CHAPTER EIGHT

Order Matters

On a brisk fall Saturday, seeking epiphanies, I swallow a slice of paper and wander along the Hudson. I marvel at the ripples on the river, the wind brushing my face, the sunlight warming me. I am blown away by this magnificent display of competence without comprehension. Think of the calculations required to construct this scene and move it forward instant by infinitesimal instant!

Seagulls utter exultant, mournful cries as they circle an old man dispensing crumbs from a bag. The seagulls and man adhere, flawlessly, to the principle of least action and the second law of thermodynamics, even though they are, I’m guessing, even more ignorant of physics than I am.

The Idea of Order in Hoboken. From this perspective, these stumpy wooden remnants of an old pier just south of Hoboken terminal look pretty jumbly and disordered, right? But if you keep walking along the Hudson River…

I pass the remnants of an old pier, rotting stumps protruding from the water. The stumps at first form no apparent pattern; their placement seems random, jumbly, as though someone tossed them from a helicopter. As I continue walking, order emerges, as the stumps line up into rows. I keep walking and turn a corner, and the stumps get jumbly again before assembling into columns. 

… the stumps assemble into a sensible matrix of columns and rows. If only that would happen with the formulas of quantum mechanics!

The physics I’ve been learning in PEP553 seems disordered, random. Will I eventually round a corner and see the order? Will the tricks, techniques, notations that now seem so jumbly snap into rows and columns, a matrix suffused with intelligent design? And will this knowledge illuminate the world? Will it help me see more clearly the cloudless sky, the gulls, the people strolling past me?

Back in my apartment, I flip open Griffiths, Chapter 2. I’m hoping the equations will move mystically, like the chess pieces in Queen’s Gambit, the Netflix series I’ve been binging. Beth, a chess prodigy, has visions of chess pieces self-assembling to reveal her winning strategy. But the equations in Griffiths are stubbornly inert, as usual. They just sit there, mocking me. I’m so confused by the equations that I’m not even confused. I hoped acid would give me epiphanies, like the hippy physicists of the Sixties and Seventies, but all I get are anti-epiphanies.

Pythagoras, Plato, Spinoza, Einstein and other smarty-pants have hinted that God, if She/He/They/It exists, is a geek, who values mathematical beauty above all else. I doubt this Geek God exists. Why create this messy world, with all its pain and injustice, if all you really care about is math? And why make the mathematical beauty so hard for ordinary souls to see?

But let’s assume for a moment that there is a Geek God. What might She/He/They/It be like? Such a God would have the personality of an extremely high-functioning autistic genius. Cold, lacking in empathy and social graces, passionate only about geometry and topology, about non-Euclidian super-symmetrical polyhedrons shimmering in unbounded Hilbert spaces. Would such a God care about our suffering? Would She/He/They/It respond to our prayers? Probably not, unless we pray for mathematical insight. Here’s my prayer:

Oh Geek God, have mercy on me. Awaken my mathematical instinct so I can feel, if only fleetingly, the divine bliss that comes from contemplating the eternally undulating wave function. If that’s too much to ask, then just help me get through the problem set at the end of Chapter 2 of Griffiths.

I tell Emily about my prayer to the Geek God, and she decides to take me seriously. She urges me to create an altar dedicated to the Geek God or perhaps to a real person whose math talent I admire, Einstein or this Witten fellow I’m always yammering about. Then I should pray as needed. She warns me not to be ironic. I must be sincere, or the prayer won’t work. My Math God, or God proxy, might punish me if I’m not serious.

I thank Emily for her advice and tell her I might build such an altar. But I’m thinking, Too late! I already prayed to the Geek God ironically. Maybe that’s why I’m having such a hard time in PEP553. Even with the help of Dean and Luis, the homework is crushing me. But I’m not dropping out. With grim determination, I keep studying Griffiths, listening to Ed Whittaker’s lectures, scribbling in my notebook.

Non-Commutation

Ed advised me at the beginning of the semester, when I worried the course would be too hard, to focus on a few key ideas. Good advice. Lately I’ve been focusing on non-commutation, which Ed has been going over in class. I vaguely recall encountering this concept in Susskind’s Quantum Mechanics: The Theoretical Minimum and in The Manga Guide to Linear Algebra, but only now am I beginning to appreciate its importance.

