“But by the end of semester, though I’d learned a fair amount, nothing else had changed. And my failure to transform made me feel like a failure, a fool, a frump.”
“A fart?” I suggest.
“A forsaken fuck-up,” Chloe laughs. “But what I’ve found, finally…”
“…felicitously…” I interject.
“…fortuitously,” she resumes, “is that practical techniques to feel the life force, are what’s needed to experience the elevated states described in the scriptures. Practical techniques of meditation, yoga, breath. Prayer, if you prefer. The resulting sensation of life force is the meaning of embodying heaven on earth, it is the meaning of being an empty vessel for a greater power, it is the meaning of aligning the ego with the universal self. There is no need, except for recreational purposes, to study the meaning of any of these concepts. The only need is to feel them as concrete bodily sensations.
“The great error of Western civilization was Descartes’ ‘I think, therefore I am.’ The reality, which is a blessing and a responsibility, is, ‘I feel, therefore I want to cultivate feelings of bliss.’”
“That’s lovely,” I say, lifting the teapot, “and do you know, there’s something I’ve been waiting to tell you—”
“A mystery poem!” she exclaims, pointing under the teapot. Her eyes widen with glee.
“That’s my second one today,” I say as I pour her tea. “I don’t think I’ve ever gotten two in a day before.”
“May I read it? Yes?” she asks. She unfolds the pale green paper.What You’ll Find Among My Ashes
Endless longing and endless fulfillment
The profound peace of the M5 globular cluster (it’s a galaxy)
All the sugar donuts I ate when I was seven
All seven oceans
The crash, rumble, and hiss of waves
The spray of salt
A snow-encrusted buffalo
The roar of lions
We sit grinning at each other.
“You’re sure you didn’t slip that under the teapot with your crazy ninja skills?” I ask.
“I didn’t,” Chloe says, “though I do have crazy ninja skills. But what have you been waiting to tell me?”
I open the folder of mystery poems and take out the six-month ultrasound.
“Aw, we’re so cute,” she says.
I smile. “I accidentally dropped this under the couch last week. And when I reached under the couch, I found the hidden variables. The hidden local variables that Einstein insisted on.”
“Although I do have supernatural powers,” Chloe says, “knowledge of physics isn’t one of them. So you’ll have to explain that to me.”
“I did, when I first learned about quantum entanglement, when I was an undergrad. Are you sure you want to hear it again?” I ask.
“Anything worth saying, is worth saying again.”
I laugh. That’s what she said when we were little, and she fell asleep as I told her bedtime stories. She’d wake up and ask me to repeat what she’d missed. I was irritated, but she said, in her adorable baby voice, “Anything worth saying, is worth saying again.”
“Okay,” I say. “There’s a particle called a pion.”
“As in, I hope I don’t get pie on my new dress,” Chloe says. “Yes, I remember the name.”
“Right. So, the pion spontaneously decays into an electron and a positron, which fly away from each other. These particles have a property called spin, which causes them to be deflected in a certain kind of magnetic field. If a particle is deflected upward in a particular magnetic field, let’s call it spin up. If it’s deflected downward, we’ll call it spin down. The original pion had no spin, and this means that if the electron is spin up, then the positron must be spin down, and vice versa. As soon as the electron’s spin is measured, the positron, no matter how far away it is, is compelled to have the opposite spin. Einstein hated this idea. He called it ‘spooky action at a distance.’”
“Am I supposed to be amazed by this?” Chloe asks. “How’s this any different from having a red marble and a green marble in a bag? I reach in without looking and take a marble in each hand. When I open my hands, am I supposed to be amazed that the two marbles are different colors?”
“That’s basically what Einstein said,” I say. “You’re saying that the two marbles had their distinct colors all along. At first, you’re simply ignorant of which marble is in which hand, and when you open your hands, the marbles don’t change. The only thing that changes is your knowledge of which marble is in which hand.
“A variety of factors determine which marble ends up in which hand: the original locations of the marbles in the bag, the way you shake the bag before you reach in, the way your fingers grope sightlessly through the bag. If we had enough information about these factors, we might even be able to calculate which marble ends up in which hand. This information that we don’t have is called ‘hidden local variables.’”
“And that’s what you found, under your couch?” Chloe says, raising an eyebrow.
“Yes!” I say. “Uncanny, isn’t it? But I still haven’t explained what’s amazing about the spins of the electron and positron. In the marble experiment, when you open your hands, the marbles don’t change. If you see the red marble in your right hand, you infer, correctly, that the red marble was in your right hand all along. The observation of the red marble did not transform it into a red marble. You then know, without even looking, that the green marble is in your left hand. But the green marble, too, was there all along. The observation didn’t make it green. We might say that hidden variables determined which marble ended up in which hand.
“In quantum physics, however, there’s the claim that the electron and positron did not have their spins all along. Before either particle is observed, their spins are undetermined. Each particle is in a kind of undecided state. It’s not that we’re just ignorant of their spins before we observe them; the spins themselves are inherently undecided and unknowable before we observe either particle. The observation is not passive; the observation transforms the particles.
