The Meaning of the Fine Structure Constant

The mirror showed a reflection that was not my own. It looked like me, and the room it reflected looked like mine, but it wasn’t. I became aware of this peculiarity as I stood regarding my reflection post-shower one day. Graduate school had taken a toll on me, though everyone, including my therapist, said it was all in my head, that I hadn’t changed since high school, but I could see the exhaustion on my face, even if I still fit into my decade old clothes.

I’d been doubting my sanity for years, but it’s not like I hadn’t been forewarned about what a life dedicated to theoretical physics was all about. Mary Shelly hadn’t invented the idea of the mad scientist out of whole cloth. Since ancient times, those who had dared ask the hardest questions and performed the most dangerous experiments had been considered eccentric at best, and downright lunatics more often than not. There were times I considered moving out of my comfortable off-campus apartment and into a barrel outside of the STEM Center. When I had floated this by my advisor he’d said, “What, like Oscar the Grouch?” but I didn’t have the energy to explain who Diogenes was so I just said, “Yes. Exactly.”

One time at a department cocktail party I’d confided how stressed I was to one of the older professors, a woman who’d found fame via some breakthrough in fission reactions before I was born. She’d laughed and said the sort of alchemy I’d gotten myself into might as well be magic, and that every answer I’d ever find would just beget a thousand more questions. She said her ex-husband had been a theoretical physicist and they’d slept in separate beds for the last five years of their marriage, or rather she’d slept. He’d spent his nights working before developing early-onset dementia and dying in a home; she was still teaching.

She’d said that we could go on and on about how everything is made of strings, or how some things can be two things at the same time, or how time moves backwards for certain particles, but the Atomic Energy Commision didn’t want to know about any of that, they wanted people to figure out how to make more electricity or bigger explosions for less money. “Life is about figuring stuff out,” she winked at me, which I certainly agreed with, but it really did feel like every concept I understood just served up a silver platter of questions to which there were often no conceivable answers. “I bet you have the fine structure constant hanging on your wall. My ex-husband did too,” she’d said. I turned beet red.

Richard Feynman had said of the fine structure constant, represented by the Greek letter alpha: “It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.” and so I had. As elegantly universal as pi or the golden mean, the constant, which quantifies the strength of the electromagnetic interaction between elementary charged particles, is notable as all the units used to express its components cancel out, leaving a pure number equaling 1/137. A 2% weakening or strengthening of this value would result in a universe without carbon, among other things. As far as we can tell, carbon is necessary for life, or at least life as we know it.

The ramifications of this were apparent to me as soon as I had learned of the constant. I realized that any alien civilization receiving a transmission of a simple one, followed by a zero, followed by 137 ones would recognize that whomever had sent such a signal at least had a basic understanding of how the universe is put together. Years later, stressed to near breaking, I told my advisor that I wanted to switch out of the program and go work for SETI (The Search for Extraterrestrial Intelligence.) He’d laughed and said that we had no way to transmit any signal faster than the speed of light, which is “damn slow, all things considered,” but that if I could “solve quantum entanglement,” I could “possibly talk to E.T. in his lifetime.” I phoned home that night.

Wolfgang Pauli famously said “When I die, my first question to the devil will be: What is the meaning of the fine structure constant?” I’ve always had the sense that Feynman and Pauli never lost their minds, because they maintained their senses of humor. Granted, when Pauli was having a crisis after his divorce and mother’s suicide, he had Carl Jung take him on as a patient. Jung later asked him to collaborate on synchronicities, but as far as I can tell, the fringes of psychology have always relied on mad science.

Feynman also said, “You might say the ‘hand of God’ wrote that number, and we don’t know how He pushed His pencil.” I tried to not obsess about it, but I did keep a printout of the constant hanging on my bedroom wall. It wasn’t framed, just put up with a red thumbtack. I rarely had anyone over, but one guy I met online had seen it and called me a nerd. He worked in finance where they dealt with real numbers, not Greek letters representing abstract concepts. At least he was cute.