Commutation is a kind of symmetry and non-commutation a kind of asymmetry. A mathematical operation is said to commute when the order in which you carry it out does not matter. Two examples are addition and multiplication: a + b = b + a, and a x b = b x a. Division and subtraction, in contrast, do not commute: a – b ≠ b – a, and a/b ≠ b/a. Substitute 3 and 2 for a and b to see what I mean. As I learned from The Manga Guide to Linear Algebra, matrices, which consist of rows and columns of numbers, usually do not commute when you multiply them. If A and B are matrices, AB ≠ BA.

The non-commutation of matrices turns out to be vitally important in quantum mechanics. Matrices are the basis of quantum operators, which do much of the heavy lifting in quantum calculations. An operator takes a wave function, expressed as a complex number, and transforms it into real numbers, which you square to get positive probabilities. Let’s say you have two operators, P and M, that let you calculate probabilities associated with an electron’s position and momentum. These operators do not commute: PM ≠ MP. There’s more: The difference between PM and MP is iħ, which can be written as PM - MP = iħ, or MP - PM = iħ. That term iħ is the square root of negative one, the primal imaginary number, times Planck’s constant, which is crucial to quantum lumpiness.

This asymmetry of position and momentum operators is called the “canonical commutation relation,” and it’s a big deal. Griffiths, our textbook author, says in a footnote on page 41, “In a deep sense all of the mysteries of quantum mechanics can be traced to the fact that position and momentum do not commute. Indeed, some authors take the canonical commutation relation as an axiom of the theory.”

The canonical commutation relation underpins Heisenberg’s uncertainty principle. The principle says you cannot know both the position of a particle and its momentum, which is a measure of the particle’s mass, velocity and direction. The more information you gain about one variable, the more you lose about the other. You can know where a particle is but not where it’s going, or vice versa. And that’s because PM - MP = iħ.

Twenty Questions 

Ed says the canonical commutation relation leads to a handy mathematical trick that Heisenberg discovered with Pauli’s help. The trick transforms college and graduate-level math into high-school math; no derivatives or integrals are necessary, just algebra. By exploiting the non-commutation of operators, you can solve problems that would otherwise be difficult or intractable, like calculating how the energy of an electron jumps from one level to another. Never mind how or why the trick works, Ed says; just learn how to calculate with it.

Instead of practicing the trick enabled by the canonical commutation relation, I dwell on its meaning. The non-commutation of operators reflects a disturbing feature of quantum mechanics: The way in which you measure things matters. More precisely, the order in which you carry out measurements matters. Let’s call this the order-matters problem.

Imagine you want to know the Moon’s mass and volume, and you get different results—a different mass and volume--depending on which you measure first. In the case of quantum mechanics, we’re just talking about tiny things, like electrons, not moons, but still. The order-matters problem undercuts the premise of scientific realism, that the world is what it is, regardless of how we look at it.

Scientific realists believe the truth is out there, waiting for us to discover it, like Pluto or the Andromeda Galaxy. If we discover Andromeda before Pluto, so what? Order doesn’t matter; the truth will be revealed eventually, one way or another. To hard-core scientific realists, mathematical theories are as real as planets and galaxies, or more real, because these theories are eternal, whereas planets and galaxies come and go.

Edward Witten, string theorist, who once told me that the order in which you discover deep truths doesn’t matter.

Edward Witten, the string theorist, is a hard-core scientific realist—or he was when I interviewed him in 1991 in Princeton. At one point, he became annoyed by my harping on the lack of experimental evidence for string theory. To convince me of the theory’s profundity, he asserted that all the “really great ideas” in 20th-century physics are “spinoffs” of string theory. Witten wrote down four “great ideas” on his blackboard in the following order: general relativity, quantum field theory, string theory, supersymmetry.

General relativity is Einstein’s theory of gravity. Quantum field theory is a generalization of quantum mechanics, which accounts for all the forces of nature except gravity. String theory is a unified theory, which says all the forces spring from infinitesimal strings. Supersymmetry is a corollary of string theory, which says that all particles have mirror twins, sometime called “sparticles.” There was, and is, no experimental evidence for supersymmetry, just as there is none for string theory.

