New York City, 1956
Leaning on a Chinese restaurant at a busy street corner in Greenwich Village, I crossed my legs, tipped my hat low, and quietly panicked. This case is turning into a nightmare: dozens of suspects, growing daily, and they all seem to swap places when you’re not looking. A pion couldda done it; pions seem to be some kind of front for the nuclear force that Madame Curie was playing with before she died. But leave a pion to itself and it disintegrates into a muon and a neutrino, neither of which claims to have ever heard of nuclear forces. Radiation in the form of muons and neutrinos has been raining down on us since the beginning of time, and it’s never even hurt. If pions are just glowing with nuclearness, where does the nuclearness go when they die?
For that matter, what is a particle, anyway? I have to admit, I wasn’t suspicious when I first heard the word— I thought they were talking about little rocks or marbles or something. But rocks don’t just change into different kinds of minerals on their own, except for Curie’s rocks, that is. What are these particles? The physicists themselves don’t seem to know: everyone I ask gives a different answer. They seem to be some shadowy energy-clouds, sometimes insubstantial and sometimes infinitely hard. What kind of world are we living in, anyway?
I felt a crumpled slip of paper in my pocket. Pulling it out, I read the well-worn handwriting under my breath, “Seek the Dragon Lady.” I scanned the crowd. I’d bet none of them knew the half of what’s going on, right under their noses! Well, not just their noses, but everywhere in fact. “Any of you folks know a Dragon Lady?”
“Are you looking for Madame Wu?” The young man startled me. From the high-necked sweater and the pipe in the corner of his mouth, I’d reckon he was a student.
“You know her?” I asked.
“Not personally, but I have a roommate who calls her that. It’s unkind, but she’s so tough on her students. Keeps them up all night, just so they can get a reading when some who’s-a-ma-whatsit stabilizes.”
“Figures.” I grunted. “Physicists.”
The man grinned in the corner of his mouth, like I was in on some secret. “Something happens to their brains when they go over to physics, you know.” He took the pipe out to gesture, then checked to make sure no one was listening. “I have a friend whose thesis advisor took apart his experiment— the love and pain of years of his life, mind you— and even though all his work’s been ripped up, the fool boy’s been hopping around ecstatic,” he said in an excited whisper. “Telling everyone that the universe is lop-sided. Lop-sided! He falls prey to some silly, jury-rigged, week-end experiment, and he thinks they’ve learned something important about the universe!” He clenched down on the pipe again. “After all, we already know that the universe is absurd.”
“Where can I find this Lady Wu?” The card in my pocket said to seek her in Columbia, so I haunted the streets around Columbia University for weeks.
“Washington, I think. Hmm, yes, that’s right: she’s developed an unhealthy interest in refrigerators.”
Without wasting a moment, I booked a train for the District of Columbia.
Washington, D.C., December 27, 1956
A few thousand inquiries about refrigerators led me directly to the National Bureau of Standards and the coldest cryogenics laboratory on Earth. Madame Wu was a visiting scientist, borrowing the cold to chase down an idea about radiation. She was hard to talk to, rushing about and short on time. “It worked last month,” explained one of her colleagues, “but the result couldn’t be reproduced. The radiation counter was loose… This is too important for shoddy work: too remarkable.”
“What’s the experiment about?”
“Symmetry of the universe!” his eyes opened wide.
“The universe? In there?” They lowered a tiny flask into a hissing cryostat, bellowing cold smoke. There was a click, a clamping into place, more smoke, and then counting machines clattered down to zero. A few seconds passed. One… Two… Three, four… The little numbers flapped down intermittently, counting like an erratic clock.
That seemed to be the moment Madame Wu was waiting for, though she didn’t look relieved. “And now we wait. Thank you, gentlemen.” She was a Chinese immigrant, though she had been in the States for some time. I’m told she was skipping out on an anniversary cruise to do this experiment. Her husband had to go alone.
I coughed to get her attention.
“Yes, that’s right; you want to talk to me.”
“Madame, I just wanted to ask a few questions. About the universe.”
“Are you a reporter?” She seemed sharp, almost scolding.
“What if I were?”
“We know nothing for certain yet— experiment is not conclusive. We need to do more tests.”
“Could you at least tell me what you’re doing?”
She seemed defensive, as though there was some struggle between competitive secrecy and some implicit oath to disseminate all truths. “Yes, of course. Come to my office.”
She didn’t have an office, exactly. The corner of the lab where her desk was looked much like the rest: all plumbing and machine-shop tools. It was only when she sat down that the dignity she projected made it seem like an office. She gestured at a chair and waited. I sat down.
Opening a bottom drawer, she pulled out a large, circular mirror, and set it on edge on the desk. “What do you see?” she asked.
I laughed a little, wondering what this was all about, but she didn’t waver. I stared deep into the mirror. Nothing was coming to me. My mind wandered: the orb in her long-nailed talons could have been the glistening sun— the Dragon poses riddles! “Um, myself?” I stammered.
“You see yourself, and everything in room. But backwards.”
“That’s right.” Oh, that’s all.
“Is there anything unusual about it?” she asked again.
Stupefied, I shook my head.
“If you look at the world through the mirror, would you even know it? Would there be any clues?”
I was good at clues. “I suppose there’d be a lot more southpaws.”
“More left-handed people, yes. And writing would be all backward, of course. Those are human conventions. If there were no humans, or if historical accident had been just a little different, we would all write backwards in real life. We would drive on left side of road.”
“Except in England.”
“Whatever,” she waved her hand. “But the universe: like matter and energy— space-time— if all that were flipped like in a mirror, would anyone ever notice?”
“Like atoms, and radioactivity?”
She slowly set the mirror down— apparently that word meant a lot to her. “Especially radioactivity.”
“No, I don’t suppose we would notice one way or the other. An atom’s round… isn’t it?”
“Not all particles are symmetric. Like pions: there are left-handed pions and right-handed pions. When you have two pions, you can make symmetric state.”
“You’re losing me.”
She held up her two hands. “Left hand,” she clapped with her left hand only, “right hand”, she clapped with her right. “This,” she held her hands together, “is symmetric state. Left-and-right hands clasped together is the same as right-and-left hands together. Reverse both of them and you have the same thing. A symmetric, two-hand particle can decay into a left-handed pion and a right-handed pion, and that looks the same in mirror, but three pions must come from a not-symmetric particle, like two lefts and a right or two rights and a left.”
“So what if a same particle sometimes decays to two pions, and sometimes three?” I could detect a glint in her eye, like she was setting a trap.
“I… I don’t know what that would mean. Maybe a symmetric particle sometimes gets asymmetric?”
“How does it know which asymmetry to choose? Right hand? Left hand? Who’s to say which way it should go?” Now I was sure it was a trap.