Due to the way in which the mirror was hung, I didn’t have a clear view of the constant, just about a quarter of the page, which was mostly blank, with the equation sitting squarely in the center in black 36 point type. I was staring at myself in the mirror, as I was prone to do, sometimes chanting encouraging mantras to myself, sometimes daring myself to just quit the whole thing and go work as a potter on the Amalfi Coast or something. I never shared that fantasy to my advisor, because it was actually his and I just tended to borrow it when my imagination ran dry of realistic possibilities.

I was thinking about how well I’d probably sleep if I spent my days throwing pots and cutting clay with a thin metal wire and the smell of salty ocean air filling my simple studio, letting somebody else figure out the structure of this whole silly, uncaring universe. Then I noticed, in the reflection, that there was writing on the paper underneath the constant. Insomnia had made mush of my memory, but I figured I’d remember doing something like that, and momentarily considered that perhaps I’d experienced a fugue state. I low-key hoped that’s what it was. A full-blown nervous breakdown would land me in a psych ward, like Louis, who’d assisted on my senior thesis. Last year, he’d walked naked into the dining hall during breakfast rush, and I hadn’t seen him since, but maybe I could pivot something like this into a couple of weeks at a wellness spa where they put cucumber slices over your eyes after every massage.

My therapist said I was prone to “magical thinking,” and the truth was that I couldn’t afford to use my grant money on a mental health retreat, nor could I afford the time away from my project. When I mentioned needing a vacation, but not having the money, to my advisor, he’d said that he’d driven a taxi when he was in grad school to make extra cash. He told me that one time a fare of his had jumped out at a stoplight and stabbed a guy. I asked him if that was him trying to advise me and he said he didn’t know.

The summer after graduation I’d dropped acid with one of the boys on the lacrosse team. He had a crush on me, and we’d spent an endless afternoon in the overgrown park at the edge of town, sitting by the water and swinging on the rusty swing set. We mostly just talked, and I could tell he wanted to kiss me, but I could see his heart beating inside his chest, and that was too much. I was in a rush the morning I noticed the writing under the constant, so I put it down to my first acid flashback and declined to investigate further, though as I snatched my bag off my desk, I gave the printout a long look. It remained blank except for the equation.

I had too much to do to indulge my madness by thinking about it, and I had all but forgotten about the odd writing by the time I got home that night. Too exhausted to even brush my teeth, I collapsed into bed and fell into a dreamless slumber. I’ve experienced sleep paralysis several times since childhood. Mercifully, I’ve never had a nightmare hag sit on my chest and crush the breath out of me, which I understand is the most common hallucination to accompany these episodes.

Mostly I just wake up, or dream I wake up, and can’t move, but one night when I was little, while my parents were having central air conditioning installed in the house, I opened my eyes to see some flexible silver ducting the workmen had left in my room crawling, snakelike, across the ceiling. I was frozen in place as it wound its way around me like an anaconda and squeezed until I could barely breathe. I tried to scream several times, but all I could manage was a thin, hissing whisper I knew no one could hear.

It was not lost on me that I had not had an episode since the acid trip years ago, but I had never probed a possible connection. My streak ended that night, when I woke up and saw myself in the mirror. I couldn’t move, but I could taste the remnants of the spicy tortilla chips I had wolfed down as I drove home in lieu of dinner. Having not brushed my teeth, my mouth felt gritty, and my eyes hurt, merely from being open.

I couldn’t move my head, but from where I was laying I could see the mirror with a good portion of the room reflected in it. There were no lights on in my apartment, but in the reflection the bathroom light was on, casting a meager beam towards the desk, where I saw a person who could only be me, hunched over and frantically writing. Only her back was visible, but she seemed unwell, pausing occasionally from the frantic scribbling to stretch and twist her neck in unnatural ways. I couldn’t see it, but she must have had the window open, because the papers on the desk and post-its on the walls kept stirring in a breeze too vigorous to be a result of her shuddering movements.

The fear was enormous, not of the scene, or the realization that the sleep paralysis had returned, any progress in relief from it seemingly undone, but rather the sense that I had finally gone over the edge and that the next inevitable step was stripping down and wandering into the dining hall. For a lot of people like me, the first intriguing step down the rabbit hole of theoretical physics is the fact that time is relative. Suggested by Einstein’s Theory of Relativity and proven by experiments with atomic clocks, the idea holds tremendous appeal for people who think a certain way.

