Katarina smiled with her mouth open, as though she were swallowing something big and sweet. “I like that,” she said. “If you keep looking, and something is really true, then the more you learn, the smaller your leaps of faith until they’re just steps and then not steps at all.”
“Yes! That’s it exactly.” Emmy pumped her fist as though she’d just won something. “You nailed it: the scientific method is nothing but watching your step.”
She and Katarina looked very happy in that instant. Then Emmy turned back to the desk. “I’m going to describe a totally simple model of a big bang—just to get a couple of points across.” She picked the pencil back up and drew a wavy line from the dot to the right. “The wavy line represents the energy in this little universe. So far, it’s just sitting there and time is passing.” She ended the wavy line with another dot and drew two lines connected to the second dot. “At this point, the energy converts into matter. The straight lines represent particles, point-like pieces of matter.”
Emmy looked up at them again. Ryan had the distinct impression that if she caught him spacing out, she would whack his knuckles with a ruler. He couldn’t quite hold back a smile. She smiled back. It was the last thing he expected. And her smile was warm and sweet.
Emmy underlined E=mc2 and said, “Remember, Einstein told us that matter is a form of energy.” She wrote e- next to one of the straight lines and e+ next to the other. “In this little universe, the little bang formed two particles. This one”—she pointed at the e-—“is an electron. Electrons carry one unit of negative electric charge. The other one is called a positron, and it carries one unit of positive electric charge.” She looked up again. It distracted Ryan. She was saying things that he’d read about in Foster’s book, and he wanted to pay attention, so he concentrated on the diagram. He hoped she was disappointed that he looked away.
She said, “The laws of nature come from different types of symmetry, and this is an example of one. When matter forms, an equal amount of antimatter also forms. The electron is matter and the positron is its antimatter equivalent—a positron is exactly like an electron except that it carries the opposite charge.”
Katarina said, “Is every electron and positron the same?”
“Very good.” As Emmy nodded, her hair floated against her cheeks and, before continuing, she tossed it back in one graceful motion. “Yes, every electron is exactly like every other electron, and every positron is exactly like every other positron—we call them identical particles.”
“How do you know? You can’t check every one of them.”
“If they differed, the universe wouldn’t look the way it does.”
Katarina looked at Ryan, and they nodded at each other. A big grin formed on Katarina’s face. “Wow…the universe would look different, that is so fucking cool.”
Ryan said, “Don’t say fuck.”
Katarina glared at him. “Lay off, Ryan.”
Emmy tore the sheet of paper from the blotter and handed it to Ryan. He rolled it into a tube. She started drawing again. “In this diagram, we start with an electron and a positron moving forward in time. When they meet, they annihilate into pure energy.”
“This is called a Feynman diagram. Richard Feynman was a physicist at Caltech who made this subject understandable. It’s called QED, quantum electrodynamics. In this case, the pure energy is represented by the wavy lines—they are called photons. Light, radio waves, X-rays are all examples of photons. The only difference between them is the amount of energy they carry. But it gets better.” She drew more diagrams under the first one.
“To predict what happens when the electron and positron annihilate, we have to include every possible way that the reaction can proceed, and there is an infinite number of them. This is where quantum physics comes in and makes things seem bizarre.”
Katarina shook her head, finally looking more like the surly adolescent that Ryan knew. “You can’t add up an infinite number of things.”
Emmy turned to Katarina and said, “Adding up all the diagrams is tricky, but it can be done, and the results of this theory are the most accurate of anything humanity has ever produced. If the universe behaved the same way at very small distance scales as it does in our world, where men like Ryan are two meters tall, then we could actually see the single process through which the reaction evolves. Instead, it’s as though the end result is caused by contributions from every possible process.”
She pointed at each of the new diagrams. “Look at the closed loops in these diagrams. An electron and a positron pop up and then annihilate back into the photon—this is where your friend claims to be able to get free energy.”
Ryan said, “You read Foster’s book?”
“No, I skimmed the web page. It’s obvious that they’re running the same basic scam as most of these idiots—whether they actually believe it or not—plus, they include enough creationist nonsense that anyone who disagrees with them can be labeled a heretic.”
The look of disgust on her face betrayed that she was indeed related to Dodge. Nothing could be a greater turnoff to Ryan. “Whoa. That’s pretty harsh—you should read the guy’s book before condemning him.”
Her eyes met his. The disgust was replaced by something that looked like concern. She said, “It’s nice of you to defend your friend, but he is not the first one to try this. You have the book?”
Ryan ran upstairs and got it. When he returned, Emmy was thumbing through Katarina’s calculus text with Katarina looking over her shoulder. Emmy was just slightly taller than Katarina. He wished he could take a picture of Katarina so engaged with this woman.
Dodge came in and set a box of pizza on his desk. “Have you two figured out what Ryan’s fundamentalist pal is trying to do with those patents?”
Ryan added, “Beer?”
Dodge disappeared and came back with beers for Ryan and Emmy and a Coke for Katarina.
Katarina said, “Dodge is almost nice when Emmy is here.”
Ryan added, “Nearly human.”
