Chapter 11: Hypotheticals
The Moon upon her fluent Route
Defiant of a Road—
The Star's Etruscan Argument
Substantiate a God—
...
If Aims impel these Astral Ones
The ones allowed to know
Know that which makes them as forgot
As Dawn forgets them — now —
~Emily Dickinson
Sometimes the equations on the chalkboard started to look like stars, planets, supernovas, and nebulas. Usually she took this as a sign that it was time to take a break, but sometimes she kept working, and it would feel like she was making a sketch of the universe in numbers, Greek letters, and mathematical functions.
She paused, chalk trailing at the end of a λ, and saw the colors of starlight, planets, moons, comets, and mysteries shining out from between the white lines.
"Professor, how many points would you dock from my paper if I got it to you a day late? I have work tonight."
The spell was broken, and she turned around to see Monica at the door she hadn't heard opening. She flashed a friendly smile. "Oh, I think we can let it go one time, as long as we keep it our little secret." Monica was one of her best students, and had never turned in a paper late before.
"Thank you, Profesdor." She looked visibly relieved, but then she caught sight of the chalkboard and her eyes widened. "Um...is this for Tuesday?"
Jane chuckled. "No. This isn't for a class. It's just my own project I've been working on."
"Oh. What is it?"
"Nothing that interesting. I'm working out the mathematical behavior of hypothetical points in spacetime."
"Are you going to get it published in a science journal?" Monica inquired.
"No reputable journal would publish it," she laughed. "It's really just...astrophysics fantasy, layers and layers of hypotheticals."
"'Astrophysics fantasy'? That sounds so fascinating. Now you have to tell me what it means."
"Do you have a few minutes?"
"Yeah. I don't have any more classes today, and my work doesn't start for an hour and a half."
"Okay. Would you like like a cookie?" She lifted a plate of chocolate chip cookies from her desk and offered it to Monica, who picked one with polite thanks and nibbled at it as she listened to Jane's explanation. "To start with, general relativity suggests that if a star were extremely massive, it would become increasingly dense under the force of its own gravity until not even light could escape its gravitational pull."
"Really? That's crazy."
"It is pretty wild. There's no evidence that they really exists. But, of course, if one did exist, we wouldn't be able to see it. General relativity has proven that gravity distorts spacetime, the very fabric of the universe." Jane took a stack of loose pages from one of her desk drawers to show Monica the equations she'd come up with over her years of working on this thought experiment. "Imagine how much one of these collapsed stars could bend spacetime. The center of this gravity well is a singularity—a point at which some of the values in general relativity become infinite, and you simply can't understand it through math anymore, at least any math we have yet. Anyway, I started wondering to myself, if the singularity were somehow destroyed—which, even if a singularity did exist, would be impossible—but if it were, what might happen to the space around it? That's what I love about math. Math doesn't care if the questions you ask it are impossible, ridiculous, or even incomprehensible: plug in the question and math will give you an answer."
"So what would happen to the space around it if the singularity were destroyed?" Monica asked between bites of cookie.
"Basically, there would be ripples, which would cause some localized irregularities in the laws of physics. But then..." She pulled out another sheet of paper with more complex equations, "...I started playing around with what would happen if there were two or more, shall we say, ghost singularities within each other's sphere of influence—the ripply spacetime left behind. That's when the math really gets wild."
"What happens?"
"Well, lots of weirdness, but the weirdest thing is there's a statistical chance the singularities pop back into existence. They might be in a different position, but when a new singularity pops up, it has the same values as one of the original singularities. It's like it wants to exist. The more of the ghost singularities you get in proximity, the more unstable it gets."
"Wow. So that's what all this is?" Monica gestured to the chalkboard.
"Not quite. You know how I said math doesn't care if the questions you give it are impossible? My latest...game...is asking if there can be singularities of forces besides gravity. What happens if you have a singularity of time? A singularity of distance? A singularity of energy? It's...it's really fun."
"It sounds like it. I think this is the most passionate I've ever heard you be about anything."
Jane smiled at her chalkboard. "Theoretical physics...I can't really explain it. When I'm working on theoretical physics, my mind feels like it's truly free."
"That's so inspiring."
Jane turned toward her with a shrug. "Would you like another cookie?"
"Sure. These are delicious."
"Professor Shade's wife made them."
"The English professor? I don't think I've ever met his wife."
"You should. She's a lovely woman."
"I'll see if I can get myself invited to their house, if all her baking's this good," Monica joked. She headed toward the door. "See you tomorrow, Professor Foster."