“Suppose the universe is not symmetric at all?” She folded her hands. “Suppose radiation favors left side over right side?”
I thought about that for a moment. “You’re saying that radiation is not symmetric, that it looks different in the mirror. What’s that got to do with the universe?”
“Radioactivity is a fundamental law of nature. The weak force is one of four basic laws of the universe. Everything comes from those laws. If radiation is left-handed, the universe is.”
I snuck a glance at the smoking caldron in the middle of the room.
“That’s what we’re testing. Symmetry.” She raised her eyebrows. What is it with physicists and dramatic gestures?
“How exactly are you testing it?”
“Beta decay is the most usual example of weak decay: many elements radiate by weak decay.” She stood and led me to the experiment. “If the mirror symmetry is violated by beta decay, then all weak-force interactions are. In here,” she pointed with a pencil, “we have tiny sample of cobalt-60 and radioactive counter on the bottom.”
“That’s the number here, right?” It was up to 86. 87.
“Yes. Cobalt-60 spins like a top. Like this:” she held out her hand and slowly closed it. “It is spinning the way my fingers curl. Around like that. It has a north pole and a south pole, like the spinning Earth. Now look in mirror.” She held up the circular mirror next to her hand and curled her fingers again. “North pole and south pole are reversed.”
“How do you figure?”
“Look closely: when fingers curl this way on my right hand, in mirror they go the other way.”
“The hand in the mirror is a left hand.”
“We define north pole as the way a right-handed thumb points when curling fingers: do what my mirror-hand is doing with your right hand.”
“I’ll be gum! My thumb is pointing the other way!”
“That’s right: poles are reversed in mirrors. Now suppose that my hand is cobalt-60 and radiates electron upward.”
“In the same direction as your thumb?”
“Yes, thumbward. Now look in mirror.”
“In the mirror, it still comes out the top.”
“But in the mirror, the top is the south pole.”
“I suppose it is.”
“What time is it?” She asked, popping open a watch. “The counter stopped. Did you get the reading?” she was asking one of the Bureau scientists as she pushed the mirror into my hands. The counter read 116. He waved a black lab notebook and reset the counter: the numbers all flapped back down to zero. He pulled a large electrical switch— the kind you see in the pictures— and a humming sound noticeably faded away. “Wait for it,” she cautioned, listening intently. “We have to reverse polarity slowly. Okay, turn it on now. Slowly!” He dialed a knob down to zero, closed the switch in the opposite direction, and turned up the dial— slowly. The humming resumed. When the little needles in a bank of meters stabilized, he clicked on the counter. One… Two…
There was still more work to do, making sure everything was running smoothly, before she had time to talk to me again. I hunkered back, trying not to get in anyone’s way. When she seemed to be just coasting, I reminded her of my presence. “So you were saying… in the mirror-world, an electron jumping off the north pole is really jumping off the south pole?”
“What were we talking about? Oh, yes: that. If the universe is mirror-symmetric, how often do electrons jump off north pole, and how often south pole?”
“I don’t know: I’m not an expert.”
“What if all electrons jumped off of north pole?”
“Then they’d be jumping off the south pole in the mirror-world.”
“That would not be symmetric, would it?”
“I suppose not.”
“If the universe is symmetric, there must be equal north-pole electrons as south pole electrons. You can’t have more, or symmetry would be violate.”
“So you’re counting,” I ventured to guess, “the number of north-pole electrons and the number of south-pole electrons. How do you do that?”
She smiled cleverly. “Inside,” she pointed with a pencil, “we have cobalt-60, and radiation counter on only one side.”
“You told me that.”
“All inside of strong magnetic field. The field forces the cobalt-60 nuclei to line up and spin in same direction. Before, we had all north poles down; now we have all north poles up.”
“And the big refrigerator?”
“All of that is inside very cold cryostat, cooling cobalt-60 to 0.003 degrees above absolute zero temperature. When the temperature is zero, the nuclei don’t jiggle as much, and they stay where the magnetic field puts them.”
“So that just makes the experiment cleaner?”
“It is very important,” she cautioned me gravely. “This is the universe we are talking about.”
“Madame—” one of her colleagues pointed to the counter. Time was nearly up, and it read only 15. The mirror slipped from my hand and cracked on the floor. Grave faces all around.
“Wow,” I whispered, sagely.
“No story!” she pointed an accusing finger at me. “We do it again, longer this time. And then positrons: cobalt-58! Promise me no story until we do it again!”
“I’ve got a confession to make, Ma’am. I’m not a reporter. I’m a private eye.”
“It’s not conclusive yet. We still have cross-checks to make. No story— promise!”
I held my hands up defensively and backed out of the lab. “I promise,” I said as I opened the door. “You won’t hear a peep out of me.”
She turned to her coworkers. “Take it apart. We do it again.”
I must have wandered aimlessly for the next few years. In this suddenly off-kilter universe, I felt as though half the ground had been pulled out from under me. It wasn’t long before I connected it to the other mysterious note: “The killer is left-handed.” The universe is left-handed. Ergo, the universe is the killer: I wanted a simple answer, but this was hardly less unsettling. What was the universe up to, anyway, throwing around a bunch of left-leaning particles that sometimes kill scientists?
I meandered into New Mexico, mostly hitch-hiking. I guess my beard grew out; I saw myself one day in a reflection and it surprised me. Avoiding Los Alamos (they seemed a little tougher there these days), I hooked up with a band of vagabonds, who put up with my sputtering nonsense about parity violation. Under the stars one night, my fellow-traveller said, “You know, it’s all expanding.”
“What’s that?” I asked.
“The universe! Stars, galaxies, everything. Expansion without a center. Or the center is everywhere. Right here is the center of the universe.”
Another of our tribe intoned, “woah.”
“And nobody knows why.”
That was enough for me. “Damnit!” I stood up. “Why’d you have to tell me that?” I left them that night.
Wandering westward, I became a scourge on the fair city of Pasadena, California. Sleeping behind a dumpster one day, a magazine in my blanket caught my eye: “The New Einsteins,” it read. Einstein was a physicist, but I hadn’t thought of talking to him while he was still alive. The article had at least as much to do with the physicists’ personal quirks as their science: who would write such trash? Still, it mentioned Madame Wu’s discovery that the parity symmetry is violated, and somehow it had something to do with Sputnik. But it didn’t stop there— apparently, parity violation was no longer a mystery! It was explained by so-called V-minus-A interactions, something alluded to as horribly complicated, with photographs of well-dressed gentlemen arguing in front of scribbled-over blackboards. “The dapper, cocky Maurry Gell-Mann,” it said, “is many physicists’ choice for the brightest light in his esoteric field. With a Madison Avenue fastidiousness about his clothes, his boyish face and quick tongue, Gell-Mann exhibits a kind of sharp intellectual fussiness that has more than once wounded his colleagues.” Amazingly enough, he also lived in Pasadena, so I resolved to find him and ask him about this V-minus-A.
