Relativity
The day Chong dreaded had come—he had to teach Newton’s law of universal gravitation to his high school physics students. In college, Chong learned that Newton’s laws of motion had long been superseded by Einstein’s theory of relativity, a new understanding of reality based on relative time and space. It seemed wrong to teach something that was clearly not accurate, but after his first semester as a teacher, Chong deduced that his sixteen-year-old high school students in Washington Heights would not understand Einstein’s vacuum field equations nor care that certain solutions only worked in a vacuum, not in situations with matter or gravitational fields present, like earth.
Earlier in the week, Chong had discovered a number of photogates hidden in the storeroom and decided it was time to put them to use. He charted the lesson in his mind. Students were to drop a picket fence, a clear piece of plastic printed with evenly spaced black bars, into a device called a photogate, which contained an infrared light paired with a sensor. The photogate would detect when the infrared beam was blocked by the picket fence and produce a series of velocity readings. Using these readings, students would then calculate the acceleration of the picket fence, minimally affected by air resistance, which should come close to 9.8m/s2—the accepted value of gravitational acceleration on earth. It was a simple experiment that could not go wrong.
Thirty minutes before first period, Chong realized that none of the photogates worked—the sensor on one was faulty, another was not calibrated, and one did not even turn on. He ran over to his colleague’s classroom.
“The photogates aren’t working,” he said.
“Chong, what are you doing with photogates?” his colleague asked.
“How am I supposed to teach?”
“This is what we use here.” His colleague grabbed a tennis ball off his desk and tossed it to him. Chong squeezed the ball with his hand. The elastic force of the rubber inside resisted against the pressure of his quivering fingers.
Back in his classroom, Chong took apart a photogate and began testing the solder joints on the circuit board. The color in a number of locations was off—not sufficiently heated. In other places, the joint had oxidized—poor quality solder. Surprised that the photogate had ever worked, he flipped the unit over. Made in Hong Kong, the label said. For a moment, Chong felt irritated at the incompetence of his own people, but reasoned that he had nothing to do with them.
The school bell rang and Chong knew he had to give up. Reluctantly, he brought out a box of old tennis balls and wrote Newton’s equation, F=mg, on the whiteboard. He divided his class into small groups and assigned them the task of dropping tennis balls and crumpled pieces of paper from specified heights, and comparing their velocities. A minute into the experiment, a paper ball flew across the classroom hitting a student in the face, and Chong knew that he had made a mistake.
The student stood up. “Who threw this?”
“Jokes,” a student on the opposite side said, laughing.
“How about I punch you in the face and you tell me if that’s funny.”
Chong sensed he needed to do something. “Stop, or I’ll write you up,” he said. “Teach, I was the one who got hit.”
As Chong tried to think of how to respond, a tennis ball struck the student’s back. “Oh, hell no,” the student shouted.
Chaos ensued.
Chong made his way to the center of the classroom, dodging a few incoming projectiles. “Stop!” he yelled. No one listened. He turned to a nearby student and tried to take a tennis ball out of his hand, but was easily pushed aside. Voices escalated and a few of the students became more aggressive. One tipped over a desk and began shouting at another student. The noise continued to intensify into a deafening roar until Chong felt his chest tighten, making each breath harder to take. The bright lights on the ceiling irritated his eyes, a high-pitched buzz reverberated in his ears, the room began to spin, and he felt every ounce of strength depart from his body.
Chong woke up to the sound of the school bell ringing above him. He inspected his surroundings before realizing he was lying on a bed in the nurse’s office. An invisible band squeezed around his head, a dull ache radiated through his back and arms, a soreness lingered in his chest as his muscles contracted to the rise and fall of each breath. The faint rumble of students in the hallway seemed another world away. He closed his eyes, comforted by the whine of the clock’s second hand rotating according to the most basic rate of uniform circular motion—time.
Chong woke again to the nurse’s voice.
“Chong, you fainted.”
He managed a grunt in response.
“Happens to all the first-year teachers,” she laughed. Chong didn’t find it funny, but remained silent as he pushed himself off the bed.
The hallways were now quiet, lights dimmed. The clock on the wall read 4:30pm. A few students walked past, whispering. He lowered his head, quickened his pace, and closed his classroom door behind him. He sat down at his desk and wondered what had happened in the hours that passed. Paper balls and tennis balls were littered all over, desks overturned, chairs scattered, posters ripped off the wall, torn into pieces. In his thermodynamics class, his professor had taught that entropy was the measurement of disorder in a system, and once a system undergoes a thermodynamic process, entropy would increase until the system reached equilibrium.
