Secret Passages

by Paul Preuss

  But he couldn’t get the Minoan treasures out of his mind.

  Two days, she’d said…

  Anne-Marie let herself into the dark auditorium and stood against the back wall, straining her eyes to find Minakis in the gloom. On the dais Peter was gesturing at equations on the screen. She could see nothing but silhouettes and the edges of unfamiliar faces rimmed in reflected light. An unreasoning fear seized her, that Minakis had slipped away.

  But he was there, only inches away, standing against the wall. Silently she nodded, pretending calm. He nodded back, his eyes reflecting the shining screen.

  After a few seconds, Anne-Marie had no trouble finding her place in Peter’s script. Moving in and out of the projector’s bright glow, he performed with his usual grace, preaching what his colleagues didn’t want to hear, pretending to be unfazed by their antagonism—although she suspected he was hurt more than he let himself show; all his life he’d been used to applause—and she found herself admiring his persistence.

  There’d been a time when she’d been as enthusiastic about ontological questions as he was, a time when she would sit with her friends in a café or a dingy Left Bank loft for hours, sipping sour red wine out of a jug and sucking on a shared reefer, talking about meaning and being and signs and significations as if truth could be extracted from the flow of words like gold nuggets from gravel in a streambed. Their motive had been the opposite of Peter’s; they wanted reassurance that the world was whatever they chose to make of it. But no matter how much they talked, reality remained. It was the stuff you had to deal with.

  When Peter had started muttering about reality in his off moments a year or so ago, her excitement was briefly rekindled; she thought a theoretical physicist might have something more substantial to say on the subject than a bunch of undergraduates mangling literary theory. The world we live in is a world of big things, Peter began bluntly enough, when she pressed him to share his thoughts. Our experience suggests that to change the position of something we have to move it from here to there, that to change the energy of a system we have to burn some fossil fuel, say, or roll a rock down a hill. These are continuous processes; they take time.

  We live in a world of big things, all right, Anne-Marie thought, a world in which the unfair, the random, and the foully obscene are as likely to make our lives hell as to give us fifteen seconds of fame, much less serenity—a world in which the greedy and evil are as likely to die in peace as the good and generous.

  By contrast, quantum theory describes a tiny world that is grainy and discontinuous. A change in the position or energy of an electron near an atomic nucleus occurs not smoothly over time but abruptly, in no time at all. The state of a quantum system is uncertain before it is measured, Peter said, and any act of measurement—in which a big-world instrument forces a link to the quantum world—irrevocably changes things. Uncertainty is not mere ignorance: until the position of the electron is measured, it has no definite position; until the energy of the electron is measured, it has no definite energy. Heisenberg, uncertainty’s creator, asserted that the quantum world does not exist except as a tangled set of likelihoods.

  Anne-Marie asked him how scientists dealt with the split between a big, smooth, predictable world and a microscopic, grainy, uncertain world. Most of us just ignore it, Peter answered; after all, the mathematics gives the right answers. But the question had posed a dilemma to quantum theory’s creators, among them Albert Einstein and Erwin Schrödinger. At first glance Schrödinger’s wave equation of 1926, the workhorse of quantum mechanics to this day, appeared to restore classical meaning to quantum processes. Schrödinger thought there was a reality and it consisted of waves, continuous and propagating smoothly through space, taking time to do so. What look to us like particles are only little bunches of waves, he ventured.

  Schrödinger’s equation held up, but not his interpretation. It turned out that Schrödinger’s waves could not have a real existence in space-time; instead, it was argued, they were graphs of probability. Einstein hated these probabilities, and he hated what they led to: his friend Niels Bohr’s complacent Copenhagen interpretation. Bohr proposed that cause and effect were irrelevant in the quantum microworld; he insisted upon the distinction between the ordinary world and the quantum microworld. The former can be understood, Bohr said, but the latter can only be described.