Witten, in 1991, considered the order of discovery of these four big ideas a “mere accident of the development on planet earth”; intelligent aliens elsewhere in the universe might have discovered string theory first and derived the other theories from it. But Witten insisted to me that those four “ideas” would eventually be discovered by “any advanced civilization.” Why? Because the ideas are true, they exist out there, like the Andromeda Galaxy.

Now contrast Witten’s view with that of John Wheeler, the adventurous quantum theorist. Wheeler was obsessed with the order-matters problem. To dramatize its significance, he came up with the following analogy: When we probe nature, we are playing a special “surprise” version of the old game Twenty Questions. In this version of the game, Wheeler leaves the room while his friends--or so Wheeler thinks--agree on a person, place or object that he must guess with yes-or-no questions.

John Wheeler, who thought the order in which you ask and answer questions matters a lot.

But Wheeler’s friends decide to play a trick on him; they don’t agree on a communal answer in advance. When Wheeler comes back into the room and asks the first friend, Is it bigger than a mouse?, only then does the friend think of something, whale, and reply, Yes. When Wheeler asks the next friend, Is it female?, the friend thinks Queen of England, and says, Yes. And so on. Each friend must think of something consistent with the previous replies; otherwise, there are no constraints on their answers.

The answer “wasn't in the room when I came in even though I thought it was,” Wheeler explained. And in the same way, reality, before the physicist interrogates it, is undefined; it exists in an indeterminate limbo. “Not until you start asking a question, do you get something,” Wheeler said. “The situation cannot declare itself until you've asked your question. But the asking of one question prevents and excludes the asking of another.”

Wheeler’s analogy is radically anti-realist. Physicists want to believe that they are discovering eternal, objective truths. But according to Wheeler, neither “truth” nor the “reality” it supposedly reflects exists in a precise, defined way before we start asking our questions; our questions define reality and truth. And our current questions are constrained by our previous questions and answers.

Another disturbing thought: The Twenty-Questions model suggests that we might get locked into accepting theories for reasons related to historical contingency, as in the case of the QWERTY keyboard. Wheeler’s analogy, which was inspired by quantum mechanics, puts the theory in an awkward position. If we believe in quantum mechanics, we must doubt it, or at least its status as an eternal, objective, Platonic truth. [1]

And by the way, if we have doubts about quantum mechanics, which is backed up by reams of experimental evidence, what hope is there for string theory, which is backed up by zilch? Or rather, backed up only by its alleged mathematical virtues? Sorry for knocking string theory again, but come on.

Decontamination

I keep thinking of more ways in which order matters. Take Covid decontamination, the ritual I perform whenever I visit Emily’s place. The decontamination problem becomes especially complex when I stop at Whole Foods to buy sushi or pasta for us. My goal after I arrive at Emily’s is to decontaminate myself and my stuff so I don’t infect her. In what order should I do the following:

a, wash my hands

b, take off my mask

c, take off my backpack

d, take my keys and wallet out of my pockets

e, decontaminate the groceries

f, kiss Emily

Should I set things down and then wash my hands? Or wash my hands, set things down and wash my hands again? Do I wash my hands before or after taking off my facemask? Should I wipe off my wallet and credit card with alcohol if I’ve taken them out to buy something on the way over here? If I bought groceries, do I disinfect myself and then wipe down the groceries or vice versa?

I’m overwhelmed by the complexities of decontamination. As with quantum measurements, order matters. I know there must be an optimal decontamination sequence, but I can’t figure out what it is. Lately some public-health experts are saying we don’t need to wipe groceries down, because the coronavirus is not transmitted via surfaces. Fortunately, Emily, who reads much more about Covid-19 risks than I do, tells me exactly what to do. Her rules might seem arbitrary, especially when she changes them, but I rarely object; she has relieved me of responsibility. Making her feel safe is my meta-rule. Kissing her always comes last, after she grants permission.