Gazing out at the chaos, Chong felt the tension in his body rise with each passing moment. He reached beneath his chair for a tennis ball, gripped it, and flung it toward the other side of the classroom. The ball rebounded off the wall and struck a ceramic mug on top of his desk, knocking it onto the floor. Chong exhaled as he observed the coffee seep out of the mug onto the old vinyl flooring. His professor had told him that if one ever wanted to reverse a process, they could do so only by introducing more entropy into the system, thereby changing the thermodynamic properties of the universe, leaving traces of that which had once existed. The now cold coffee edged closer to a crumpled paper ball before devouring it, coloring it in its dark brown hue. Was the entropy of life just a necessary process by which the universe reaches equilibrium? He picked up his backpack and left.
Chong walked out the double doors of the school and turned the corner. A cab driver held his horn down at the backed-up traffic. He had first heard about this place in his Urban Studies course: Washington Heights, Wash Heights, Quisqueya Heights, the Dominican Heights. The White Flight of the 80s and 90s and the settlement of Dominican immigrants. The proliferation of crack cocaine, the rise of homelessness, the tightening of police control and aggression. A teacher had come on campus to share about the needs of the school and said it was the responsibility of those in privilege to share their resources with the marginalized and restore equity amidst an unjust system. It made complete sense to Chong—as with the production of heat, energy flowing from a location of high temperature to one of low temperature. That day, Chong decided it was what he needed to do with his Columbia education. His parents vehemently protested, but it was the first time Chong felt in control of the course of his life.
A merengue song blasted out of an apartment window on 181st Street, the smell of fried plantains emanated from a busy restaurant. Chong walked past the bodega where he had eaten countless soggy sandwiches, past the liquor store from where he bought his first Presidente, past the barbershop where he inadvertently requested a mohawk in his broken Spanish. He could now tell a tortilla from a casaba, the sound of fireworks on the Fourth of July from gunshots in the middle of the night. The smell of haze flooded his nostrils as a young man walked past.
The evening rush flooded out of the 168th Street station. Chong forced his way through, weaving in and out of the crowd, something he had done since he was young in Hong Kong. He made his way down the steps into the station underground, swiped his MetroCard, and found a spot to wait near the front of the platform. Water from yesterday’s rain, now today’s sewage, had settled in the tunnel, radiating a familiar odor. A large rat scurried across, its claws scraping against the steel tracks. A man next to him dressed in a fancy suit cleared his throat before spitting forcefully onto the train tracks.
The train screeched into the station as the conductor applied the brakes. The doors banged open and the crowd began to enter when the man in the suit cut in front of him. Chong squeezed into the carriage, almost feeling the sweat on the man’s neck adhere to his face. Stand clear of the closing doors, the conductor announced over the crackly intercom. The crowd behind Chong pushed harder, and he felt himself thrust against the man’s back. As Chong tried to gather his balance, he felt someone elbow him in the chest.
“The fuck’s wrong with you?” someone said. Chong looked up. It was the man in the suit.
“What the hell?” Chong asked.
“Go back to China, asshole.”
He wasn’t from China; he was from Hong Kong. “Someone pushed me,” Chong managed to say before noticing everyone staring. Lowering his head and averting his eyes, he mouthed, “Sorry.” The man glared at him and shook his head in disapproval before putting on a pair of headphones.
The doors shut. Chong gripped the handrail, releasing the tension in his arm onto the metal rod. The train rattled along the old tracks, intermittently stopping before accelerating to full speed. Chong closed his eyes and began visualizing the motion of the train, the friction of the wheels against the tracks, gravity pulling downwards, and the power of the engine driving the rotation of the axel overpowering the numerous forces that hindered its motion, thrusting the train forward to its next destination.
At Columbus Circle, a young woman carrying a black carbon fiber cello case got on and stood next to him. She had on a pair of professional in-ear monitors, her eyes focused on something in the distance. Every so often she would wrinkle her forehead, as if trying to analyze something she just heard—a note, a phrase, a fingering—before tapping her fingers on her leg. Watching the cellist absorbed in the music, Chong imagined the array of frequencies and resonances that reverberated within her brain.
At Penn Station, she maneuvered the cello case onto its wheels and headed towards the platform. Chong followed. She set the case down in the middle of the platform and proceeded to open it. Curious, Chong waited next to a set of stairs. The cellist set a rock stop on the ground, extended the cello’s endpin, and tightened her bow. She glided the bow over the strings with her right hand, while turning the pegs with her left, calibrating the tension of each adjacent string until they reached a complement of harmonic frequencies.