Strolling onto the Caltech campus, I got a lot of nervous glances. I guess they weren’t used to ragged men such as myself at institutions of higher learning. In the physics building, I found Gell-Mann’s office and pounded on the door until I heard a voice inside: “Come in, come in.” I burst into the room, but couldn’t think of what to say. He gazed at me in horror. “What are particles, anyway?” I asked in a raspy voice. “Are they really shaped like little hands? And why is the universe so lop-sided?”
He pondered in amazement for a moment, then said, “I think you want Mr. Feynman. He’s the expert in these fields.”
“Feynman?” The name was awfully familiar. Wasn’t I supposed to be trailing him?
“He’s the one whose van is covered in Stueckelberg diagrams,” he explained with some contempt. “Go ask him. Shoo-shoo,” he waved me away with his wrist.
Feynman, of course! He’s the guy Fermi told me to follow. He’s the guy who made so much sense teaching introductory physics. And he’s also the one who revolutionized the quantum theory with his little diagrams— if anybody can explain what this is all about, it’s him! And he lives in Pasadena, too!
In the parking lot, I found his van: white with squiggily diagrams drawn all over it. I got into the passenger side seat and waited. I waited long enough to have fallen asleep, but woke up when Dr. Feynman got into the driver’s side. I don’t think he noticed me. Clogged up with sleep, my voice croaked when I asked, “So, what are particles?”
“Woah!” Dr. Feynman jumped out of the van faster than I thought possible. “Woah! Woah!” He was still jerking and jumping about outside.
“If a pion emits a muon when it decays,” I continued, “does that mean that the muon was inside the pion?”
He was speechless for a moment. Then he said, “I’m having that dream again.”
“You’re— just a dream, right?”
I pondered that for a moment. Given the circumstances, I wasn’t sure. “Are particles even real?”
“Well, sure— well, it depends on what you mean by real. Uh, no, not really.” He thought for a moment, then came to some kind of a decision. “Look, this is gonna take a while. How ’bout I buy you a drink?”
We went to a strip bar, where the waitress apparently knew him. “The usual, Dick?” She was bright and cheery to Dr. Feynman, but scowled at me. The usual was apparently a soda-pop.
“Drank too much in a bar in Buffalo,” he explained, “and ended up with a lulu of a black eye. Never gonna do that again.”
“And there’s something special about left-versus-right, isn’t there? What is V-minus-A?”
“Jeez, you’re fulla questions, aren’t you? Look, I think I know how to explain this. Just forget about particles: there’s too much mental baggage hanging on that word.”
“We sometimes say that electrons and whatever are particles, and sometimes that they’re waves, but there’s something wrong with both these words because we already think we know what ‘particles’ and ‘waves’ are. Particles are like little pebbles and waves are like on the ocean, right? Well, if you start thinking like that, you’ll be wrong right away because they’re not either. Electrons, pions, muon: they’re all something entirely different, something new.”
I started to dispair of understanding it at all. “But I like to think in analogies.”
“Analogies are good, yes, but you need to know where the analogies apply, and where they don’t. You can’t say what electrons are in a one-word analogy. It’s gonna take, well, more words.”
I let him go on.
“Let’s start by thinking about a field. A field’s a good word, because you don’t really know what it is from common experience. I mean a field like a magnetic field, not like a field of grass. What do you think of when I talk about a magnetic field? What do you visualize?”
“I think of a kind of invisible glowing: it makes any metal nearby want to fly toward the magnet.”
“Yeah, basically. At every point in space, there’s a number, and that number just says how strong the magnetic forces would be on any metal object that might be there. Near a magnet, the numbers are big, and far away from any magnets, they’re small or zero. It’s three numbers, really, representing a little arrow at every point in space, pointing in different directions with different lengths, swaying this way and that when we move magnets around.”
“Now it is beginning to sound like a grassy field.”
“Yeah,” he seemed amused. “That could be why they called a field in the first place. An analogy, but the arrows are at every infinitesimal point in space, and they’re all invisible. Grass doesn’t do that.”
“So what does this have to do with particles?” I asked, impatiently.
“There you go with the particles again! Forget about particles!” He took a delicate sip of his soda-pop and continued. “So we’re happy with magnetic fields, and then you know there are also electric fields: Maxwell back in the 1800′s figured out how they relate to one another. Magnetic fields and electric fields are actually both just parts of a single electromagnetic field. So there’s just this electromagnetic field, lots of numbers at every point in space, and different components of it were historically named ‘electric’ and ‘magnetic.’ He also found the equation that describes how those numbers relate to their neighbors: if the field has a big value here and a small value right next to it, the small value is gonna want to get bigger and the big value wants to get smaller. Wait a moment in time and they change. Wait a moment longer and they change more. On and on until they equalize, and then even further because the equation says that they tend to overshoot.”
“I’m having trouble visualizing this.”
“Don’t worry— the short story is that large values in the field tend to propagate, so that if I jiggle a magnet or something, I can start these waves undulating in the field; they spread out all over the place and bounce off of mirrors and such.”
“Like water waves,” I added. “Drop a rock in a lake and the waves spread out everywhere.”
“Yeah, the analogy works so far. The difference is that we know what the field is for water waves and we know why its equation works: the field for water waves is the height of the water everywhere on the surface of the lake, one number at every point. When the water is higher at one point than at a neighboring point, it wants to flow downwards, increasing the low field value and decreasing the high field value. Then it overshoots because of inertia: it’s all just gravity and Newton’s laws. But the electromagnetic field is not water, it’s something else. We don’t know what the numbers at each point in space mean or why they have this equation relating them.”
“Ether?” This was sounding familiar, from somewhere.
“Ether was a popular theory, again in the 1800′s, but it was really just a problem of them taking the analogy too far. Ether was this idea that there was a material, uniformly filling all space, but invisible and so evanescent that we don’t notice that we’re walking through it all the time. In fact, planets don’t even slow down when passing through it for millions of years.”
“Are you saying that’s impossible?”
“No, no, anything’s possible, especially when we’re dealing with the unknown. But the problem with the ether theory is that they assumed too much: they thought this ether was made of some kind of weird atoms or something, something with a velocity like you and me, you know? The whole space-filling ether would be a kind of object with a definite position, and we should be able to tell if we’re moving relative to it or not. The electromagnetic wave equations don’t suggest anything like that, they’re just waves in the equation, abstract numbers without any hint of a stationary medium; the ninteenth century physicists just assumed it because of the analogy with water. In fact, a famous experiment showed that the speed of this so-called ether always seems to be zero relative to us, even when we go through it at different speeds, in different directions. An equation can do that, but matter can’t. What made Albert Einstein famous was just looking at the equations and asking what they imply, without ever assuming that they must be waves in some material.”
