“Each ... is a perfect little puzzle-box: one marvels at their perfect geometries while anticipating that dazzling moment where every piece slots flush. These finely-crafted, emotionally resonant tales will stay with me a long, long time.”
The collection is both speculative and lit fiction, and its stories "push boundaries—into the surreal, into the playful, into the irresistible energy of uncertainty."
We are pleased to present an excerpt from the collection's story, "The Concept of a Photon." Boundary Problems will be published in March.
“. . . it is better to regard a particle not as a permanent entity but as an instantaneous event. Sometimes these events form chains that give the illusion of permanent beings — but only in particular circumstances and only for an extremely short period of time in every single case.”
— Erwin Schrödinger
The Rabbit shudders and the grinding of steel on steel competes with the rising engine roar as I hit the brakes — too late or unnecessarily, I’ll never know. In accordance with some obscure law of inverse proportionality, I have discovered that the engine volume rises as the RPM drops. Check the speedometer: 130 kph. Early March 1995, this is the era of Ontario’s abortive photo-radar program. A second or two ago, I thought I saw a camera flash. It’s eleven o’clock, the sun long set, and I’ve been driving since six with that damn muffler getting worse the whole time. Which is to say, that flash could just as easily have been a figment of an increasingly vibration-addled brain.
Bruce warned me about the brakes but said as long as I took it easy they should be fine. The muffler is a surprise, though. When I left Waterloo three days ago, I thought the road noise seemed a bit much. Then again, who expects a borrowed rattle-trap of a Rabbit to float down the 401 in coddled plush silence? No, it’s going to rattle and bump and bounce and be a bit loud, and that’s par for the course. On the drive to Ottawa, it seemed to be getting worse, but I had no stereo (no benchmark) and therefore no certainty. Now, five hours into the return journey, the hole in the muffler has developed well past the point of a plausible maybe. Two hours ago, a guy passed me on a Harley — some kind of maniac to be on the 401 at this time of year, this time of night — and I couldn’t even hear him.
For the last while, I’ve been using the engine-noise/RPM proportionality to my advantage — raising the RPM to lower the noise. Unfortunately, the Rabbit’s not a standard, so this strategy has meant driving a little fast. Apparently 130 kph fast, and that’s after hitting the brakes. Damn. Then again, maybe that wasn’t my photo-flash; could’ve been the guy in front of me, or behind. No way to know until the ticket arrives (or doesn’t) at the home of the registered owner. Which, come to think of it, is not yet me.
And though I know I should, I won’t mention the photo-flash to Bruce. Rather, I’ll drive the rest of the way to Waterloo at an eardrum-battering 110, stumble dizzily into my apartment at two in the morning, and return the Rabbit as soon as I wake up. When Bruce asks how it went, I’ll tell him (apologetically) about the brakes and the muffler. It’s not like I can complain. At three hundred bucks, the car’s still a steal. In the meantime, Bruce will reassure me that mufflers and brake shoes are cheap if you install them yourself, which he’ll be happy to do. I will thank him profusely, and I will remain grateful for Bruce’s ignorance, which has led to this exchange of a cheap car for a virtually worthless stack of Quantum II assignments.
THIRD YEAR QUANTUM
Our Quantum II exam will ask the following question: “Assuming a single photon of wavelength λ has been sent through the system diagrammed below, what is the probability of detecting that photon on the indicated range?” The mathematical solution to this problem requires two or three pages of calculations (depending on your handwriting), including the derivation and normalizing of an appropriate wave function, the translation of that wave-function into an expression for probability density, and the final calculation of probability on the given range. Ninety percent of the students in the class will take this approach, and about fifty percent of those will get the math right. This answer, though procedurally flawless, will be incorrect.
The correct answer, as Dr. Pintar has proclaimed vigorously and repeatedly throughout the term, is that “There is no such thing as probability for a single measurement!”
I’m working on a particularly difficult Fourier transform when the guy crosses the physics workroom, weaving his way between heavy wooden tables and clunky matching chairs. Each table provides ten or twelve square feet of pitted, varnished white pine upon which to work. In the corner, I hunch amid drifts of shredded eraser, texts piled high and loose papers scattered across half a table. I see the guy but pretend not to. We’re the only ones in the room.