Without hesitation, she began to play a piece Chong had studied in his acoustics class—the first Cello Sonata by Brahms. The quiet introduction would open to a melodic intensity that would gain and lose through the course of the first movement before its resolution. While Chong had heard the piece numerous times, there was something unfamiliar about the way she played. It was clear that she had exceptional control of the bow, but the way she phrased each note seemed to linger just a bit longer than he expected, ending almost a bit too late. The dynamic range as she moved through the piece sometimes seemed abrupt, even exaggerated. The way her fingers crawled on the fingerboard looked ugly and creepy. Her hand positions were contorted. The timbre of her cello was warm, powerful, but at times, almost rough. As she kept playing, however, Chong and the large crowd gathered around couldn’t stop listening to her performance. He was surprised, but captivated—it seemed wrong, but felt right, and despite attempts in his mind to explain and reduce her playing to pure theory or mechanics, he wasn’t able to understand what was happening.
As she continued into the next two movements, Chong began to feel a familiar sense of relief and joy. It was the same feeling he experienced in the physics lab—the comfort in oscillations and resonance, the excitement of quantum mechanics and angular momentum and spin, the warmth of thermodynamics and blackbody radiation, the dependability and consistency of particle physics. Though he did not know how to play the cello, he began tapping his fingers along to the music, oblivious to the train rattling its stainless-steel cage along its age-old tracks continuing steadily into the darkness.
At the end of the school year, Chong was told that his contract would not be renewed. That same week, he received an email from a family friend in Hong Kong offering him a position as an engineer for the MTR. Chong was reluctant to take up the job, and an endless barrage of comments from his parents confirmed his hesitation. We didn’t pay for your Ivy League degree for you to be a teacher, they said. But after a month of unanswered job applications and notice from his landlord that the rent for his studio was increasing, he bought a one-way ticket back to Hong Kong. Chong was offered a flat in the Mid-Levels overlooking Victoria Harbor paid for by the company. His salary, four times as much as he earned in New York, allowed him a lifestyle worlds away from the soggy bodega sandwiches of the Heights. A few weeks after he returned, the family organized a meal for his grandmother’s ninetieth birthday.
“Tell them where you work,” his mom said in front of the whole family. Chong, the youngest at the table, told them. “There’s a higher position opening up soon too,” she smiled, nudging him with her elbow. He forced a smile, even though she had made that part up.
“Finally putting that Columbia degree to use,” his dad said.
Chong’s uncle cut in, “Ellen just got promoted, the youngest VP at the bank.” Ellen, Chong’s older cousin, shook her head—a humble gesture—but he could tell by the faint smile on her face that she was proud.
Chong’s aunt interrupted with a loud sigh. “Larry is always traveling. I don’t even know where he is half the time,” she said in an exaggerated tone, a brag disguised as a complaint. Larry, the oldest cousin, was a professor at the medical school.
Chong remained quiet throughout the rest of the dinner, eyes focused on the rotation of the circular turntable at the center of the dining table—the Lazy Susan, as he had learned it was called in the States—observing each member of the family project rotational forces on the turntable before stopping it to pick food into their bowls. Chong’s grandmother, who had Parkinson’s, sat in a wheelchair next to her domestic helper. He watched as she raised her arm with what seemed like a herculean effort, motioning towards a bowl of yam and sago dessert soup. She unbent her finger and pointed at it, arm shaking. Nothing came out of her mouth except for a dab of saliva that ran down her chin and onto her bib. Chong wanted to reach over and wipe her face, but the effort felt too much for him to conjure up. He began to pick up a piece of soy sauce chicken with his chopsticks, but let go when he realized it was the last piece.
Chong was put in charge of reengineering the routing and controlling system for the Island line in preparation for a massive expansion. The work needed to be precise—sorting through thousands of lines of code, updating new parameters according to the equipment in the new stations. Knowing that any error could impact thousands, Chong was careful, double checking not only his work, but his colleagues’ as well.
Two months after the new line expansion was implemented, there was a massive track failure, leaving a number of passengers hurt and the entire system suspended for over twenty-four hours. The local newspapers ran front page articles on the fiasco, saying that the hasty expansion of the MTR led the company to compromise the safety of the people of Hong Kong. Chong’s boss, the family friend who had offered him the job, was not happy, blaming him for the disaster and threatening to ruin his career if he wasn’t able to fix the problem.
That night, lying in bed, Chong could not stop thinking about work—lines of code, equations, formulas, parameters. He got up and looked through the stack of documents he had brought home, running over a number of calculations, before confirming that there was nothing wrong with the system his team had implemented. After a moment of deliberation, he decided that he needed to confirm the calculations for himself. Chong walked down the old cobblestone streets of Soho towards Central station. The night was alive with expats flowing out of bars and pubs in Lan Kwai Fong.
