A/N: The easiest way to follow along with Hermione here is to look up 'DR. QUANTUM - DOUBLE SLIT EXPERIMENT' on YouTube. It's a 5 minute clip posted by 'Angel Art', and watching that will make all this much easier to follow.
When the day of her experiment came, Hermione could barely contain her excitement. Classes seemed to drag on and on forever, and Hermione had to force herself not to bolt from her chair she moment the end of classes bell had rung. She was trying to walk more slowly and confidently now, after all – but it was a very near thing.
Dinner seemed like an obstacle, just another thing standing in her way, and when Hermione was finally done, she stood up, and Professor Vector gave her a nod from the head table, making excitement jolt through Hermione.
It was happening. She was really going to do this.
Hermione met Professors Vector and Snape at an abandoned classroom not far from the Charms classroom. Draco and Blaise had commandeered it to store all of her requested materials in, and once everyone had arrived, Hermione happily hurried in to begin setting up.
Professor Vector watched Hermione as she set up her experiment, while Professor Snape gave Hermione doubtful looks. Hermione hummed to herself as she worked, pleased Blaise and Draco been able to get enough tin and copper to free transfigure what she wanted. The sheets of drywall they'd found were ideal, too – the stone wall of the castle wouldn't have exactly worked with what she'd wanted. The back wall she'd enchanted to be sticky; now she was making sure her metal screen had a perfect rectangular slit in the middle of it, just wide enough to give it a definable shape.
"Explain to me what you're doing," Professor Vector instructed. "Right now it looks like you have a wall and a gun set up, which doesn't tell me anything about what's going to happen."
"I'm conducting the famous double-slit experiment," Hermione said absently, carefully setting up her transfigured pipe-and-marble contraption. "It'll help me understand just what magic is."
"You said that before. I've still never heard of the double-slit experiment," Snape snapped. "What is it?"
"I will tell you," Hermione said, turning to her professors and grinning. "Actually, I'll just show you. It'll be easier, and I have a demonstration prepared."
Both Vector and Snape looked surprised, and Hermione did her best to suppress a very unprofessional nervous giggle that threatened to bubble up.
"This is a pea shooter enchanted to shoot marbles," Hermione told them. "I have enchanted this back wall to be sticky, so marbles that touch it will stick to it. If I shoot marbles at this giant piece of metal with a slit in it, what happens?"
"Marbles ricochet everywhere and cause a hazardous mess?" Snape said dryly.
Hermione rolled her eyes. With a flick of her wand, she triggered the pea shooter to fire marbles at the slit.
"The marbles that go through the slit form a pattern on the back wall where they went through and hit, in the shape of the slit," Hermione said, as marbles tinged off of the screen while others flew through. The ones that made it through the slit stuck to the far wall, forming a rectangle composed of tightly-clustered marbles. "If we add a second slit, there is a similar result."
She turned off the pea shooter, gathered up all the marbles, and levitated her second screen into place, this one with two rectangles cut out. She waved her wand, and as the pea shooter started shooting, two rectangles of marbles began to form on the back wall.
"Groundbreaking," Snape said, sarcasm dripping from his tone. "I never would have guessed."
Hermione pulled another sheet of drywall into place, moving away the one that had two rectangles of marbles stuck to it. She pulled the first slit back into place.
"Now, if I fire a wave at this slit," she said, "the crest of the wave will be the strongest—"
"A wave?" Snape interrupted, raising an eyebrow, and Hermione winced.
"I don't know how to fire just 'a wave'," she admitted. "I was going to try and use sound, but I couldn't figure out how to enchant the wall to recognize sound."
"That's easy enough," Vector said, surprising her. Vector went over to the new wall and tapped it with her wand, murmuring, before tracing runes in the air before it. "There. It'll be visually reactive to sound, now."
Hermione blinked. "Oh." She paused, then grinned. "Wicked."
She set up the gramophone she'd been hoping to use.
"So I fire a wave at this slit," she said, turning on the gramophone. Heavy jazz music began to play quite loudly. "As the wave goes through, the crest of the wave will be directly in front of the slit, but the curves sloping down to the troughs of the wave will be less reactive. The line on the back shows that intensity."
It was as she said: as the gramophone played, a gradual gradient lit up the wall. The wall was black on the far left, gradually shifting to dark gray, then gray, then to a blinding white directly in front of the slit, then back to gray, dark gray, and black, where there was nothing.