On Sunday Mac and Skye, my son and daughter, visit me here in Hoboken. Skye has taken the subway from Brooklyn; Mac has driven down from Newburgh, a town on the Hudson River. We stay outside for the most part, sitting on benches on the Hudson, but they come briefly into my apartment, wearing masks, to use the bathroom. If I catch Covid from one of my kids, that would be bad. But it would be much, much worse if I got infected and passed the virus on to Emily. I need deniability. If Emily gets sick over the next week or two, I need to be able to assure her, without feeling like I’m lying, that I didn’t catch Covid-19 from my kids and give it to her. These are hard biomedical/psychosocial/ethical problems, with no perfect solutions. I wish I simply knew what to do, like those uncomprehending but highly competent seagulls spiraling above the Hudson, effortlessly adhering to the law of laziness.

Dean’s Decision 

In my next study session with Dean and Luis, I confess that I’m not taking the midterm exam, even though Professor Whittaker is giving us a few days to complete it. There’s no point, I know I’ll fail. I’ve given up on homework too, it’s too hard. I’ll keep attending class, reading Griffiths and meeting my study buddies, if they’re up for it, but I’ve abandoned hope of passing the course.

Dean announces that he’s in the same situation. He is leaving graduate school; this is his last semester. He’s going to keep showing up for PEP553, to learn as much as he can, but he’s not going to complete the midterm. He is frustrated with conventional STEM instruction, which is expensive and inefficient. He’d love to do something about these problems, to help people learn on their own. Yeah, I say, do it! Start a revolution! Topple the ivory tower! Luis can’t bail on PEP553; he needs a good grade to get his master’s degree. Later, bouncing around the internet, I come across a quote from the scholar and novelist C.S. Lewis:

It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. The fellow pupil can help more than the master because he knows less. The difficulty we want him to explain is one that he has recently met. The expert met it so long ago he has forgotten.

Yes, that’s a paradox of education: Knowledge can blind us, leading to competence without comprehension. Dean is thrilled when I read him the C.S. Lewis quotation during our next study-buddy session. It reminds him of the Lancaster system of education, which is based on the idea that students learn best from each other. He would love to see something like the Lancaster system replace or supplement conventional STEM education. The system could be a live-stream channel where young people interested in science and math help each other. Dean has already created a chat room for STEM undergrads on a platform called Discord, which he hopes might be supported by donations and ads.

Dean’s plan gets me excited. I imagine how the Lancaster system could be incorporated into a physics class such as PEP553. Perhaps class time could be set aside for student presentations on readings and homework. I could talk about my acid anti-epiphanies, or about Wheeler’s Twenty Questions model of science. Of course, that would mean less time for the stuff that Ed needs to cover, like non-commutation; education is a zero-sum game.

After our study session, I google the Lancaster system, also called the “Monitorial” or “Madras” system, and discover its dark side. European powers such as England, France and Spain employed the Lancaster system for educating colonial subjects. Under the system, teachers enlist stronger students to help them instruct weaker students. The native students, in effect, help their overlords brainwash their fellow natives.

Nothing in our fallen world is purely good.

Treknobabble

My brain feels cluttered; I rarely have flashes of illumination. When I was totally ignorant, the tiniest revelation seemed dramatic, because it stood out against the darkness. Now that I’m in a state of dim, twilit comprehension, there is less contrast between a new piece of information and my ground state of knowledge.

Chief O’Brien, a character on Deep Space Nine, fixing something that almost certainly involves quantum mechanics.

My lack of technical knowhow, about which Emily loves to tease me, is getting to me. Even watching Deep Space Nine, the Star Trek spinoff, makes me feel inadequate. I envy the casual expertise with which the fictional officers talk about and solve fictional technical problems. Example: Chief O’Brien, the gruff head of engineering in Deep Space Nine, says to handsome, fatherly Captain Cisco: “Sir, I think we can stabilize the shields by re-routing the plasma injectors through the subspace field. But the wormhole fluctuations aren’t making it easy.” Oh, to have that technical mastery! Trekkies call this pseudo-technical talk Treknobabble.

Cisco replies to O’Brien: “Do your best, Chief.” Chief O’Brien’s best is very good. He is no mere theorist, he’s a troubleshooter. He crawls down conduits, pops panels out, fiddles with glowing crystals in the bowels of the ship, fixes the problem. He’s smart and competent, except when it comes to romance. He keeps messing up things between him and his gorgeous, loving wife Kiko. I can relate to O’Brien’s marital ham-handedness. Romance, for some of us, is an extremely hard problem.