If time is a factor of speed, then if you need more time, you just need to move faster, right? There’s no way to employ this practically to any sort of benefit, but it can be an empowering perspective to have. I must have been moving very fast that night, because it felt like an eternity that I was frozen there watching myself work on some terrible task. I was scared of the woman in the mirror, but at the same time I wanted to help her. I tried calling out, but just like before, all I could manage was a barely audible moan. At the second pathetic little squeak I managed, the me in the mirror cocked her head as if listening, but she did not turn around and I am thankful for that.

The next morning I texted my advisor from bed, saying that I wasn’t coming to the lab. He responded by reminding me it was Saturday, which was set aside for home-brewing and to leave him alone. When I finally mustered the energy to get up, motivated more by my bladder than any true sense of purpose, I noticed that the printout of the fine structure constant was gone from the wall. The hole from the thumb tack that had held it in place was still there, but the paper itself was missing. The window was ajar, and I wondered if I had gotten too hot in the night and opened it, though I knew I hadn’t. Regardless I told myself that the constant had just blown down and fallen behind the desk.

Around mid-morning, in an attempt to either distract or indulge myself (I couldn’t tell,) I looked up Louis on social media. There were pictures of him at the CERN supercollider and fishing with his dad, followed by one of him standing at a whiteboard with a massive equation written on it. Then there was a nearly year-long gap in his posts. Two weeks ago he’d put up a picture of the sun rising over some smokestacks tagged #home, and I supposed that to mean that he was at his parents house, which I knew was about an hour’s drive outside the city.

One of the adjunct professors is a devout fellow who sings as a cantor at his synagogue. He is undoubtedly the most helpful person in the department, the kind of guy who leaves a box of donuts in the lab every time he’s there. I asked him once why he’s so nice and he said it was his duty to perform mitzvahs, individual acts of kindness, in keeping with the commandment to love thy neighbor as you love yourself. I convinced myself it would be a mitzvah to visit Louis. We were friendly, if not particularly close, and I suspected he could use a friend, though in my heart I knew I was projecting.

Louis had grown up in one of those planned factory towns where the houses all looked the same except for the color and every street was named after a bird. Decades of additions and renovations had altered the look of many of the residences, but it was evident that they all shared the same bones. Most still had three steps leading up to a porch and the front door. I felt like I was driving through a graveyard for giants as I wound my way down Oriole Avenue to Magpie Lane. I tried to avoid meeting my gaze in the rear view mirror, uncertain of who I might see looking back at me.

The smokestack post was geotagged, so it wasn’t too hard to find the house. Louis was a smart guy who presumably understood the dangers of sharing too much information online, so I figured he simply didn’t care who knew where he was, but that’s not the same thing as an invitation, so I was feeling a bit apprehensive as I pulled into the driveway, and sat there for well over a minute giving myself the pep talk necessary to knock on the door.

I flushed when I got out of the car and saw Louis sitting on the porch. “Talk to yourself much?” he asked, smiling at my embarrassment. I felt less ashamed when I remembered that everyone eating breakfast one day had seen all of him on full display. “Have a seat,” he said, indicating a rocking chair which matched the one he was sitting in with a steaming mug in his hand. He didn’t rise to hug me, which I was grateful for. Louis was oddly perceptive. I was afraid if he touched me, he’d sense the tension wound up in me like a spring.

I suddenly realized I didn’t have a good excuse for showing up unexpectedly, so I stammered something about craving the fried oysters at that place down by the beach and figured I’d stop by and offer him an invite, because it had been a while. He seemed unfazed by my presence. Maybe he was performing a mitzvah in that, but regardless, I was grateful. I asked him how he’d been and tried to not think about my hazy reflection cast in the window behind me.

“An incalculable amount of death and suffering went into the global spice trade, but now I can sit here and drink chai every day and it’s like none of it ever happened. Is that progress?” I was glad to see it was the same old Louis. He said the place he’d gone to had been nice. Evidently the department had hastily put together a grant and set him up in a place he could get better. He wasn’t the first person in the program to need some time off.