  Where does the quantum world end and the classical world begin? At five atoms? Fifty atoms? A trillion atoms? Bohr had no answer, which emboldened others to take the Copenhagen interpretation even further—the illusory classical world has no real, independent existence either, they proclaimed; it is somehow brought into existence by the very act of measurement. Anne-Marie knew the feeling. As a poet had put it:

  Or perhaps it is

  that the house only constructs itself

  while we look—

  opens, room from room, because we look.

  The wood, the glass, the linen, flinging themselves

  into form at the clap of our footsteps.

  Einstein, incredulous, demanded of a friend, “Do you really believe the moon exists only when you look at it?” His friend pondered for many years and wrote, after Einstein was long dead: “The twentieth century physicist does not, of course, claim to have the definitive answer to this question.”

  To Einstein, causality, limited by the speed of light, was the essence of experience. Einstein said that separate events which influence one another must somehow be in touch with one another, and the fastest possible way was at the speed of light. To prove his point, in 1935 he and two young associates proposed the Einstein-Podolsky-Rosen experiment. In this imaginary experiment, two identical particles interact and then go their separate ways. A measurement is done upon one of them, establishing its position, say, or its energy. What does that measurement tell us about the other particle?

  Quantum theory says we cannot know anything about the state of a particle until we measure it—that whatever quality we set out to measure does not exist with any definiteness until it has been measured. But these identical-twin particles set out together. If we know the position of one, we can infer the position of the other. If we know the energy of one, we can infer the energy of the other. Each measurement establishes an aspect of reality—so Einstein and Podolsky and Rosen asserted—not only of the particle measured but also of its distant twin.

  Common sense finds no problem here. Why does quantum theory have a problem here?

  Because, Peter explained, according to quantum mechanics neither particle has a definite position or energy until it has been measured. A measurement of one particle forces the state of both, even if the unmeasured twin is well on its way to Jupiter by now. And by the way, the “information” the distant particle receives about its own state reaches it infinitely faster than the speed of light—it gets there in no time at all.

  Why must the distant particle be uncertain about its state? Why does a remote measurement force that state rather than merely reveal it? Why can’t quantum theory admit the pre-existing reality of the states of both particles?

  Because whatever you find is an aspect of your whole experimental setup, Bohr replied. Different processes, different realities.

  Because quantum theory is not an adequate description of nature, said Einstein and Podolsky and Rosen. There must be a way around uncertainty. There must be more to nature, perhaps “hidden variables” that, if we knew them, could explain what quantum theory cannot.

  Heisenberg argued that hidden variables are worse than unnecessary, they’re impossible. Then a young American theorist named David Bohm showed that hidden variables are possible in nonrelativistic quantum mechanics, but for thirty years no one paid him any attention until an Irishman, John Stewart Bell, demonstrated that you can have quantum mechanics or you can have hidden variables, but you can’t have both. Bell suggested that it was now possible to settle the question by actually performing the Einstein-Podolsky-Rosen Gedankenexperiment.

  Bell
showed how to make the Gedanke wirklich, Peter said, the thought real. Measure one particle, then the other. Measure the spin of an electron pair, say, or the polarization of a pair of photons. If your measuring devices are aligned just so, you should find perfect correspondence. Which tells you nothing—that’s what you’d expect. But if your measuring devices are not perfectly aligned, there will be a discrepancy.

  Here’s the gist, here’s the crux, Peter had exclaimed, and listening to him, Anne-Marie had been certain that some great revelation was imminent. If the microworld is smooth and continuous after all, and there are hidden variables which can explain why it looks otherwise, the discrepancy between measurements will be so big, this big—but if quantum mechanics is right, and the microworld is grainy and discontinuous and the uncertainty relations are the best we can hope for, the discrepancy will be different. That difference is known as Bell’s inequality. To save Einstein’s classical, smooth, causal world you cannot violate Bell’s inequality.