“So there’s nothing but equations? Nothing’s real?” I felt a “woah” coming on.
“Of course they’re real! When you get to thinking about this stuff, you have to decide what you’re going to count as real. We started out by looking at matter, undeniably real stuff, and asked, ‘what is this stuff, really?’ We find that it behaves differently than we might have thought at first. We find that our traditional descriptions break down, and we have to step back and let Nature tell us what it’s all about. And then we try to describe it in the only precise language we know, a language without preconceptions. That’s mathematics.”
“So let me get the picture, then: the universe is a space-filling field of numbers that obey an equation?”
“In a nutshell.”
“What about electrons and pions and muons and all that? Whenever I talk to physicists, they usually talk about these particles bouncing off of each other and breaking apart.”
“Each of these particles, electrons, muons, and the like, each one of them is a separate field. Or they’re different components of the same field, which is the same thing, just more numbers at each point. Ya know, when we talk about The Electron, we don’t make a distinction between a single electron particle and the whole lot of them. It’s as if we would talk about all the geese in the world by saying, The Goose. And that’s actually the right way to think about it. There’s just one electron field, and it has different intensity values in different places. You’ve heard of photons, right?”
“Photons, they’re bits of light, right?”
“Photons are light— and radio waves, and gamma rays, microwaves, infrared, ultraviolet, X-rays, the whole spectrum. But ‘photons’ are just a modern way of talking about the electromagnetic field that Maxwell discovered. Maxwell discovered that combining the equations for electricity and magnetism, you get waves that propagate all over the place, with any imaginable wavelength. And then it was slowly discovered that all of these different kinds of waves, light included, were really just waves in the electromagnetic field with vastly different wavelengths.”
“But I’ve heard that photons are particles.”
“If you say ‘particle’ one more time, I’m gonna knock your lights out! The whole particle business comes from quantum theory. For some reason— and this gets even more mysterious— energy comes in clumps, ‘quanta,’ a certain fixed quantity, such that you can only have zero, one, or two of them, and so on. For any given wavelength of electromagnetic wave, the intensity of that wave is restricted: it can be enough to give you one quantum of energy, zero, or two, et cetera. Einstein also showed how mass and energy are equivalent, so unsplittable units of energy are unsplittable units of mass, which made people think they were dealing with some kind of indivisible particles.”
“So they were wrong: there are no particles, it just looks like there are.”
From the strained expression on his face, I don’t think he liked that conclusion. “We’re defining words as we discover this stuff, so you could just say that this is what ‘particles’ really are: quantized excitations of fields. A lotta my friends define the word that way just so that they’d be retroactively right. Which is fine, of course.”
I thought for a long drag, trying to take it all in. “That doesn’t explain decays. How does a muon come out of a pion? I mean, they’re both excitations, sure, but how does one excitation come out of another?”
“Sit tight: I haven’t given you the whole story, yet.” He thought for a moment. “I said that the field obeys an equation; the equation tells it how to propagate. Maxwell’s equations for electromagnetism are only the simplest example. You can re-write the equations in a form called the Lagrange Equation, which makes explicit how energy wants to flow from one point in space to another, and from one field to another. The Lagrangian is an expression that Nature wants to minimize, so you can think of it almost like economics: it’s a cost function. In classical physics, Nature exactly minimizes it— a strict book-keeper— but in the quantum theory, Nature allows a little loss here and there if it will get a bigger return on its investment later.”
“Should I be taking this analogy literally?”
“No. The form of the Lagrangian is a series of terms added together, and each one has a physical meaning. The electromagnetic Lagrangian, the one that comes strictly from Maxwell’s equations, has only one term: changes in field values multiplied by changes in field values.” He wrote something down on a napkin, something with lots of subscripts and superscripts. “By ‘changes,’ I mean derivatives in calculus, a calculation of how much the field values vary from one place to the next and how much the field values vary from one time-step to the next. By multiplying them together and minimizing that, the way economists do with cost functions, you get waves. Another way to look at this term is as a kind of connector: it connects field values at one point in space and time with field values at the next point over; hence, energy flows from place to place.
“When we look at a different kind of field, like an electron field, we need to add another term to the Lagrangian. Electrons propagate all over the place, just like photons, so that first term is similar, but unlike photons, electrons also have mass. This allows them to do a curious thing: sit still. As a consequence of the wave equation, photons have no choice but to zip around at the speed of light. Photon energy can’t sit still unless you put it between two mirrors or something. For photons, energy absolutely must flow from place to place, because only neighboring points are connected by a term in the Lagrangian, but electron energy can sit still, or move at any speed less than the speed of light. The second term in the electron’s Lagrangian is just the field multiplied by itself, effectively connecting the field value at one point with the field value at that same point. Therefore, energy doesn’t need to flow from one point to the next, it can flow from the point to the same point again, going nowhere.”
“That’s another reason that electrons look like particles.”
“If you like your particles to be stationary, then this is a good feature for you. Thinking of this term as a cost function, what do you suppose it looks like?”
Reading his napkin closely, I said, “it looks like two tridents next to each other, like Neptune had twins.”
“What? Naw, I don’t mean the letter.” He scribbled out what he had been writing, probably only writing by instinct. “The letter psi is just how I’m representing the numerical value of the field as an unknown in the equation. I mean what does the graph look like, the graph of psi times psi, or if you like, x times x— x squared?”
“I wasn’t expecting an algebra exam!”
“Why shouldn’t you be? We’ve been talking about numbers and equations— didn’t you think that math would come in at some level? I can tell you how the equations generally go, but to learn this in any detail, you’ve gotta do some math. Besides, this is easy— high school stuff.”
I thought really hard, remembering only Sister Drummy’s hard-edged ruler. Then it came to me in a flash: I drew a large cross for the x and y axis, then x squared was a U-shaped cup whose lowest point passed through the x-y intersection. “It looks like a trident!” I exclaimed, with some glee.
“Well, I’ll be durned,” he chuckled, “it does look like a trident, after all. Okay, where were we? Oh yeah: this U-shaped cup, that’s the value of x squared for each value of x. When x is 1, x squared is 1, when x is 2, x squared is 4, when x is minus-2, x squared is 4 again, et cetera. This ‘x,’ or my ‘psi,’ is the value of the field at some point in space, like here.” He picked a point in space from the air in front of him, somewhere over his soda-pop. “If the field is fluctuating around small values like 1 or minus-2, this term in the Lagrangian is small but always positive. If the field is fluctuating around large values like a thousand, the term in the Lagrangian is large, like a million.”
“Does that mean it has more energy?”
