She didn’t have to work too hard to imagine standing by a door with the monster on one side. She remembered the night before. But which monster should she choose to be: the monster in the dark or the monster who was Weldon Merrimax?
She thought about the dark corridor. She imagined herself as a monster, crouching in the darkness, watching a woman try to open a door. The door wouldn’t open. The monster could smell the woman’s sweat, the scent of fear. The woman was staring wide-eyed into the darkness, waving a silly little flashlight around. The woman was r
attling the doorknob, calling out for help. Then the door opened and the woman was gone, rushing out of the darkness, slamming the door closed.
The monster was alone in the darkness.
“Think about how the monster feels,” Max said. “What does the monster smell? What does the monster hear?”
How did the monster feel? “The monster felt strong,” she wrote. “The monster could still smell the woman’s fear. The monster breathed deeply, enjoying that scent. Such a foolish, weak woman, the monster thought.
“The monster could hear voices from the other side of the door. The woman’s voice, high-pitched and trembling. Another voice, a man’s voice.
“The monster went to the door and leaned against it. He did not push on the door—he didn’t want to open it. He didn’t want to go into the light, where she could see him. He liked it in the shadows and the darkness.
“He could hear her frightened voice—what a lovely sound. It would take so little to make her scream. She would cry out and ask for mercy. That would be good.
“Women were weak, the monster thought. He loved that about them. Such lovely playthings—they broke so easily.
“He smiled in the darkness, leaning against the cold metal door. The voices were moving away. The monster could hear the sound of footsteps on metal stairs, fading in the distance. The woman was gone.
“That didn’t matter, the monster thought. He was patient. There would be other chances. No need to hurry.”
At the end of class, Ian showed up at the back of the library. Pat waved to him, grabbed Susan’s arm, and hailed Max before he could leave. “I thought maybe you would join us for lunch,” she said. “I was hoping to talk to you about quantum mechanics and a few ideas I had.”
Max looked a little startled, but nodded. “Of course,” he said. “I’d be delighted.”
They went to Penelope’s for lunch and found a table by the window. Outside, the sky was still overcast. The ocean was a restless surging gray.