  Experimenters soon began trying to violate Bell’s inequality. Their experiments fit on bench-tops and used pairs of photons. Quantum mechanics predicted that polarizers would show a certain correspondence between the states of the photon pairs, while hidden variables would show a different correspondence, and Einstein would win.

  Quantum mechanics won.

  The experiments kept getting more refined. Quantum mechanics kept winning. Telling her this, Peter got more frustrated, and Anne-Marie knew the great revelation would not be forthcoming. The perfect experiment hasn’t been done yet, but as Bell said, it’s hard to believe quantum mechanics works so nicely for inefficient setups but is going to fail badly when enough refinements are made. We have to look at what the experiments tell us, and they tell us that causal information can move faster than light. Which makes me wonder why the causes we see always come before their effects, and why we never get messages from the future…

  Effects before causes. Messages from the future. Anne-Marie had read a science fiction novel once about people who could foretell the future: they did it to demonstrate that not knowing what happens next is what makes life possible. Their grail was “unknowing.” If she had the choice, she would welcome a message from the future, even if it persuaded her that life was not worth living at all. Best to get the bad news over with.

  In the hot auditorium, in her sweat-drenched reverie, she sensed Minakis moving nearby, standing up straighter, and she tried to focus on what Peter was saying, to find her place in the script again.

  “…for example, are virtual particles real? They’re useful devices, certainly, but it’s a mistake to argue whether or not they’re real just as it’s a mistake to argue about whether the electron really goes through one of the slits in the two-slit experiment…”

  Peter had moved beyond Bell’s inequality, beyond nonrelativistic quantum mechanics into quantum field theory, into symmetries and local coordinate systems, into a tangle of fiber bundles, mathematical entities beyond her comprehension. But she knew where he was headed, and it was far short of where he claimed he wanted to go; in the end he retreated into word games like any undergraduate.

  “Once again we’re fooled by our language,” he said. “We have to make an effort to remember we’re not talking about particles at all here, even if the imagery is useful; we’re talking about the processes in which fields couple…”

  A voice boomed in the darkened hall. “Professor Slater, if you will permit me.”

  “Professor Minakis, is that you? Sorry, I’m blind up here.”

  “I am bold enough to say what our colleagues are too polite to say.”

  “Please do.”

  “That your equations are very pretty, but we don’t know what you’re trying to prove. Which makes us wonder why you’re telling us all this.”

  Peter’s smile turned to a grimace. “If you’ll indulge—”

  “You start by saying the world is real,” Minakis interrupted, “then you draw a distinction between commonsense reality and objective reality. Is that a distinction with a difference? You banish the word ‘observer’ from our vocabulary, then you tell us the objects in the world that seem most real to us are already conceptualized in our minds—replacing one form of mentalism with another. Immanuel Kant couldn’t have put it better, but is there any advantage to today’s working physicist in what a Prussian noodler wrote two hundred years ago?”

  “I hope to persuade you that the philosophical advantage is worth a great deal, namely the recovery of a meaningful concept of reality,” said Peter.

  “Then you will have to show us a scheme that solves real problems better,” Minakis replied. “How else are we to choose between Bohm and Bohr, or Bell and Born, or Schrödinger and Heisenberg, or whomever?”

  “I’m prepared to discuss an approach that—”

  “In the fifteen minutes that remain to you? You should have started by showing us how your predictions differ—quantum mechanics versus whatever. Demonstrated that your scheme is more accurate.”

  “Both schemes yield equivalent results, as I hope to show.”

  “If that’s all you hope to show, I wish you well,” said Minakis’s voice in the darkness, “but you must forgive me for wondering why you are taking the trouble.”

  A moment later the door opened, admitting a column of sunlight. Minakis’s shadowy silhouette momentarily blocked it, filling the doorway, and then he was gone.

  Others quickly followed by ones and twos. Peter found himself facing an emptying room. Anne-Marie watched him standing there helplessly. As much as she felt his pain, there was nothing she could do for him. She pushed herself in front of two guffawing men and fled into the sunshine.