"Interesting," Professor Vector said. "Continue."
"If I add a second slit," Hermione said, turning off the gramophone and levitating the second screen into place, "something different happens."
Professor Vector obliged her by resetting the wall at the back, and Hermione once again turned on the gramophone. The back of the wall began to form stripes of black and white, not unlike the bars of a jail cell.
"If the top of one wave meets the bottom of another wave, they cancel each other out," Hermione explained. "So now we get an interference pattern on the back wall. Places where the two tops meet are the brightest intensity, and where they cancel out, there is nothing."
Hermione went to the forgotten chalkboard hanging on the side of the classroom, quickly drawing out what she meant by the sound waves cancelling each other out.
She levitated the second wall out of the way, floating a new one into place.
"So when we shoot things at two slits, we get two distinct slit shapes," she said, pointing to the marbles still stuck to the first wall. "And when we shoot waves, we get an interference pattern."
"I am following along," Professor Vector said mildly. "I've yet to see anything mind-boggling, though."
"That's the next part," Hermione said, taking a deep breath. "So scientists took this experiment and shrunk it down to the quantum level. They fired a stream of electrons at a slit—"
"Tiny pieces of matter," Snape told Vector. "They compose atoms—"
"I know what an electron is, thanks," Vector snapped.
"Um," Hermione said. "They fired electrons at a slit, and they got a rectangle of electrons on the wall. But when they fired electrons at two slits, they got this."
She gestured at the interference pattern, and Vector frowned.
"Wait," she said. "What?"
"They fired tiny bits of matter through the slits, but they got an interference pattern like a wave," she said. "They got an interference even when they slowed everything down, being careful to shoot them through one at a time, to make sure they weren't bouncing off of each other."
Snape was looking at the interference pattern suspiciously.
"Scientists concluded that the electron leaves the gun as a particle, becomes a wave of potentials, goes through both slits and interferes with itself, and then hits the wall as a particle," Hermione said carefully. "I don't understand the finer bits of it, but I know there's a thing in quantum mechanics where two possibilities are true at once."
"Superpositions," Professor Vector said, surprising Hermione. "Fascinating."
"What happened next is the really mind-boggling part," Hermione said. "So while they had all these possibilities in— err— in superposition, existing at the same time with each other, scientists wanted to see what slit the electron actually went through. So they put a measuring device next to one slit to observe which slit the electron went through. But when they observed, the electron went back to behaving as a particle, resulting in two bands, not an interference pattern."
Vector's eyes widened.
"Wait—"
"The act of measuring, of observing, made the electron only go through one slit, not both. The electron decided to act differently, as if it was aware of being watched," Hermione said, unable to contain the excitement in her voice. "And when they took the measuring device away again, it went back to being an interference pattern."
"So the act of observing collapsed the wavefunction," Professor Vector said, amazed. "That's incredible."
Snape frowned. "That doesn't make any sense."
"It doesn't," Hermione admitted. "Electrons aren't conscious, as far as we're aware, so they can't really decide anything. But that's what happened, anyway. And the same thing happens with photons, too."
"So you want to try this with magic," Vector said, rubbing her chin thoughtfully. "To see if magic behaves as a wave or a particle?"
"Yes!" Hermione beamed. "Exactly."
Vector looked at Snape.
"It would explain that paper in Arithmancy Today that denounced quadratic equations in certain systems," she said. "Partial differential equations are used for quantum mechanics, I believe. If magic behaves at the quantum level…"
"Conduct your experiment, Miss Granger," Snape said, waving a hand. His eyes gleamed. "Let's see what you find."
Hermione grinned. "Gladly."
Professor Vector charmed the new back wall to register magic, and Hermione reached inside of herself to her core, finding her magic, and aimed her wand at the slit.
"It's a little unintuitive to use just magic, not a spell," she said, "but I want to see what happens."
She pushed her magic up and out of her through her wand, visualizing it coming out like a cone. She'd never done something like this before, and she was surprised to see a purple light come out of her wand, lighting up the room like she'd cast Lumos. Most of it was blocked by the slit, but what wasn't made its way across the room, where, to her astonishment, a single rectangle of purple light shining against the black wall.
