by Greg Egan
He said, “Any more children?”
She nodded. “One. Emine. She's six hundred and twelve.”
Tchicaya smiled. “That's very restrained. I've had six.”
“Six! Are any of them with you here?”
“No.” He took a moment to realize why she was asking; he'd always sworn that he'd never leave a child before a century had passed. “They're all on Gleason; large families are common there. The youngest is four hundred and ninety.”
“No travelers among them?”
“No. What about Emine?”
Mariama nodded happily. “She was born on Har'El. She left with me. We traveled together for a while.”
“Where is she now?”
“I'm not certain.” She admitted this without a trace of reticence, but Tchicaya still thought there was a hint of sadness in her voice.
He said, “One thing about being planet-bound is, once you've committed to the place, that's it. Even if you wander off to the other side of the world, everyone else who's chosen to stay is just a few hours away.”
“But two travelers? What does that guarantee?” Mariama shrugged. “Chance meetings, every few hundred years. Or more often, if you make the effort. I don't feel like I've lost Emine.”
“Of course not. Nor the others. What's to stop you visiting the ones who've stayed put?”
She shook her head. “You know the answer to that. You're like a cross between a fairy-tale character and some kind of...rare climatic disaster.”
“Oh, come on! It's not that bad.” Tchicaya knew there was a grain of truth in what she said, but it seemed perverse to complain about it. When he was made to feel welcome, it was as a visitor, a temporary novelty. When your child had lived with three or four generations of their own descendants, for centuries, you were not a missing piece of the puzzle. But he never expected to slot in, anywhere. Once he'd told the crib on Turaev that his birth flesh could be recycled, he'd given up the notion that somewhere there'd always be a room waiting for him.
He said, “So what about Emine's other parent?”
Mariama smiled. “What about your partner back on Gleason? The one you raised six children with.”
“I asked first.”
“What is there to say? She stayed on Har'El. Not even Emine could drag her away.” Mariama lowered here eyes and traced a fingertip over the edges of one of the abstract carvings.
Tchicaya said, “If you could drag everyone with you, what would be the point of leaving? There were cultures back on Earth that traveled across continents, whole extended families together—and they were usually more conservative than the ones that stayed put, or the ones that spawned diasporas.”
Mariama scowled. “If two travelers happened to have a child, would that constitute a tribe?”
“No. But traveling is not about a change of scenery. It's about breaking connections.” Tchicaya felt a sudden sense of déjà vu, then realized that he was quoting her own words back at her. He'd got into the habit long ago of using them on other people. “I'm not saying that there'd be anything wrong if six whole generations uprooted themselves together, if that's not a contradiction in terms. But they wouldn't stay together for long—or at least, they wouldn't without imposing rules on themselves a thousand times more restrictive than any they'd needed when they were planetbound.”
Mariama said irritably, “You're such a fucking ideologue sometimes! And before you call me a hypocrite: it's always the converts who are the worst.”
“Yeah? That's not such a convenient axiom for you, if you remember that it cuts both ways.” Tchicaya raised his hands in apology; he wasn't really angry or offended yet, but he could see where they were heading. “Just...forget I said that. Can we change the subject? Please?”
“You can tell me what happened on Gleason.”
Tchicaya thought for a while before replying. “Her name was Lesya. I was there for a hundred and sixty years. We were in love, all that time. We were like bedrock to each other. I was as happy as I've ever been.” He spread his arms. “That's it. That's what happened on Gleason.”
Mariama eyed him skeptically. “Nothing soured?”
“No.”
“And you don't wish you were still there?”
“No.”
“Then you weren't in love. You might have been happy, but you weren't in love.”
Tchicaya shook his head, amused. “Now who's the ideologue?”
“You just woke up one morning and decided to leave? And there was no pain, and no rancor?”
“No, we woke up one morning, and we both knew I'd be gone within a year. Just because she wasn't a traveler doesn't mean it was all down to me. What do you think? I lied to her at the start?” He was becoming so animated he was messing up the bed; he stroked the sheet, and it tightened. “You know how I think she'll feel, if the border reaches Gleason?”
Mariama resisted answering, knowing that she was being set up. After several seconds, she succumbed anyway.
“Terrified?”
“No. I think she'll be grateful.” Tchicaya smiled at Mariama's expression of disgust. It was strange, but she'd probably given him more confidence in his stance, now that she'd turned out to be his opponent, than if they'd been allies willing to reassure each other endlessly.
He continued. “You don't take a traveler for a partner if you hope that the world will always stay the same. You do it because you can't quite break away, yourself, but you can't live without the promise of change hanging over you every day.
“That's what the border means, for a lot of people. The promise of change they'd never be able to make any other way.”