  15

  The olive-shaded courtyard bustled with the villa’s white-uniformed staff, busy carrying serving dishes to the buffet and setting places at tables scattered among the trees. Dazzled by the midday glare, Anne-Marie took a moment before she spotted Minakis on the lower terrace, talking to a tanned staffer in white.

  Minakis, his back to the low terrace wall, saw Anne-Marie and waited for her as the young man nodded and turned away; behind him the blue-and-white harbor embraced its tourist fleet.

  “That was horrible,” she said. “You deliberately humiliated Peter.”

  “No, I challenged him,” Minakis replied serenely. “Your husband has undergone a profound crisis of faith. He has rejected everything upon which his former success was based—the world-view of Bohr, of Heisenberg—and he seeks an alternative. I came to this conference hoping to hear him propose a new path. Instead, as indeed you warned me he would, he rehearses old ideas because they seem new to him. It won’t do; he needs to transcend this pack of stale paradoxes. He needs a fresh approach, which can only come from himself.”

  “Or from you?” she said, anger coloring her cheeks.

  “I would be honored to exchange ideas with Peter Slater, whenever he is ready to listen.”

  “Do join us for lunch, then—this buffet you were so excited about. You two can exchange away.”

  Though her invitation was issued through clenched teeth, he pretended it was genuine. “I don’t think Peter wants to hear what I have to say just now. He has a lot of baggage to sort through.” He smiled sadly. “As I do, in fact. I’ve made arrangements to leave the island this afternoon.”

  “Because you didn’t like his speech?” Anne-Marie felt sudden panic. “It meant that much to you?”

  “I thought I made that plain. It was the reason I came.”

  “It’s not fair. You promised to tell me how you got your name.” Her smile was a lopsided pout, as if to convey that her temper had been an act.

  He stared at her from his imposing height, as if passing judgment on her sincerity. “I enjoyed our conversation this morning, perhaps because you made me do all the talking. If you want to talk more, come to Crete. For now, good-bye.” When he put out his hand she thrust hers out awkwardly, surprised and offended, but he took it warmly. “My invitation st
ill stands. Be my guests on Crete, you and Peter.”

  “Where in Crete?”

  “You know where to find me. Do me the favor of giving this to your husband.” He handed her a sealed business envelope, thick with folded pages. “Oh, and be sure to try the garithes me feta while they’re still hot. And the Minos Kava, very cold. It goes well with shrimp.”

  She glanced at the envelope, and when she looked up, he was walking away. This time she didn’t run after him, for with sudden conviction she knew that his invitation was bait.

  He was right, of course; she knew exactly where to find him on Crete. She had done her best to seduce him into giving away his secrets, but he had told her only what he wanted her to hear.

  A plump young man wearing a T-shirt with a picture of Einstein sticking his tongue out approached Peter and Anne-Marie at their table. Not noticing or not caring that he had interrupted their meal, he went on like a movie fan about his admiration for Peter’s work on the I particle. Peter was gracious, flattered even, until the fellow came around to the present moment.

  “Reality? Don’t know about that. Won’t get anywhere until you tackle string theory, quantum gravity. Solve that, what you call reality falls out of it. Rest is a waste of time. My opinion. Not alone, either.”

  Peter made demurring noises until the self-satisfied youngster grew bored and went away. Peter waved cheerily after him. “Be sure and don’t kick any stones,” he called. He turned back to Anne-Marie with a bleak smile. “I’d say the early reviews are in: ‘Slater goes too far but not far enough. Tilts at windmills, falls off hobbyhorse.’”

  In the dappled shade they were enjoying sizzling shrimp baked with cheese and herbs in copper pans, along with a cool bottle of the Cretan wine Minakis had recommended. No one else had interrupted them since they’d sat down, much less asked to join them, and Peter was quickly sinking into melancholy. “Then there’s Minakis,” he said. “I saw you with him afterward. Did he add anything to his oh-so-useful remarks in the hall?”