Emmy said, “This is an investment to him. He expects to make a fortune suing that company.”
“What?” Ryan said.
“Aren’t you suing Creation Energy?” Emmy asked.
Ryan said, “I’m not going to sue my best friend.”
Emmy looked at him again. She motioned toward the door, toward Dodge, and said, “He thinks you are.”
As Ryan and Katarina ate pizza, Emmy opened Foster’s book. “Look, it says so on the first page.” She set the book on the desk, indicated the second paragraph, and read aloud: “‘By reconstructing the conditions just prior to Creation, an opening is provided between the spiritual and physical worlds where energy can be derived from what are called vacuum fluctuations.’” She looked up. “See? Vacuum fluctuations, that’s what the loops in these diagrams are called. Electron-positron loops pop out of the vacuum and then disappear—a fluctuation in the vacuum. They are, however, fundamentally impossible to observe directly.”
Ryan said, “Foster must have found a way to get energy from them.” He hated the tenuous feeling of defending something he didn’t understand.
“I’m sorry, Ryan. Perhaps your friend genuinely believes it, but he is mistaken, okay?” She seemed to really mean it. She seemed to really mean everything she said. Ryan realized he’d never hit on a woman before who so fully lacked bullshit.
Emmy caught something in his look and leaned toward him. “Ever since quantum mechanics was formulated, about eighty years ago, people have tried to get around the Heisenberg uncertainty principle.” She took a piece of pizza. “I’m sorry, but your friend has made a mistake.”
“I like that,” Katarina said. “An uncertain principle. That’s perfect for me.”
Emmy laughed and almost choked on her pizza. She set her slice down, wiped her fingers on a napkin, and picked up her pencil. “The Heisenberg uncertainty principle can be interpreted in two ways.” She wrote an equation on the blotter: ΔEΔt ≥ h/4π. “The
ΔE is the energy scale, Δt is the time, and h is Planck’s constant—it’s a wicked tiny number. Anyway, I call this thing the watermelon-seed principle. You know how slippery watermelon seeds are? Right when you get your fingers on them, they squirt away.” She pointed at the E and then the t in the equation. “This means that once you measure the energy, all the information about time squirts away. Conversely, if you determine the time it takes for something to happen, all the information about the energy squirts away—like trying to pick up a watermelon seed.”
Katarina said, “But you can pick up watermelon seeds.”
“Yes, but you have to be careful. If you squeeze too hard, it slips away. To pick up a seed, you localize it, cradle it in the watermelon flesh, and then you can scoop it out.” Emmy tapped the equation again—there were several dots underneath the E and t now. “What this means is that we have to balance how accurately we measure energy with how accurately we measure time. Heisenberg’s uncertainty principle limits the accuracy of measurements—it is the mathematical realization that we are part of the universe and that we cannot separate ourselves from our observations.”
Katarina’s eyes were wide. Ryan had never seen her look so unguarded, guileless, so much like a little kid before. She said, “You can actually prove that we are part of the universe?”
Emmy had the same look about her. She nodded rapidly and said, “Isn’t it awesome when the math corroborates the obvious? It’s like following a treasure map and seeing that you’re on the right track.”
Katarina said, “I’m thinking that if the math says we aren’t part of the universe, it might be wrong.” On the corner of the blotter, she manipulated the equation, solving for E and then t.
Emmy continued, “Okay. That’s the first interpretation. The second one is more important. It is the reason that these vacuum fluctuations can’t be observed directly. From the watermelon-seed argument, you can see how the picture is blurry. You know the seed is there, but you can’t get a good grip on it. In a blurry picture, it’s hard to tell one thing from another. They smear together, and we have to try to account for what we can’t see, what’s hidden by the blurriness.” She pointed at the loops in the two diagrams again. “We can’t decipher processes like these. Heisenberg’s uncertainty principle tells us that these processes occur too fast and with too little energy to be observed. We call these virtual processes to distinguish them from real processes. A real process is a watermelon seed we have in our hand. Virtual processes are the seeds buried in the flesh. We know they are there, but we have to cut up the watermelon to see them.”
Katarina said, “Didn’t you have to cut the watermelon to get the real seed?”
“Exactly.” Emmy’s voice resonated with excitement. “That’s how we isolated it, and if I want to observe a virtual process, I can change the system, usually by injecting energy, and make it into a real system. Of course, then I don’t have a watermelon anymore.”
Emmy set the pencil down and picked up her beer. “Your friend thinks that he’s found a way to violate the uncertainty principle to extract energy from vacuum fluctuations.”
“Why are you so certain that he can’t?” Ryan felt like he had to talk fast to get words in before she swallowed. “It’s a theory, right? Why are you so dogmatic? Has there ever been a theory that wasn’t flawed in some way?”
Emmy put her beer on the blotter. “If the amount of energy that came out of whatever process they’re using is larger than what went in, it would violate the first law of thermodynamics. Remember, energy is neither created nor destroyed; it can only change form.”
Katarina said, “Sounds like something came from nothing, to me.”