“Hey,” he says. “Is that the quantum assignment?”
Cornered, I admit his presence and look up. “Yeah,” I say.
“Hi, I’m Bruce.” Hand extended in greeting, he has a bluff good-natured look about him. Average. Nice leather jacket, short dark hair, a little swarthy. A spray of acne down his neck. Now I recognize him from Quantum II. He always sits in the back, shows up late about half the time and not at all the rest: a fifty percent probability. “Any luck with question #4?”
“It was a bitch. But yeah, I think I got it.”
“Mind if I take a look? I’m stuck.”
“Sure, no problem.” I hand over the sheets in question. “There’s a photocopier in the lounge.” Bruce thanks me, leaves, and returns five minutes later.
“Hey, thanks man,” he says, handing back my originals. “I owe you.”
“No problem,” I repeat.
At twenty-one years old, I know that physics can (and will) explain everything. I gleefully yet reverently tug at the doors of perception, stepping through into a clockwork universe. Everything here is linear, one dimensional, or at most two. In calculus, we learn the math for three but aren’t yet asked to use it in physical applications. Dimensions have new definitions, mathematical as well as spatial. The solution to a physically one-dimensional problem might involve two or three mathematical dimensions, but that isn’t so hard to wrap your head around, really. It’s just math. There are clear differences between accelerated and non-accelerated frames of reference, the latter yielding accurate results, the former, faulty. Gravity is more or less constant. Waves are physical, ripples across water or down ropes, compressions and rarefactions in air.
In first year, Newton still rules: cause and effect, action and reaction. Predictions are both deterministic and determinate. Given a set of initial conditions, I can tell the future with perfect accuracy. With my newfound kinematics knowledge, I could calculate every possible trajectory for a collection of imaginary point-mass pool balls on a frictionless table with perfect lossless banks. A tedious and time-consuming exercise, but possible. And yet, when I try to play pool based on this knowledge, I lose. Badly.
Bruce continues to “borrow” my assignments for the duration of the term. Every week, regular as clockwork, he finds me in the empty workroom. These are the only times I see him, and we rarely exchange more than three sentences, but I can extrapolate. For example: Bruce seems entirely unaware of standard protocols for cloning. Cloning is a widespread and (covertly) accepted practice whereby a group of students divides an assignment into single-question chunks, one per person. Each student takes a question and completes it, then solutions are exchanged. This exchange often occurs in the physics workroom: a crowd of classmates working in tandem, openly passing papers back and forth, copying out answers, consulting. These weekly assignments are worth practically nothing, and the marks are not the point. The point is to learn enough to pass the final, which usually counts for 100%, assuming one has failed the midterm, which most do. Although cloning isn’t a practice you would mention to your professor in casual conversation, neither would he be ignorant of its existence. Myself, I don’t clone, but that’s another story entirely.
From the given set of initial conditions, I construct a probabilistic picture of Bruce:
(1) Bruce is an outsider. An insider would feel no need to thank me (sheepishly) each time he borrowed an assignment. I have the impression Bruce thinks he’s cheating. I don’t disillusion him.
(2) Bruce is a slacker. Every week, he borrows my assignments at the last minute, and I doubt he understands the answers. I don’t mind, as I fully expect him to fail the final. This allows me to feel simultaneously generous and superior, both particle and wave.
(3) Bruce, an outsider who is nonetheless enrolled in an upper-year quantum course, must have transferred in from another department, something science- or math-based. Otherwise, the powers that be would never have let him take it.
(4) Bruce isn’t too bright. If he was, he’d realize the assignments weren’t worth shit.
Greg Bechtel’s occasionally prize-winning stories have appeared in several journals and anthologies, including The Fiddlehead, Prairie Fire, On Spec, Qwerty, and the Tesseracts anthologies of speculative fiction. Originally from Kitchener-Waterloo, Ontario, Greg has lived at various times in Toronto, Deep River, Jamaica, Ottawa, Quebec City, and Fredericton while working (among other things) as a lifeguard, technical writer, mover, visual basic programmer, camp counsellor, semiconductor laser labtech, cab driver, tutor, and teacher. Currently, he lives and writes in Edmonton, where he teaches English Literature and Creative Writing at the University of Alberta whenever they let him. Boundary Problems is his first book.
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