I feel my technical ignorance acutely during my study sessions with Dean and Luis. In our first session after the midterm exam, Luis is in a great mood. He got a high score, 92 out of 100, on the exam. He has signed up for a class on quantum information next semester. He’s excited about it but wishes he were stronger in computer science. Dean says he’ll be happy to help Luis with computer science. Luis thanks him and says he’ll be happy to help Dean and me with this week’s homework. I tell my study buddies that I will be happy to answer any questions they might have on psychedelics and mysticism. They laugh, as if I’m kidding. 

Many Worlds

Over the weekend I read a classic paper that Ed assigned as homework: “Quantum Mechanics and Reality,” published in Physics Today in 1970. The author, Bryce DeWitt, notes that quantum theory, despite its “enormous practical success,” defies understanding. The theory divides the world into a “system” being observed and an “apparatus” making measurements. The apparatus exists in “a kind of schizophrenic state in which it is unable to decide what value it has found for the system.” Note the anthropomorphism of that statement. 

One solution to the measurement problem, DeWitt says, might be to have a second apparatus observing the first, but this leads to a “catastrophe of infinite regression.” Theorists have proposed various other solutions:

1.     Wigner and others propose that measurement, which forces quantum events to shift from possibility to actuality, requires “the consciousness of an observer.”

2.     Bohm and de Broglie conjecture that quantum particles are subject to unseen factors, or “hidden variables,” which might take the form of a “pilot wave.”

3.     Bohr’s Copenhagen interpretation depicts the quantum realm as a “ghostly world where symbols, such as the wave function, represent potentiality rather than reality.”

4.     Hugh Everett and others speculate that although we observe only one outcome of a quantum experiment, all the possible outcomes described by the wave function happen in other universes.

DeWitt calls the final option EWG, after Hugh Everett and two physicists who helped him refine the theory, John Wheeler and R. Neill Graham. DeWitt initially found EWG shocking; the idea of 10 to the 100th power “slightly imperfect copies of oneself all constantly splitting into further copies,” he writes, “is not easy to reconcile with common sense.” But DeWitt, on reflection, decides that this “bizarre” interpretation is the best of the lot. It eliminates the apparent randomness of quantum mechanics and its reliance on observation.

A half-century after DeWitt’s paper, many physicists take EWG, which is now called many worlds, seriously. Sean Carroll contends in his bestseller Something Deeply Hidden that many worlds are an inescapable consequence of quantum mechanics, our truest theory of reality. Branching doesn’t require human observation, Carroll argues; it happens whenever one thing jostles another such that their wave functions collapse, a process called decoherence. Decoherence happens a lot. It’s happening to particles in your body right now, and now, which means that zillions of your doppelgangers are veering off into other universes. Carroll estimates that the number of universes created since the big bang is 2 to the power of 10 to the power of 112. That’s a lot of universes.

I get the appeal of many worlds: quantum mechanics, which seems probabilistic and subjective in our little cosmos, becomes deterministic and objective on the scale of the multiverse. But come on. In our next PEP553 session, Ed grimaces when I ask for his take on many worlds. In the 1980s, he worked at IBM with a brilliant physicist, Bernie Yurke, who liked the many-worlds hypothesis. Ed could never buy it. The universe is constantly splitting into other universes? Like right now? And now? With other versions of him and me? Ed can’t get his head around that. But Ed admits that he’s never given quantum interpretations much thought.

Someone recently sent me a paper, written by a psychiatrist, that invokes the many-worlds hypothesis to explain psychosis. Hallucinations and “thought intrusions” stem from interference between our minds and minds in other worlds. Supposedly. Yeah, I’m sure that conjecture will be helpful to people struggling with schizophrenia and their caregivers. I used to find speculation about multiverses titillating, in a sci-fi way, but no longer. Now it strikes me as unseemly, even decadent, for highly trained scientists to harp on other worlds when so many people in this world, the real world, are suffering.