“EXACTLY!” He seemed very happy that I got something right. “The Lagrangian describes energy flow: thinking economically, this mass term is like a bank. You can deposit energy into a point in space and it stays there: a phenomenon we’ve traditionally called mass. And since you can only do it in fixed amounts, one dollar increments, let’s say, you can only create an integer number of particles. Then you can just as easily take the energy out of the particles and use it to make motion if you want.”
“This is why particles decay, isn’t it?”
“YES!” He was still very excited. “And it’s how you can make them in collisions, too. It’s just another term in the Lagrangian; there’s nothing more mysterious about making and destroying particles than there is in things moving from place to place. Heck, ‘moving’ is essentially the same thing as destroying a particle in one place and making another one right next to where the first used to be. Take the energy out of one point in space and put it in the next— like switching banks. And that gets to your question about pion decay: when a pion decays into a muon and a neutrino, energy comes out of the pion field, part of it goes into the muon field, and part of it goes into the neutrino field. There’s a bit left over because the mass of one pion is more than the mass of the muon and the neutrino, so that’s put into the motion of the two final particles, er, waves.”
“How does the pion know it should decay into a muon and neutrino?”
“Oh, I forgot to tell you: there’s another term in the Lagrangian, expressing the connection between the different types of fields. The Lagrangian is a wonderful little package: it explains the existence of wave motion, stationary mass, and transitions between all the types of particles in one stroke. They’re all just connections between field values, a subway map saying where energy can flow to. You can write Lagrangians down to describe all sorts of situations. You know, I was listening to a concert cellist the other day, thinking about the way that sonorous old cello reverberated around the room, and I came up with this cartoon Lagrangian,
L = bow*string + string*string + string*cello + 100 cello*cello + cello*air + d(air)*d(air) + air*ear
She pulled the bow across the string, transferring energy to the string, the string reverberated with itself like a little particle, then the string shook the cello body and the cello body reverberated with itself a lot, a really heavy, massive particle— that’s why there’s a factor of 100 there— and then that flowed into the air and propagated through the air as waves. That’s why it’s got the derivatives term. Then that is connected to my ears and I heard it. Like some kind of complicated decay chain, a Xi particle to a Lambda to a pion to a muon to an electron.”
“Didn’t the music reverberate in your head?”
“Oh yeah, let’s add that! + ear*head + 10 head*head. It didn’t reverberate as loudly in my head as it did in the cello, but it had a longer lifetime before it decayed. Look, we can also draw it like this.” He drew a chain of lines, each labeled “bow,” “string,” “cello” (with a loop), “air” (as a wavy line), “ear,” “head,” loop. “This diagram encapsulates some of the information in the equation, which can be really helpful when things get complicated. Like the cascading decay from the Xi to electron. That’s a big, hairy tree of a diagram: Xi to Lambda pion, pion to muon neutrino, muon to electron neutrino, Lambda to proton pion, pion to muon neutrino, and finally, muon to electron neutrino. All told, 13 particles! All just coming from one Xi: it has quite a lot of mass energy to divvy up. Each one of these points, where the energy flows from one field into two others, is related to a term in the Lagrangian. There’s a prescription for turning diagrams into equations, and now these funny little pictures are all over the literature.”
It looked like the drawings on his van. “Are these Stueckelberg diagrams?”
“These,” he roused in contempt, “are Feynman diagrams! Hey! Have you been talking to Maurry?”
“Gell-Mann? He sent me to you.”
“That rat! Oh, no offense— it’s been a pleasure talking with you. When I see him tomorrow, though, I’m gonna pop him!” He doodled for a while.
“So what about forces?” I asked. “If everything is a field with a Lagrangian Equation, how come there are forces? Don’t these waves just flow through each other, being different fields?”
“Forces are the same thing,” he seemed a little surprised, “interactions in the Lagrangian. Energy of motion flowing from one particle to another. Here, look, I’ll give you an example.” He started drawing again: two kinked lines with a wavey line connecting them. “These are two electrons, and the wavey line is a photon. The line represents the trail that the particle follows in space and time, occupying one point in space which changes as a function of time.”
“I thought that electrons are waves of energy, kinda spread out.”
“Yeah, yeah, you got me there,” he bobbed his head, chuckling, “but that would be hard to draw. The idea behind these diagrams is that they just describe the connections and approximate the space-time description by showing one possible path. When we convert this into equations to try to calculate something, we have to add together all the possible paths that this represents.”
He waited for me to assent. “Okay, fine. Go on.”
“Okay! So remember that photons don’t have a mass term. There’s no minimum balance in the photon account. You can make photons with as little energy as you want. Well, this little photon wave propagates from this electron here to that electron there, taking not just energy but momentum: that’s why the top electron pulls away, to balance the momentum given to the photon. And then when the photon wave gets to this other electron, it gets absorbed, and pushes the other electron away. Thus, two electrons repel each other when they get close. Neat, huh?”
“That’s why all electrons repel each other?”
“That’s why any charged particles attract or repel. They transform part of their momentum-energy into an intermediary, which then gives it to another particle nearby.”
“What if you replace the photon with a pion? The pion’s the nuclear photon, I’ve heard.”
“For a bum off the street, you know a lot about some things! Yes, we could put a pion in there in place of the photon, but then the electrons wouldn’t notice, because electrons don’t connect to pions. There’s no such term in the Lagrangian. But also replace the electrons with, say, protons, or neutrons, and then the pion is very happy to connect them with a force. That’s the nuclear force, holding the nucleus together!”
“The Lagrangian describes everything, doesn’t it?”
“You’re tellin’ me! We’ve got motion, mass, particle decays— which is radiation— and now forces, all in one neat package. All that’s left is to find out what exactly is in the universe’s Lagrangian, the weltformel, or ‘world-formula,’ as Heisenberg liked to call it.”
I blinked. “Wow. And I thought physics was a mess. All these perplexing, contradictory discoveries, the lop-sided universe…”
“These are the best of times!” He seemed stunned. “Perplexing discoveries are a physicist’s dream come true! It’s like being lost in a candy shop: all these mysteries to unravel. Did you ever experience the joy of figuring something out?”
“I’m a private detective…”
“It’s wonderful! Absolute pleasure. So much fun when you’ve got it that you’ll willingly spend months or years struggling with another problem to get it again. Did I ever tell you about the time I figured out V-minus-A?”
“You know, I’d love to know.”
“I had this idea in Brazil, when I was coming home from vacation. I was thinking about these parity violation experiments, the ones that were showing that the universe is mirror-unsymmetric.”
“Like Madame Wu’s experiment?”
“Madame Wu’s was the best, but there were others. Leon Lederman— now there’s a character— he took apart his poor student’s thesis project to get a quick result and scooped her. But I think we wouldn’t have totally believed it without Wu’s result. There were a few others, and some of them contradicted each other in the exact way that the symmetry is violated. You could put some terms into the Lagrangian to explain some of the experiments, but not other experiments.”