“So, there are two things that are supposed to amaze you. First, the observation of a particle determines its spin—a spin it didn’t previously have. It previously had latent possibilities of spin. The observation selects the particle’s spin from two latent possibilities. Second, the observation of just one of the particles instantaneously selects and determines the spin for both particles. The observation of the electron determines the spin of the distant positron.”
“Okay,” Chloe says, sipping her tea, “I now see why this is amazing, if it’s true. But how can you possibly know that your observations are changing the particles? You certainly don’t have any evidence about the particles’ spins before you observe them. The only way to get any evidence is through observations.”
“This is where Bell’s theorem comes in,” I say. “Someone named Bell said, suppose the particles really have their spins all along. We don’t know their spins yet, but their spins are determined through some unknown factors, which we call hidden local variables. Bell showed that any possible choice of hidden local variables must contradict the predictions of quantum physics. But experiments agree with quantum physics, so therefore experiments contradict hidden local variables.”
“And yet you found the hidden variables, under your couch?” Chloe asks.
“Yes. But I still believe in quantum physics. It doesn’t really make sense, does it?”
“No,” Chloe says. She rotates her mug on the coffee table, making a soft scraping sound. “How do you know you found the hidden variables?”
“That day I looked under the couch,” I say, “I saw our six-month ultrasound, as well as a lot of dust, dog hairs that I’d never vacuumed up, cracker crumbs, and sesame seeds. Then I saw a churning purple mist which had no reason to be there, but for some reason I wasn’t scared. The purple mist spilled out from under the couch and entered the soles of my feet, rising up to the t
op of my head. And then I knew everything.”
“Everything?” Chloe says.
“Well, everything I turned my attention to. I saw red lava bursting from the bottom of the ocean, shooting out jets of steam while blackening and hardening. I saw mammoth tusks, megaliths, and stone altars reddened with blood. I saw galaxies collide and rip each other apart. I can look anywhere in the past, present, or future, but I turn away from the future because it freaks me out. I can see lottery numbers, but I don’t need any more money.”
“That’s really exciting, to say the least,” Chloe says, stretching her arms and rotating her ankles. “But I don’t think you found the hidden local variables.”
“No?” I frown, gnawing my lip. I feel unreasonably irritated and strangely alarmed. “But that’s part of this knowledge, knowing that the knowledge, itself, is made up of all the hidden variables, all the factors that determine everything that is.”
“Yes,” Chloe says. She smiles, but sadly, and she sweeps her fingers across the mole above the left corner of her mouth. “But you didn’t find the hidden local variables. You found the hidden global variables. The hidden variables that don’t contradict quantum physics. The hidden variables that permit spooky actions at a distance: a positron’s spin depends not only on local conditions but also on the measurement of the distant electron.”
“That’s right,” I say, narrowing my eyes in concentration. “If hidden variables determine a particle’s spin based on something far away, there’s no contradiction with quantum physics. Bell’s theorem is limited to hidden local variables.”
“So you can have your cake and eat it too,” Chloe says with a maddening smirk. “You found the hidden variables, and you preserved the implications of quantum physics.”
“But how did you know this?” I ask, feeling an inexplicable harrowing dread. “How did you know about hidden global variables?”
“Because they’re mine,” Chloe says evenly, unblinking.
“What do you mean?” I gasp, but I can already feel the knowledge slipping away. The vast realms within my awareness shrink, they crack and splinter like glass, they recede like a tide, leaving behind parched sands and sun-bleached shells.
“They’re mine now,” Chloe sighs.
“You can’t have them!” I shout. “I found them first!” I can almost see purple mist pouring out of me and gushing into Chloe, as though she were a vacuum cleaner.
“Give it back!” I yell, and I leap over the coffee table to tackle Chloe. But she somehow anticipated my move, and I slam into the vacated couch. I spin around and see her slowly pacing around the coffee table.
“This will be easier for you if you relax,” Chloe says, swinging her arms gracefully as though wading through water.
“Thief!” I shout, clenching my fists and springing to my feet. “Hypocrite! Is that what years of spiritual searching has brought you to? You put on a great show of cultivating inner peace, but you steal from your own sister?”
“Which of us is behaving more peacefully right now?” she asks, languidly bending a knee and circling one foot in the air.
“Don’t turn my words against me! How dare you do this to me!”
I lunge and swing my palm towards her face, but she somehow ducks under my arm and trips me. I stumble into the display table. Her pottery jitters. A small vase tips over and rolls onto the floor, but the carpet saves it from shattering.
“A karate strike,” she says. “How cute.”
“It’s not cute!” I say, and I throw a punch, which she deflects. “I can break a stack of two-by-fours with my hand!”
“Like an angry child throwing a temper tantrum,” she says, continuing to parry my strikes. “Cute.”