Bound and Scattering States

Ed begins our next class by mentioning the looming Presidential race; the gap between Biden and Trump seems to be closing. Then Ed says, I guess we should stop talking about politics. Quantum mechanics transcends politics. I brood over Ed’s comment after class. Quantum mechanics evolved during a tumultuous period. Schrodinger proposed his famous cat paradox in 1935; that same year Hitler started rearming Germany in violation of the Treaty of Versailles. Are these events really unrelated?

Consider the details of Schrodinger’s experiment. He imagined a cat in a box with a uranium lump, a radiation detector and a bottle of poisonous prussic acid. The uranium has a 50 percent chance of decaying after a certain time has passed; if the uranium decays, the radiation detector releases the prussic acid and kills the cat. Before you look in the box, the wave function describes everything in it, including the uranium, the detector and the cat, in a superposition of states; hence the cat is both alive and dead before you look in the box. Schrodinger found this “prediction” absurd; that’s why he, like Einstein, thought quantum mechanics must be flawed or incomplete.

Googling “Schrodinger cat experiment,” I find an essay on its historical context by historian of science David Kaiser. Kaiser comments: “It’s no coincidence that, in the face of a looming World War, genocide, and the dismantling of German intellectual life, Schrodinger’s thoughts turned to poison, death, and destruction.” The details of Schrodinger’s imaginary experiment are creepily prescient. Uranium serves as the explosive core of fission bombs; prussic acid is the basis for Zyklon-B, with which the Nazis poisoned Jews in concentration camps.

Meanwhile, I try to transcend politics by focusing on bound and scattering states. Ed, following up on Griffiths, notes that particles described by the Schrodinger equation can behave in two fundamentally different ways, corresponding to “bound states” and “scattering states.” Particles in bound states oscillate back and forth, like guitar strings, pendulums or yoyos. Bound states are typically described by quantum versions of harmonic oscillators. The particle in a box is in a bound state, because the particle bounces back and forth.

A particle in a scattering state flies off “to infinity and beyond,” as Griffiths puts it. Actually, I added “and beyond.” I loved watching Toy Story, in which Buzz Lightyear exclaimed “To infinity and beyond!,” with my kids when they were toddlers. Infinity has a precise mathematical meaning here; it means that the particle can veer off onto virtually any trajectory, as allowed by the Schrodinger equation. Particles can jump from bound states to scattering states. For example, if a particle tunnels through the walls of the box, it becomes a “free particle” in a scattering state, flying off to infinity and beyond. Free particles are not bound to other particles, as an electron is bound to a proton and as quarks are bound to each other inside protons.

Graphical depictions in Griffiths of bound state (a), scattering states (b) and hybrid quantum state.

The connotations are impossible to ignore. There are times when I feel like I’m in a bound state, doing the same thing over and over, like a particle in a box. Then something happens, and I tunnel out of the box. I never really become a free particle; I just tunnel from one box to another. I’m a happily single guy, then I fall in love and get married. My wife doesn’t want kids, then she does, and we have a son and a daughter. I start teaching at Stevens because I can’t support my family on a freelance-writer’s income. My wife and I divorce. I meet Emily. The pandemic happens. I start studying quantum mechanics.

Life as a whole, from one perspective, seems like a bound state, consisting of the cycles of birth and death, creation and extinction at the levels of organisms and species. But life on Earth began with a spectacular tunneling event, in which inanimate chemical compounds coalesced to form replicating, evolving cells. And evolution has a direction. Unicellular species spawned multicellular ones, including our ancestors, who created language, art, mathematics, science, civilization. Lots of tunneling events. Evanescent waves.

There is clearly a direction to human history; we’re not in a bound state. Except of course I would say that, because I’m a liberal, a progressive. Progressives hope we can transcend our box of mindless, cruel capitalism and militarism; we won’t achieve total freedom, because that makes no sense, but we’ll tunnel into a much better box, with more peace, prosperity and justice. Conservatives, at least the old-fashioned kind, prefer to stay bound by tradition. They fear the unpredictability of scattering; tunneling out of the box might result in chaos. I get that; revolutions, especially violent ones, can make things worse.