“Sounds like a mess to me.”
“A mess, sure, but exciting! So I tried this one particular combination: a vector current minus an axial one— that’s the ‘V’ minus the ‘A,’ they’re mathematical forms which have the properties of arrows, that’s the vector, and rotational poles, like the north pole and the south pole. That’s the axial form.”
I could see he wasn’t sure if that was a good explanation. I held out my hand and curled my fingers to show that I was at least partially on board. It seemed to be a universal physicist’s gesture, like a secret hand-shake.
“Yeah, that’s right. One flips direction when you look at it in the mirror and the other doesn’t. If you subtract the two, you get only the flipping. On a lark, I tried assuming that was the right form and just seeing what happened, if you push it all the way through the equations. And wouldn’t you know it— I got the right answer, nearly, for all of the experiments! All except one, and that one turned out to be wrong. It was… sparkling!”
“Yeah, sparkling! As I thought about it that night, as I beheld it in my mind’s eye, the goddamn thing just shone brilliantly! You know, it was the first time, and probably the only time in my scientific career, that I knew a fundamental law of nature that no one else knew. Now, it wasn’t as beautiful as Maxwell’s, but it was a bit like that. It was the first time that I discovered a new theory, rather than just a more efficient method of calculating someone else’s theory, or a little solution to a problem. It was the most amazing night of my life.”
“Until you got to work the next morning,” said a woman with a Yorkshire accent, “and found out that Maurry had thought of it first.” Who was she? We weren’t in the bar anymore, but in Feynman’s backyard in Altadena, under the stars. When did we relocate?
“Now Gwen,” (that must have been his wife,) “Maurry han’t entirely worked it out.”
“And he got it from that poor student you scooped.” She was having fun with this, apparently not for the first time.
“I couldn’t possibly have known about that. I was in Brazil at the time!”
“Still, you weren’t the only one in the world knowing it. Including the student’s advisor, I’d count four.”
“Okay, so I knew something only four people in the universe knew about. Still, it was beautiful!”
She smiled. “I’ve heard all this before,” she said as she got up. “I’m off to bed. You two have fun.”
“Good night, Gwen.”
“Good night,” I added, still a little shaken by the change in locale. How did I not notice driving here?
“Listen—” he turned to me, conspiratorially. “I want you to help me play a trick on my old pal Maurry. It’s only fair, after all.”
“Okay,” I said, hesitantly.
“Tomorrow we’ll be working in his office on some Buddhist thing of his. I want you to barge in, claiming to be Chairman Mao’s secret police, come to put a stop to all this illegal religion.”
“He’s got a theory, but for fun he’s phrasing it all in Buddhist terms. I think it’s time someone zings him for that, clouding up the literature with weird words.”
“So you want me to barge in… again?”
“‘Strangeness!’ Can you believe it? He got everybody saying things like ‘strangeness.’ What’ll be next, ‘quirkiness?’”
“Sure! Why not?” I said. “Do you think I could pass for Chinese?”
“Listen, I’ll drop you off at your place. Where is that?”
“Oh.” And then I proceeded to explain where I lived.
Pasadena, January, 1961
I had forgotten the simple luxury of taking a bath in a hotel. To make the most of the experience, I shaved and cut my hair, too. What a mess! The whole sink was full of hair, and much of the floor, too. While I was cleaning it up, getting on my hands and knees to sweep it up in my fingers, you wouldn’t believe what I found. Stuck in there, behind the fixture, another note! My fingers trembled as I shook it out, and read,
“You struggle in vain to make out what you see,
But I run in your loops, and you don’t know me.
– signed, 0++“
“Zero-Plus-Plus? What in Hades… Feynman! All this time, it was him! All those notes, stringing me along, and I thought I was following him. That fink!”
In a moment, I was dressed and out the door. I returned to the sunny campus a changed man, literally, as I was now dressed in the grey trenchcoat and fedora that let me blend into a crowd. I burst into Dr. Gell-Mann’s door, and pointed an accusing finger at Feynman, sitting smug while Gell-Mann caressed the blackboard with Kabbalistic diagrams. He was already laughing.
“You!” I shouted.
“Me?” he seemed a little surprised, the cunning fox.
“You! You thought you were so clever, but I’m on to your ruse.”
“Me?” he asked again, still laughing, probably more now than ever, “Don’t you mean him?” Gell-Mann was equally surprised.
“You’ve been sending me all these notes!” I held out the latest one.
Until this point, Gell-Mann’s mouth had been hanging open like a trout. He composed himself and asked, “Do you two need privacy?”
“No,” we both said, at the same time.
Feynman, through fits and chortles, managed to get out, “Weren’t you supposed to be Chinese?”
“Let me see this,” Gell-Man took the note from my hand. “‘I run in your loops?’ What kind of love-letter is it, hmm?”
“It’s not a love-letter— it’s a red herring!” I exclaimed, “He’s been steering me off the path all this time!”
“I should say that’s not unlikely.” He pushed up his thick-framed glasses with his middle finger. “‘Signed Zero-Plus-Plus,’ well, that is interesting.”
“Lemme see it,” said Feynman, grabbing for the note. Gell-Mann didn’t let him have it.
“‘You struggle in vain to make out what you see,’ he read, and actually started writing it on the chalkboard, amid all of his mathematics. ‘But I run in your loops, and you don’t know me.’Repeated stress on the last three syllables: how appropriate.”
“But I do know him— now,” I explained.
“‘Signed, Zero-Plus-Plus.’ You suppose that Dick is the mysterious Zero-Plus-Plus, do you?”
“Lemme see that,” Feynman grabbed for it again, this time successfully. “I didn’t write this.”
“Oh, come now— who else could have?” I said triumphantly. “Ithaca, Rio de Janerio, Ithaca again, and now my hotel room in Pasadena. Who else would have known my hotel room?”
“That does sound like Dick,” Gell-Mann wrote the cities in a column on the board.
“I didn’t write this,” he protested, but not too hard.
“No, this isn’t even my handwriting.”
“Who else could it have been?” I demanded. “And who’s Zero-Plus-Plus?”
“That’s the question,” Gell-Mann continued, “the heart of the riddle. Do you suppose it might be the JPC?”
“Does that stand for something I don’t know about?” I asked.
“JPC, like quantum numbers?”
“It would be a scalar,” he continued, “invariant under parity and charge conjugation…”
“Are you saying that a particle wrote the note?” Feynman was obviously following this.
“Could you two please explain what you’re talking about?”
“Sure,” Feynman turned to me and said, “each type of particle, each field like we were talking about last night, has certain properties that can be neatly written up in in a few numbers, its so-called quantum numbers, and we call that a signature.”