I soar toward her with a leaping spinning hook kick, but she dodges and slaps my foot in the same direction it was going. Losing my balance, I land on my back and break my fall by slamming my arms downward. My right arms catches the corner of the coffee table. It flips over, hurling the teacups and teapot against the wall. The teacups shatter, but the teapot falls onto the carpet, dripping and unharmed.
Chloe squats deeply on one leg and extends the other leg fully along the floor. A ridiculous pose, an easy target. But when I descend on her with blows, she evades me again.
“Karate is no match for taijiquan,” she says placidly, shifting, receding, always just out of reach. “The Supreme Ultimate Fist. According to one account, invented by a general for people who were already experts at the martial arts.”
She again deflects my fist, causing me to punch several of her pots off the display table. Clay shards are beginning to litter the carpet. The faster I strike, the more forcefully Chloe redirects my limbs.
“It’s not fair!” I say, starting to pant from exertion, but I don’t pause in my attack. “I do all the work, and you have all the fun! The whole time I was working, you were on a dream vacation to temples and mountain hermitages! And now that finally everything is perfect for me, you come and take it all away!”
Chloe gazes at me imperturbably, almost pityingly. Her arms are a blur as she deflects my strikes. I feel her fingertips like hailstones against my arms and legs.
“It was inevitable that we’d fly off in opposite directions,” she says. “One to the east, one to the west. Opposite sides of the globe. Our heads pointing in opposite directions. While the sun in your sky sets, mine rises. As smoke ascends, snow falls. Now I am in the season of blossoms, and you face your day of autumn.”
“No!” I scream, and I hurtle toward her with my strongest punch, a lethal punch. But, predictably, she whisks herself out of the way at the last minute. I crash into the display table, which topples. The two glass table-shelves shatter, along with all the clay artwork. I steady myself, try to catch my breath, and begin to circle Chloe around the coffee table.
I must have hit my head at some point because my vision dims and returns. I have the sense of circling faster and faster, though I hardly feel that I am moving. I glare at Chloe and gasp.
“Your hair!” I shout. “How did your hair get long again?”
But then I see it’s worse than that. The mole is over the right side of her mouth. She has my mole. She has my hair. She’s me.
The room is spinning even faster, though Chloe—in my image—is standing still.
“Once we were two, but now we are one,” Chloe says.
She lifts the six-month ultrasound from the wasteland of broken ceramic. The room is spinning so fast that all the colors are blending into white.
“Oh look!” she says, pointing to the floor that I can barely see. “A new mystery poem, which was hiding under the ultrasound! That’s three in one day!”
But I’m not looking at the mystery poem. I’m looking at the ultrasound. And though I can’t see anything else clearly, the ultrasound image is immaculate. And only one fetus is visible.
“From now on, there is no Chloe Elghenyin,” Chloe says. “There is only Stephanie Elghenyin. So it is not you who vanish. It is I.”
Chloe—me—whoever she is, raises her arms as though summoning spirits. Tears streak her cheeks, and her face is clenched in sorrow.
“I’ll miss you,” she says. “Though soon I, and everyone else, will remember the last 33 years differently from what we remember now.”
The room fades to white, which suddenly turns to black. I am alone in blackness. Then I hear Chloe’s voice.
“Here’s your final mystery poem,” she says.I was a rock, a willow, a moon
I waited for the rain to fall, but I was the rain
I was a snow leopard, a heron, a nightingale
I watched until the thundering waves shattered skyscrapers, but I was the waves
Because the reason spiders eat their young is neither cruelty nor hunger
But yearning for reunion with their offspring
So the roar of my funeral pyre is the red giant sun when it
Becomes the sky
And expands past the orbit of Venus
I float in the dark, sullen, alone, and only a little bit scared. I hear a faint buzz and see purple mist rising everywhere. It has come to carry me to the realm of unwavering bliss and unending tranquility. But I know this mist. It permeated me for a week, so I know that it permeates all things and all times. So I direct my attention to a time 33 years and three months ago. And I ask, and receive, permission to go.
Hello Stephanie.
Good to see you again.
Thought you were alone in here?
We’re all soft little arms and faces in a warm dark salt bath. Cozy and cuddly.
Anything worth saying, is worth saying again.
Afterword
A lot has been written about quantum entanglement. My favorite is How the Hippies Saved Physics by David Kaiser.
I’d like to work through an example adapted from Quantum Non-Locality and Relativity by Tim Maudlin.
This example is based on experiments with light, which is made of photons. We can shine light on something called a polarizer. Each photon reaching the polarizer will do one of two things: it will pass through, or it will be absorbed. The probability that a particular photon will pass through depends on the orientation of the polarizer; we change the polarizer’s orientation simply by rotating it. Let’s say that we’re interested in orienting a polarizer in one of three ways: horizontally, 30° above the horizontal, or 60° above the horizontal.
Suppose we create a pair of photons that go in different directions (left and right). The photon on the left goes toward a polarizer (oriented either horizontally, at 30°, or at 60°), and the photon on the right goes toward a different polarizer (orientated in one of the same three directions). It’s possible to create pairs of photons about which the following observations are made:
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