Ryan pointed at Foster’s book. “Maybe he’s found a way to change spiritual energy into physical energy.”
“Please.” Emmy sighed. “That’s absurd.”
Ryan licked his lips. “Hey, I’m not saying that he knows something you don’t, just that neither of you knows everything.”
Katarina said, “And once again, I must ask, where’d it come from?”
“There was no ‘where.’ It is here,” Emmy said. “Okay, language evolved for us to describe a world where our hearts beat about once each second and a piece of pizza has a couple of hundred calories. Now remember, Planck’s constant, that h, is way tiny, so tiny that it might as well be zero as far as our senses are concerned. It can be confusing, but fortunately, by describing it mathematically, we don’t run into any of these semantic problems.”
“Lame,” Katarina said, looking back and forth at the two of them. “Lame, lame, lame. It had to come from somewhere. The universe is proof that something came from nothing, so there must be a way for it to happen again.”
“She’s got a point. The existence of the universe is what engineers call proof of principle,” Ryan said. “Something came from nothing—the obvious conclusion is that it came from God.”
“Okay, this is another one of those questions like, what was here before the universe? Saying that something had to create the universe doesn’t make sense. You end up with an infinite series of origins: if God created the universe, who created God, and who created whoever created God, and so on.” Emmy put her pencil in her pocket. “Anyway, I need to get going.”
Ryan said, “You should read Foster’s book before you attack it.”
“Okay, I’ll read it. But I have a book I want you to read too.”
Ryan held out his hand. “It’s a deal.”
They shook on it and, in that instant, Emmy held her head at a slight angle. Her eyes narrowed at Ryan as though she were looking inside him. The flirting had felt like a game, but with those eyes on him, he wondered.
Katarina interrupted them. “You had no problem with an infinite sum of these loop diagram thingies, but you don’t like a creator creating a creator creating a creator?”
Ryan added, “Einstein believed in God; don’t you?”
Emmy took her hand away from Ryan. “Einstein referred to whatever set the Big Bang in motion as a Divine Spark. It is a much different idea of God than the deities invented by human cultures.”
Katarina asked, “You really don’t believe in God?”
“Define what you mean by God.”
Katarina said, “God is just the energy or maybe God is the particles and forces or maybe God is space and time.”
“If you define God as energy, then, because I believe in energy, I believe in God. That would be a small step of faith. But it would be a huge leap of faith to believe that the energy in the universe requires that I worship it or that I should kill people who don’t.”
“That’s kind of extreme.” Ryan stared at her. She looked almost playful. He said, “Which do you think came first, matter or consciousness?”
“Consciousness is the result of biochemistry, so the chemicals had to come first.”
“What about the soul?” Ryan asked.
“There is no reason to believe in anything like—”
Emmy had raised her voice, but Katarina’s was louder. “You said that when we look at an interaction, we have to include every way that it can happen. Why not include the soul? Isn’t a soul just as possible as a universe? I mean, what if we had asked you about the soul, and you were like a priest or something? Wouldn’t you have gone through the same argument about the creation of the soul that you did with the Big Bang?”
“No.” Emmy settled back into her lecturing voice. “There is compelling evidence for the existence of a universe and no evidence for a soul.”
Ryan took the last slice of pizza. “What do you think happens when people die?”
“They die. It’s over.”
“Wrong,” Katarina interrupted. “You might know a lot about electrons and energy and stuff, but you don’t know anything about where someone goes when they die. Saying it’s over is mean.”
Emmy leaned forward and spoke calmly, as though her expectation that this child would have a tantrum had been confirmed. “What do you thin
k happens when someone dies?”
Katarina caught her tone and, instead of speaking through clenched teeth like she did when she was angry with Ryan, assembled her composure. “I don’t know what happens, but I am going to figure it out. Watch me.”
A week after Emmy’s visit, two packages arrived. One was a six-foot whiteboard with twenty colored markers. The other contained two copies of Richard Feynman’s QED and the three-volume set of The Feynman Lectures on Physics. Emmy had included a card for Katarina with four sets of arcane mathematical symbols surrounding a light bulb and the caption “…and God said, let there be light” but she’d scratched out “God” and written in “Maxwell.” Ryan explained that Maxwell’s equations were named after the nineteenth-century physicist who formulated electrodynamics.
In the card, Emmy told Katarina how she had loved the purity of mathematics as a teenager and that she envied Katarina seeing “infinitesimals, differentials, integrals, and derivatives for the first time—someday you will use these tools to discover truth in the universe. I hope that I will be working with you when you do.”
Ryan and Katarina stared at each other. Katarina squinted and set the note aside, brushing it off. Ryan said, “That’s a lot to live up to, kiddo.”
Katarina said, “What. Ever.”
Emmy included a note for Ryan too, just a few words that it was “nice to meet you” and “call if you have any questions,” but there was also a cryptic phrase: “I promised to read Foster Reed’s dissertation and you promised to read Feynman’s QED. Don’t ever break a promise to me!” The thing that made it hard to figure was that if you looked long enough at the dot over the i in promise, you could convince yourself that it was heart-shaped.
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