“Purely a book-keeping device,” Gell-Mann chimed in.
“So this ‘signed’ business followed by ’0++‘ looks suspiciously like a particle’s signature. ‘J’ is the internal angular momentum, a scalar without any spin at all, just a single number at each point in space.”
“The minimum possible structure.” Gell-Mann added. “Do we know of any 0++ particles?”
“The first plus is the parity, what the field does when you replace it with its mirror-image. Plus means nothing happens at all. Same thing for the second plus, that’s what the particle does when you reverse the charge, replacing all particles by anti-particles. This 0++ is unaffected. In a sense, it is its own anti-particle.”
“I don’t think there are any 0++ particles,” Gell-Mann had written all the particles he could think of on the board, with their signatures. He was running out of room.
“Maybe we just haven’t thought of it yet,” Feynman answered. “After all, the note does say, ‘you don’t know me.’”
“Are you two saying that a particle wrote these notes?” I asked, finally catching on.
“Stranger things have happened,” Gell-Mann answered dryly.
“Could it be a bound state?” Feynman asked, now fully engaged in this puzzle.
“I don’t know everything there is to know about particles,” I chipped in, “but I’m fairly sure they don’t write letters.”
“What about that Omega-minus in your theory?” he offered.
Gell-Mann seemed a little indigant. “That’s three-halves-plus, you remember?”
“Oh, yeah, of course. Yeah, it’s a baryon, that’s right.”
“‘I run in your loops’ suggests a virtual particle,” Gell-Mann went on, “That was the first thing I noticed. What else runs in loops?”
“Dogs?” I offered.
“If it’s a virtual particle, it could be anything.” Feynman was scratching his head.
“What’s a virtual particle?”
Feynman graciously paused to explain again, “Do you remember those diagrams I drew last night?” He grabbed the chalk from Gell-Mann and drew a Feynman diagram with a circle in the middle of it.
“Shuddup, Maurry. These diagrams are schematic; they just describe connections. When you calculate something from them, you have to add up all the possible paths with the same topology. These lines on the outside, they’re external legs, corresponding to particles we measure in the laboratory. Their momentum is fixed. We measure it, so there’s only one possibility for what it can be. With me so far?”
“This particle in the middle, the loop, it has to transfer the right momentum to and from each of these legs, but its own momentum can be anything.”
“ANY-thing.” Gell-Mann stressed.
“It could be something close to zero, something on the same order as the external legs, or an enormous value. It could be thousands, millions, billions of times the momentum of the external legs, there’s no limit.”
“You have to integrate to infinity,” Gell-Mann added, nodding helpfully.
“The trouble is,” Feynman shook the chalk in the air while he talked, “the trouble is that there could be dragons up there.”
He let the import of that settle on the room, but I was perplexed. “Dragon particles?”
Gell-Mann rolled his eyes. “Metaphorical dragons.”
“New physics, things we haven’t discovered. We only know how the universe works at low energies, low energies and whatever we can cook up in colliders, which isn’t much.”
“Much less than infinity.”
“So if the universe has new laws, new interactions, well, new to us at least, it would have an effect on any diagrams involving a loop, and we wouldn’t know what it is.”
“Oh.” So any diagrams that have internal loops are essentially uncalculable. “How many physics processes involve diagrams with loops?” I asked.
Gell-Mann smirked. “All of them.”
“All of them? Then you’re telling me you can’t calculate anything?”
Feynman seemed a little defensive. “We can and we do.”
“But they’ve all got this uncertainty! You just told me that you can’t calculate that, that— dragon diagram, there.”
“It could have contributions from as-yet unknown particles,” he admitted.
“That seems to be what the couplet is plainly saying,” said Gell-Mann.
Feynman chuckled at my indignation. “God himself could be running in the loops.”
“I prefer to think it’s a yin-yang.”
“Right, Maurry, I forgot you were on your Buddhist kick.”
“Please, Dick, the yin-yang is Taoist. And I rather like the way we can’t know anything until we know everything, don’t you?”
I stamped my foot. “But that’s not science!”
Silence. I struck a chord.
“If we don’t proceed from the known to the unknown,” I lectured, “we can’t be confident in our conclusions. It’s all just guessing games.”
Gell-Mann smiled from ear to ear. “You’re quite right. Sorry, Dick, we don’t know what we’re doing.”
“Actually, I think his point needs a serious response—”
“I am serious. I mean what I say. Methodical discovery is impossible. It’s as impossible as learning to talk.”
Feynman gave up his offensive, sat down and crossed his legs. For my benefit, he said, “Keep in mind that this is the guy who know some— how many is it? Twenty languages or so.”
“It’s impossible,” he raised both eyebrows, “to learn even one.”
“I seem to have managed it,” I said.
“How do you learn new words?” Gell-Mann challenged me.
“I look them up in the dictionary, I reckon.”
“And what do you find in the dictionary?”
“Words! More words! How did you learn them?”
“People told me what they meant?”
“In words! Tell me, how far back does this chain of words go?”
“To my mother’s knee?”
“Where you learned simple words, ‘Mama, Dada,’ and the like, but did anyone ever tell you what they mean?”
“They were evident from context.”
“But that context had to be communicated somehow, didn’t it?”
“How did you learn what the gestures mean?”
“They were obvious. Look, I don’t know where you’re going with this.”
“‘Obvious’ doesn’t cut it, does it? Aren’t we scientists?”
“Is this an analogy?”
“Science is communicated in words— wouldn’t it be infected with the same uncertainty?”
“Well, there’s no way around that, is there?”
“How ’bout math?” Feynman chimed in.
Gell-Mann turned to him. “How did you learn math?”
“From books. But it’s not like I was just told that it works, and had to trust it. I fiddled around with it. After I read about something, I fiddled around to see how it works. Then I knew first-hand.”
“Are you two saying that’s what science is?” I asked.
“I think that’s where Maurry’s driving.”
“That’s EXACTLY where I’m driving. Look, as far as I’m concerned, learning to read Nature’s book is like learning any other language.”
“Except that it wasn’t written by people,” I protested.
“That’s irrelevant. Look, suppose you’re dropped in France and you know no French. You listen. If you listen for a while and you’re clever enough, patterns emerge. At least you think they’re patterns, so you try them out, you ‘fiddle around’ as Dick was saying. If you’re right, people understand what you’re saying and they sell you cheese. If you’re not, they shrug and you try again.”
“Sounds like the theory-experiment cycle to me,” said Feynman.
“It goes deeper than that. Look,” he erased a space on the blackboard, “what patterns do you hear when you’re learning, French, for instance? Conjugation, primarily. Je sais, tu sais, il sait, nous savons, vous savez, ils savent.” He drew them in a table on the board. “Singular on the left, plural on the right, first person, second person, third person. Every one of these must be filled, because any one of them might come up in conversation. Most verbs follow the same patterns.”