"So this indicates magic is a particle, correct?" Vector questioned.
"So far!" Hermione hurried to get the second slit into place, then pulling another wall into place. "But we have to test with two!"
Vector obligingly cast the reactive spell on the wall once more, and everything was set up. Hermione went back behind the slits, peeking out through them at the far wall, feeling very much like she was standing on the precipice of a cliff, like she was about to discover something monumentous and great.
Hermione held her breath, closed her eyes, and pushed her magic out through her wand once more.
"Would you look at that." Vector's voice was amused, and Hermione's eyes popped open. "It's just like before."
Hermione hurried to look, her eyes widening at the sight: there were bands of bright purple on the wall, interspersed with stripes of pure black – an interference pattern once more.
"It's the same!" she crowed, dancing around. "It behaves as both! It's a particle and a wave!"
"Did you think it would not?" Snape questioned, his curiosity betraying him.
"I kind of thought it would just be a wave," Hermione confessed. "I'm not sure why – maybe because I always think of light as a wave, not as a particle? But to know magic can be both – oh, this is fascinating!"
Snape was frowning at the board behind the single slit.
"Does this mean magic is a physical thing?" he asked. "That it has mass? It has weight?"
"I guess," Hermione said cheerily. "Isn't that mad?"
"Ah, we're not done," Vector chided. She grinned at Hermione, a slight manic glint to her eyes. "Now, we have to observe the same experiment, so we can see if magic behaves the same and observing collapses the wave function."
"Right." Hermione bit her lip. "Though – I don't know how to really observe things at the quantum level—"
Vector went over to the chalkboard, cleared it away, and began scrawling out a complicated equation on the board. She then went over and put two identifying runes next to the two slits on the screen, before returning to the board, completing her equations, and tapping them with her wand. Immediately, part of the chalk turned gold and peeled away, flying over to hover in a weird haze of magic and glitter near the screen.
"Oh, clever," Snape said, his tone approving. "I see what you did there."
"Thank you," Vector said, pleased. "I thought it was a rather creative work-around."
Hermione had no idea what Vector had done, but Vector gestured for her to conduct the experiment once more, impatient. When Hermione centered herself, aimed her wand at the slit, and poured her purple cone of magic out at the screen once more, the exclamation she heard on the other side of the screen gave away the results.
"—entirely explains the interaction at the spell level!" Vector was telling Snape, waving her hand wildly at the two purple rectangles that had formed on the back wall. "If observation of the magic itself changes the magic, it will have to be accounted for!"
"Which would explain why partial different whatsits better mimic true effects?" Snape drawled.
"Linear partial differential equations, you neanderthal," Vector corrected. "And yes, it would! Oh, the implications of this are staggering!"
Hermione watched incredulously as Vector did a little dance right then and there in the middle of the classroom, a little happy, triumphant jig she'd never have imagined her teacher would do. Snape snorted, and Vector shot him an annoyed look before whirling to face Hermione.
"And you!" she exclaimed, beaming. "You were right – the absolute potential this has to completely revolutionize advanced Arithmancy—oh, fifty points to Slytherin!"
Hermione's jaw dropped open, and Snape smirked.
"Another ten for coming to your professors before conducting a groundbreaking experiment this time," he added. His eyes gleamed.
"Twenty," Vector corrected, laughing. "After all, there were two professors present."
"Just so," Snape agreed, smirking. He gave Hermione a calculating look. "I trust you will continue to alert your professors in this manner in the future?"
"If it earns me seventy points in one night?" Hermione said, amused. "Sure."
Snape snorted, folding his arms. "That is not why—"
"I'm a teenager. I'm motivated by reward," Hermione told him, laughing. "My amygdala's driving my choices, not my prefrontal cortex."
"—What?"
"Give me points, and I'll continue to alert you," Hermione simplified, eyes sparkling. "Does that work for you?"
Snape looked exasperated, but Vector broke the tension, laughing.
"If he won't give you points, I will," she promised. She laughed again, beaming at the wall. "Would you be okay leaving all your materials here? I want to see if I can replicate this myself before I start drafting a paper."
"Of course," Hermione said. "I don't exactly have another use for them lined up."
"Another five points to Slytherin for your generosity, then," Vector said, grinning. "And more once you're officially co-author, I think. I'll let you know when the draft of the paper is done."