Maybe on the biggest, trans-cosmic scale, the scale of the multiverse, we live in a bound state, even a stationary state. That’s what conservation laws imply. Maybe all the wave functions of all the universes cancel each other out and add up to zero. Maybe when our universe was born, another universe died. But I have faith that in this universe, on this planet, progress is real. Things are scattering in a good direction, they are getting better, no matter who wins the election next month.

Trains Hiding Behind Trains

Emily has an uncanny way of steering me toward readings relevant to my quantum project. I often don’t see the connection at first, I think she’s wasting my time, but then I get it. Recently, after listening to me rave about how order matters, she read me a poem by Kenneth Koch. The poem’s title, “One Train May Hide Another,” comes from a sign Koch encounters at a railroad crossing. The sign warns that behind the train in your line of sight there might be another train, which might kill you if you see it too late.

Sign at a railroad crossing warns in French: “ONE TRAIN MAY HIDE ANOTHER,” which is profound if you think about it.

Koch’s concern seems to be missed opportunities, and especially romantic opportunities. You get locked into a relationship with one woman, and then you discover that she has a hotter sister. Emily loves the poem except for this creepy sexual subplot, which reminds her of a class she took with Koch in the early 1980s at Columbia. Koch was rumored to seduce female students after praising their poems in class. Koch, after praising one of Emily’s poems, invited her to meet him outside of class, but she declined.

I see the connection between Koch’s poem and physics. When you look at the world as a physicist does, what are you failing to see? What is hiding behind your theories? Your equations? Maybe you fail to see the key to happiness. The lesson applies to all of us: When we pay attention to one thing, we miss other things. But you might have the opposite problem: You become so worried about what you’re missing that you fail to appreciate what is right before you. You might live your life waiting for a train that never comes, that doesn’t even exist.

That’s the theme of the Henry James story “The Beast in the Jungle.” The narrator keeps expecting something momentous to happen to him, but it never does. Meanwhile, he fails to pay attention to his life and to the woman who loves him. Henry James is a Debbie Downer, but he hits his targets. There is nothing more precious, revelatory and, yes, perilous than this very moment. And this one. And this one. It’s easy to know this truth, intellectually, not so easy to feel it, and to live without regret or expectation. 

After leaving Emily’s, I read “One Train May Hide Another” online, carefully. The poem ends with these lines:

One teacher,

One doctor, one ecstasy, one illness, one woman, one man

May hide another. Pause to let the first one pass.

You think, Now it is safe to cross and you are hit by the next one. It can be

important

To have waited at least a moment to see what was already there.

Quantum Notebook #3, notes from the day after the Presidential election.

My understanding shifts. The poem is less about the quest for love and happiness than the quest for truth. The poem implies that timing matters, the order in which events unfold matters; this is true of quantum measurements and of life. As soon as you think you get things, your perspective shifts, just as my view of Koch’s poem has shifted. You can glimpse truth only in retrospect, perhaps when you’re on the verge of death, and maybe not even then. Or you become so obsessed with death, that big train bearing down on you, that you forget to live your life.

Koch’s dark poem makes me see the upside of the many-worlds model. Many of us are haunted by the order-matters problem. We can’t help thinking of what might have been if we hadn’t made this decision, which locked us into this timeline. We can take comfort, perhaps, from imagining our counterfactual selves scattering away from us to live freely and happily, with competence and comprehension, in worlds much, much better than ours.

Notes

  1. Journalist Philip Ball proposes a Wheeler-esque interpretation of quantum mechanics, which he calls “Ifness,” in his excellent 2018 book Beyond Weird: Why Everything You Thought You Knew about Quantum Mechanics Is Different. Quantum mechanics, Ball notes, forces us to accept that all our knowledge is contingent, conditional: If we look at an electron in this way, then we will see it behave in a certain way. “We’re used to science telling us how things are,” Ball says, “and if ‘Ifs’ arise, that’s just because of our partial ignorance. But in quantum mechanics, Ifs are fundamental.” It is possible, Ball says, that further research will reveal “an Isness beneath the Ifness.” But it will not resemble “the Isness of everyday life,” Ball warns. “It will not be a ‘common sense’ Isness.” I also like Ball’s description of quantum mechanics as a “ragbag of lucky guesses and clever tricks.” Yeah, kludgy and ad hoc, like I said!

 
 

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