“There are irregular verbs.”
“Yes, Dick, and those are the interesting ones, aren’t they?” Feynman shrugged. “The pattern must be generated somehow. It just wouldn’t do to have ways of saying plural, ways of saying first person, second person, and third person, without, say, a plural third person, would it?”
“But you could,” I complained, “in principle.”
“Maybe. But probably not. And you start by assuming not. Only when some strange feature is forced upon you, like parity violation, do you assume the non-obvious. And so it is with science. What Dick and I were discussing before we were interrupted is the perfect example. Tell me what you think of this,” he pointed to his Kabbalistic diagram, “This is the Eightfold Way—”
“The Buddhist thing!” I interrupted.
“— indeed. It is nice how its eight group generators can be mapped onto Buddhist precepts, but given the variety of religions in the world, something could probably have been found for any small number. This diagram is generated by a simple but abstract mathematical object called a group, and the wonderful thing about this particular group is that its operations can be associated with particle properties, quantum numbers like strangeness, isospin, and the like— their meaning isn’t important, just the fact that they have labels that are semi-preserved— and each element, each spot on the diagram, can be associated with a known particle.”
“Yes, Dick, except one. But I think that’s the beauty of it, don’t you? That particle hasn’t been discovered yet, and by predicting its properties from this model, we’ll pose a little challenge to see if we were right. It would lend credibility to the model.”
“We would get the cheese.”
“Hopefully.” Then he turned to me. “But do you see how this is like guessing at a language? These properties, strangeness, parity, spin, these are properties like singular versus plural. Knowing about pluralness tells us to build a table and be on the look-out for words to fill the empty slots. Then when we realize there’s a past tense, we have to expand the table, and we have a lot more slots to fill. But it’s always provisional, because at heart it’s a guess.”
“The experiments, too, have their share of uncertainty.”
“There’s that, too.”
I gazed at the diagram; each corner was labeled with a Greek letter. “Are those all of the particles?”
“It’s most of them,” he said, proudly.
“You have to remember,” added Feynman, “that this is no small trick. We’d been bewildered by all these different particles for a while. I keep saying there ought to be a Periodic Table of them, just like the elements in chemistry, and it looks like this could finally be it.”
“It’s not rectangular like the Periodic Table I remember from school.”
“No,” said Gell-Mann proudly, “it has an SU(3) structure.”
“All the suspects,” I said to myself, “in an SU(3) line-up…”
“The thing I’m looking forward to,” said Feynman, “is learning what it means. Figuring out how to line them up is just the first step.”
“Say,” Feynman pondered, “where would 0++ go in here?”
“It wouldn’t,” Gell-Mann answered him flatly.
“It’s another mystery, then,” I sighed, taking back the card. “I’d best be going.”
As I put my hat on and opened the door, Gell-Mann smiled and said, “Let us know if you find that left-handed killer, gumshoe.” Feynman seemed a little puzzled, but I gave them both a thumbs-up and disappeared into the sunset.
I couldn’t help but feel that there was something not quite right.
I was pacing in my hotel room all night. Something had been left unsettled, and I wouldn’t sleep until I knew what it was. Frustrated, I threw myself into an armchair and let my eyes rest for a moment. “That’s it!” I shouted. “Of course!” I threw on my coat. “Gell-Mann!”
I raced to the Caltech physics department in the moonless night. Only one light on under the door— he was still there! I burst through and pointed, “You!”
He was seated behind a typewriter with drafts of his Eightfold Way paper scattered about in heaps. He pulled off his glasses and said angrily, “Oh, what now?”
“You!” I pointed again. “You never explained how to calculate loop diagrams!”
“I never what?” He put his glasses back on.
“There’s a serious problem with the theory— loop diagrams depend on unknown physics— and you gave me a lecture on the methodology of science! You evaded the question! How do you use quantum field theory at all if the loop diagrams can’t be calculated?”
He thought hard to remember the conversation, then laughed out loud. With the low light casting horn-like shadows across his face from his glasses, it was kinda scary. “You want to be let in on a little secret?”
“Close the door.”
I closed the door.
“Technically, they can be calculated. It’s hard, but Dick and a few others found a way to do it. But it’s completely unsatisfactory.”
“We can’t use the theory as it ought to be used, calculating physical quantities such as the mass of a particle from first principles. As you know, gremlins run in the loops and change the answer.”
“Dragons, too. But things like the masses of particles are experimentally known. In dry tables of particle masses are clues to the Omnitheory, Naure’s fundamental rule book. Physics at all possible scales has been averaged over and is sitting in the mass of an electron.”
“Golly, I’ll never look at an electron the same way again.”
“I never do.” He licked his lips. “Now, with the answer sitting in front of us, Dick does the obvious thing— he takes that answer and runs the calculation backward.”
“What does he learn by that?”
“Nothing, at least nothing about the problem he cheated on. But it gives us a handle on certain theoretical quantities that can be plugged into other problems, and now we’re able to solve them because of the experimental input.”
“It doesn’t sound kosher.”
“Many of us think it isn’t. But don’t dispair— there’s another theory, something a few of us have been working on to go deeper than quantum field theory, something more fundamental than fields.”
“What is it?” I was whispering.
“You know what?” he said, a bit too briskly and loud. “That would take too long, and I have work to do. I really need to get this finished.”
“What? You can’t leave me hanging!”
“No, I really can’t be bothered. I can send you to someone who would only be too happy to tell you all the details.”
“Who?” I asked, clutching his desk.
“A brilliant mind named Lev Landau. Yes, he’s probably thought more about this than the rest of us put together. Yes, you should see Lev.”
“Where can I find him?”
Moscow, February, 1961
The train chugged slowly to a stop, hissing steam and casting shafts of light into the darkness. Snow and smoke whirrled together in the spotlights as metal ground against metal, then relaxed. I lowered myself onto the platform and into a black and white film— the grainy kind, where blacks are blacker and whites are whiter than they should be. I lit a cigarette: the only spot of color in the dark night.
A lone figure approached along the quai, lit from behind, arms folded behind his back. I tipped my hat, but he knew who I was already. As he came closer, I saw that his hair didn’t lie about his head, but shot up in the middle like a saluting guard. Somewhere in the distance, dogs barked.
“Are you Dr. Landau?”
I could barely tell he nodded.
“Good to meet you,” I held out my hand. “I’m a private eye.”
He didn’t take it. After a steely silence, he boomed, “Aren’t you aSHAMED of yourself?”
I was taken aback; I didn’t know how to answer.
“Shame on you! They tell me you actually beLIEVE in quantum field theory.”
“Can’t say that I’ve committed to the question either way,” I fumbled.
“Very well. Follow me.” He turned around. I followed. I never even saw his face.