Solution experiment

"So what do we do first?" asked Mark, showing up to work at the laboratory.
"I'm working on reproducing the results of Ashfar's experiment," Sam said. Mark looked puzzled so Sam explained, "Ashfar is an idiot who claims the impossible. He ranks up there with those who believe in cold fusion, time travel, and perpetual motion. Not to put too fine a point on it."
"Those don't exist?" Mark joked.
"No, they don't," said Sam. "Ashfar thinks that it should be possible to perform a double-slit experiment with a wire mesh blocking the dark part of the interference patterns and use separate light sensors to count photons with sensors. He believes that by blocking certain light paths with the mesh he can deduce which slit each photon traveled through."
"Maybe you should explain that a little better. I know the double-slit experiment. But the mesh part is confusing."
"Okay. Let's start a little earlier. The double-slit experiment which you say you know and most people say they know is not actually as well known as you and they think. The concept is relatively simple but has far reaching consequences. Feynman said that the double-slit experiment contains all the secrets of quantum physics. He said that anyone who didn't comprehend the impact of the experiment did not understand quantum physics."
"I understand it," Mark said.
"I know you think you do," said Sam and smiled.
"Light travels through a narrow slit and it behaves like a wave." Mark said. "If you allow light to travel through a double-slit then an interference patter appears. This interference pattern is the result of the two waves interacting. But if you measure which slit a photon travels through, then the interference pattern disappears and light behaves like a particle."
"Not really. No one really observes the interference pattern disappearing and reappearing. That's the ultimate effect of the math. But there are a few flaws in your statement. First, light is not the only thing that behaves this way in a double-slit experiment. Electrons and even atoms can display interference patterns in a double-slit experiment. Although they behave like waves and particles, they're clearly particles. Secondly, you can't 'measure which slit' a photon passes through. You can't detect a photon and have it continue on without interruption. The double-slit experiment is just the embodiment of quantum states and superposition."
"Superposition is the waveform math that describes multiple scenarios being present simultaneously," Mark said. "And when any one version is observed, the other waveforms collapse around the one scenario that is observed."
"In a very loose sense, yes" said Sam. "You know Schrödinger's equation?"
"Yes," said Mark. "That's some heavy math."
"Not really," said Sam. "Schrödinger described quantum positions using standard wave equations but that doesn't mean that superposition is just a wave. It's more complex. As his cat experiment showed, the state of the cat is unknown until such time as the cat is observed."
"I like the cat experiment," Mark said. "The cat is inside a box with a gas that will randomly sublimate into a poison and kill the cat. The cat is both alive and dead at the same time until you open the box."
"That's a bit too simplistic again," Sam said. "When the box the cat is in is closed to observers, the cat's state is both alive and dead. But that doesn't mean the cat is actually alive and actually dead at the same time. The cat is only alive or dead not both. You're a card player?"
"Yes. I mean, online."
"So if you take a deck of cards that are shuffled into a particular order, you never know what order the deck of cards is in unless you look. By simple combinatorial analysis, a deck of cards has 52 factorial distinct orderings. That's such a big number, it might exceed the number of stars in our galaxy, or even the number of galaxies in the universe. Imagine each star in the Milky Way being named after a unique ordering of a deck of cards. Now the Sun is just the one deck of cards you've shuffled and hold in your hand."
"Yeah," said Mark grinning.
"So this unique deck that you've shuffled that you hold in your hand is a unique deck among all shuffled decks as the sun is unique from all other stars in the Milky Way."
"I like it."
"But I'll repeat again that this deck of cards is set in a particular sequence. It doesn't change. It is not 52 factorial number of decks simultaneously held in one hand, like a Milky Way Galaxy in your palm. It is only one deck and no other deck. Do you see the difference?"
"Sort of," said Mark. "I really like the idea of the galaxy in my palm, like the galaxy on Orion the cat's belt in _Men in Black_."
Samantha rolled her eyes. "I don't even know what you're talking about," she said. "I assume it's the Will Ferrel movie."
"No, Will Smith."
"Oh," said Sam.
"No, but I get it," said Mark. "There are no multiverses. Only one universe with the present state. The superposition is possibility but only because we haven't observed all the information available yet."
"Now you're getting it," said Sam. "We don't know the position of each card in the deck until they're turned over one by one. Only after they're turned over do we know which specific deck we hold from the galaxy of all possible decks. Schrödinger's cat could be alive or dead but we have no way of knowing."
"How does that refer back to Ashfar being an idiot?" asked Mark gesturing at the table in the lab.
"Ashfar believes that we can infer from two sensors at the diffusion pattern where a particular photon originated, either through one slit or the other. He believes that we can see the cat as both dead and alive at the same time."
"Impossible if you describe it that way," said Mark.
"Exactly. But it's not that simple."
"It never is," said Mark.
"No, it isn't. The basic derivation of the double slit experiment is that the probability of viewing the diffraction pattern which is V squared plus the probability of determining which slit a particular path was chosen called D squared is less than or equal to one." Sam turned and wrote on a white board:
V^2 + D^2 <= 1
"That is," she continued, "Our intuition tells us that when we measure the interference pattern at the back of the experiment with very high probabilities, then the probability of measuring with determination which slit was traversed by a particular wave or particle should go to zero. And vice-versa. If we determine which slit a particle or wave travelled through, the probability of viewing an interference pattern should go to zero. Since a probability of one means that an event is guaranteed to happen, then the probability of one increasing means the other must decrease.
Sam continued, "You can't know for sure which path a light wave travels through the double-slit experiment at the same time you also know for sure there is an interference pattern."
"It's like the Heisenberg uncertainty principle," Mark said.
"The equations are interpreted similarly. Heisenberg actually turned out to be wrong. But his math was correct. His explanation that the observer affects the outcome of the measurements (for example, knowing a particle's location affects the particle in such a way that the momentum cannot be measured) was the wrong explanation. The fact that we cannot observe two pieces of information about a wave or particle is due to the underlying quantum properties of the particle rather than any flaws related to how or what we use to measure things with our sensors."
"Heisenberg's formulas used Planck's constant, though."
"It's similar enough," said Sam. "And please say 'forumlae' although both are correct. Heisenberg used the sum of the standard deviations and set them greater than half the standardised Planck's constant. He used standard deviations and we're using the square of probabilities. What's a standard deviation?"
"The square root of the deviation," said Mark. "Oh yeah, duh."
"So let me show you how I laid out Ashfar's experiment."