He said there was a river that ran through the facility’s property that was attractive to geese, and to keep the flocks away the hospital had put fake coyote silhouettes down by the water. They were made out of sheet metal with a hole punched out for an eye and stuck into the ground with a metal pole that allowed them to turn in the breeze, offering the illusion of movement to their two-dimensional forms. Louis said the geese weren’t stupid, they were just programmed to be afraid of certain things by instinct and there was a lot they couldn’t comprehend.

When you start learning about really big numbers, they teach you that, as impossible as it may seem, no two decks of cards have ever been shuffled into the exact same order. There are eight-hundred quadrillion times more ways to mix up fifty-two cards than there are atoms in the earth. Most people live their whole lives never needing to consider such large numbers. My advisor once told me that few people can truly conceive of infinity and I thought about all the sleepless nights I’d spent staring up into the darkness imagining a line drawn from my heart into the endless forever of the cosmos.

Louis offered me a cup of chai, which I accepted. He told me that he’d developed a fondness for making pottery while he was away, and that the mug I was holding was one of his early efforts. It read “HOPE” on the side. Slightly jealous, I asked him what he liked about it, and he said that it was full of good life-lessons, like how no matter how much care and effort you take with a piece, it will sometimes explode in the kiln. Plus, he liked that the numbers were small. You’d never have to make a quadrillion ashtrays.

“I’d like to order an infinite number of ashtrays,” I said, laughing.

“An order that big comes with a freebie,” said Louis, “So, it’s actually infinity plus one.”

“Some infinities are bigger than others,” I offered reflectively. That was one of the things I tried to remind myself when I’d stand in front of the mirror, full of doubt. It was true not just of giant numbers, but also of personal pain and joy.

“Is a photon a particle or a wave?” I asked him.

“You’re stuck in the aristotelian binary. A photon is a quantum object that comfortably exists as both simultaneously. The fact that you can only perceive one at a time is a function of your limited senses. In a lot of ways we’re just like a flock of geese afraid of some tin coyotes, because we can’t tell what they really are. We could learn a lot from photons.” Louis looked at the smokestacks and sipped his chai. I rotated the mug in my hands and thought about what a fine professor he would have made.

“What is the meaning of the fine structure constant,” I asked him.

“I’m not the devil,” he replied, draining his mug.

I decided to tell him about the mirror. When I was done he told me that he always thought I was particularly observant.

“You don’t think I’m mad?” I asked.

“No more than any mad scientist,” he said, “There are other worlds than this. I’ve seen them too. The only way I can make sense of the whole thing is to assume that there are an infinite number of permutations of this whole place. I get the feeling it’s like a faucet left running in a soapy sink, just a pile of bubbles expanding and bursting for as long as the water is left on, with a universe forming within each.

Most wouldn’t survive, of course. Their physics would be too inconsistent to maintain integrity, but of those that did, some would have life, and even if that only represents a fraction of a fraction of all the possibilities, there would be near infinite numbers of worlds just like this. With enough permutations there would be nearly infinite versions of everyone on earth leading nearly identical lives. Based on what I saw in my mirror I think photons may pass through these dimensions with ease. Gravity seems to.”

“But?” I asked, having already come to the same conclusion, but needing to hear it from him.

“But nearly identical isn’t exactly the same,” he said, “So that means there’s versions where things have gone way better for you, where every lucky break broke and everything went your way easy-peasy every step you took.” He looked wistful.

“Or worse, harder every strep of the way!” I shot. Too late, I realized I sounded insensitive. Louis seemed to be doing alright, but at one point it had seemed like his career might eventually garner a Nobel Prize. “Sorry,” I offered, looking at the smokestacks to avoid his gaze.

“Or worse,” he admitted, “Some infinities are greater than others.” We sat a while in silence. A crow perched in a tree nearby and cawed at us, annoyed by our presence close to the bird feeder.

“I’m afraid it means we get to choose,” I said, “That if it’s just happening over and over and over again, this world right here could be the one where I make it, whatever that means.” I thought of the frantic person I’d seen in the mirror. Is that who I wanted to be? What if that’s what it takes? I didn’t know, but I also had the sense that it might be okay. “Want to go to the beach?” I asked, turning to look at him, mindful of my reflection in the window behind our chairs.

“Let’s go to the beach,” said Louis, and as we stood I thought about how out of all the infinities spread out before us, this one was ours.