The station lobby was filled with rows of stainless-steel gates and ticket machines. LED lights and LCD panels lit the station with an alien glow. He tapped his Octopus Card at the gate, then descended the long escalator to the platform before waiting in front of a set of spotless glass screen doors. He peered down the curved platform created decades ago by tunnel boring machines—two janitors were methodically mopping the floors. The refurbished Metro-Cammell M-stock train roared into the station on a set of near-standard gauge tracks. Regenerative brakes slowed the train riding on chevron springs and air bags down to a silent stop. The train doors slid open synchronously with the retrofitted platform doors, opening up the bright interior of the train.
Chong took a seat and leaned his head against the window. He thought about the measurements that he needed to verify—the gradient of the tracks, the elevation of the ballast, the length and condition of the ties, and the tension of the fasteners. The complexity of the problem felt overwhelming, and as he tried to relax his body against the hard metal seat pressing hard against his spine, the train jerked to a screeching halt. He was sent flying across the empty row of seats into a Plexiglass partition. A scream echoed through the carriage and a number of objects skidded across the ground. A dull ache radiated down his arm. A middle-aged man was on the ground retrieving a number of oranges that had fallen out of his bag. Some people were helping an old woman who had fallen. The conductor came on the intercom, apologizing for the abrupt stop, announcing a delay while he called in a crew to help with emergency repairs. Chong knew what that meant—another track failure.
Chong made his way to the conductor’s cabin and introduced himself to the conductor, an older man, who asked him how old he was. “No wonder the system is falling apart,” the conductor said. Chong knew better than to respond, and let the man take him to the emergency exit. With a swift motion, the conductor pulled on the lever and kicked the door open. A set of stairs descended into the dark tunnel. “Do what you need,” the conductor said before walking away.
The tunnel was dark, illuminated by a faint glow from the train windows. Chong knelt down at the front end of the train. The damage was evident—not as significant as the previous failure, but the track looked like a vinyl record someone had managed to warp in a number of locations. Chong walked further into the tunnel, got down on his hands and feet, and began to record measurements, checking his figures each time before moving on.
By the tenth page of notes, Chong glanced at his watch—an hour had passed. Dirt stuck to the sweat covering his body. Polished by countless rotations of each wheel, the tracks reflected in the dark, the only source of light as the tunnel grew dimmer with each passing step. Chong sat down and began evaluating his notes before noticing an abnormality in the track geometry—the cant, the difference in elevation between the outer and inner track, was too low to allow for the train to use its regenerative brakes efficiently when it steered around the curve, leaving the train to rely on conventional friction brakes, which generated heat to stop. Over time, this was what led to the track failure. It wasn’t his team’s fault, but the consequence of a poorly engineered track from years past.
Chong began to make his way back when he heard a hum coming from the direction of the train—the sound of a machine coming back to life. A set of lights on the face of the train flashed, signaling its departure—they must have fixed the problem. Chong was stationary for a moment, deliberating what to do next, before his instincts took over, sending him into a sprint in the opposite direction. His heart began to thump, legs began to ache, breath began to quicken. At full speed, he maneuvered his way over the tracks, careful not to fall.
The sound of the train inched closer and calculations began to circulate in Chong’s mind—projected velocity, distance ahead of the train, estimated distance to the next station, the train’s acceleration and maximum velocity, potential for human error—and he quickly came to the conclusion that the probability he would arrive at the next station before the train was close to zero. But as the beating of his heart boomed in his ears, and as the train’s wheels squealed against the tracks, he heard a tune he remembered from another world—the cellist’s performance of Brahms’ Sonata. The horse-haired bow, fluid, pulling and pushing on thick gut strings, sending a mist of rosin into the air. Fingers sliding down the cello’s neck, modifying the frequency of each note that danced on the tiled walls of the station. The resonance of each string traveling through the hand-crafted bridge, into the maple body, out of the sound holes. The tempo that wasn’t quite steady, the execution of each phrase too slow, or too quick, but also the allure and charm of each mistake that generated something novel, beautiful, beyond rationalization.
As Chong turned his head, he could make out the rows of lights illuminating the white interior of the train and the faint outline of a figure in the conductor carriage when it came to him—something he had known all along. He wasn’t sure why it had taken this long, but it didn’t really matter, because he knew in that moment it was what he had been looking for this whole time—the answer, the proof, the solution to the most fundamental question of all: Rμν=0.
Chong stopped. And as he entered the darkness, he felt, for the first time, light.
Wayne Mok is originally from Hong Kong and now lives in Sydney, Australia.