Sophus's presentation took place in a theater that the ship had improvised in the middle of one of the accommodation modules, folding up all the cabins that happened to be unoccupied to create a single large space. When Mariama realized that this included her own, she was not pleased.
“I have glass in there!” She pointed across the theater. “Right where that person's sitting.”
“It'll be protected,” Tchicaya reassured her, as if he were a veteran of the concertina effect. “Anyway, what's there to lose? If anything's broken, it can be reconstructed.”
“They've never been broken,” she complained.
Tchicaya said, “I hate to be the one to point this out, but—” He held up his thumb and forefinger and adjusted the spacing to atomic size.
Mariama glared at him until he dropped his hand. “It's not the same thing. But I wouldn't expect you to understand.”
Tchicaya winced. “So now I'm an all-round philistine?”
Mariama's face softened. She reached over and ran a hand affectionately across his stubbled scalp. “No. Your failings are much more specific than that.”
Tchicaya spotted Yann coming through the entrance with a small group of people. He raised a hand and tentatively beckoned to him. Yann responded by bringing the whole group along to sit beside them.
Rasmah, Hayashi, Birago, and Suljan had been involved in designing the new spectrometer. Catching the tail end of the conversation they'd been having made it clear that all but Birago were Yielders; the other three were joking about his plans to sneak in a filter to conceal the telltale signature of Planck worms devouring the scenery. Birago seemed to be taking their teasing with equanimity, though it struck Tchicaya that he had the quietness of someone outnumbered, who had decided that there was no point in speaking his mind.
Perhaps Mariama felt outnumbered, too, but she appeared genuinely amiable toward the Yielders as introductions were made; she was certainly more than diplomatically polite. Tchicaya had been wondering whether their friendship had caused her to conceal the full measure of her distaste for his position, but whatever effort she was making for his benefit, she was nowhere near the point that Kadir and Zyfete had reached.
Yann said, “The new spectrometer looks good. We'll be able to resolve a whole new band of gamma rays, and with twice the precision of the old machine.”
Tc
hicaya nodded, unsure how much difference that would make. “Do you know what this is all about?” He gestured at the podium that was now growing before their eyes. His Mediator had explained that the timing was meant to encourage people to stop talking among themselves—like a change of lighting, or the raising of curtains—but apparently this was an aspect of the Rindler's local culture that had been documented without ever being practiced.
“Not really,” Yann admitted. “There's usually something on the grapevine about these talks, weeks in advance, but this one has come out of the blue. Sophus is always interesting, though. I'm sure he'll be worth listening to.”
“He said something to me earlier about time asymmetry.”
“What, time-reversal asymmetry? He's talking about an arrow of time in the novo-vacuum?”
“No, time-translation asymmetry.”
Yann's eyes widened. “‘Interesting’ might have been an understatement.”
Sophus appeared and made his way to the podium, but then he stood to one side. People were still entering the theater, and it looked as if they'd keep on streaming in until it was completely full.
Mariama surveyed the latecomers irritably. “Why can't they watch this in their heads?”
“It's a flesh thing,” Yann confided. “I don't understand it either.”
Tchicaya glanced up. People were sitting in chairs suspended from the ceiling, accessed via corridors through higher levels that would otherwise have come to a sudden end. The ship had made use of every square meter of available surface, even though there was no prospect of cramming every last passenger in. Rasmah caught Tchicaya's eye and joked, “I always wanted to be at a performance where people were hanging from the rafters.”
Sophus cleared his throat, and the audience fell silent almost immediately. Tchicaya was impressed; even if he'd known everyone on the ship personally, he would probably have asked his Mediator to plead on his behalf for their attention.
Sophus began. “We've been scribing probes and gathering data now for more than two hundred and fifty years, trying to understand what's going on behind that wall.” He motioned with a raised fist, as if pounding against the border. “The results are there for everyone to see. Theories come and go, and all we have gained is the ability to rule out ninety-nine percent of new models without performing a single new experiment, because we already have enough data to kill off most of our ideas at birth.
“To some people, it's beginning to look hopeless. How can the laws we've failed to understand be so difficult to grasp? It only took three and a half centuries to get from Newton to Sarumpaet. What's wrong with us? We have the mathematical tools to model systems far more arcane than anything nature has ever actually thrown at us, before. The acorporeals grew bored with physics ten thousand years ago; expecting them to live with such meager intellectual stimulation was like asking an adult to spend eternity playing with a child's numbered blocks. But even their boundlessly flexible minds can't make sense of the new toy they've come here to admire.”
Tchicaya glanced at Yann, who whispered plaintively, “Maybe I should be grateful whenever it slips someone's mind that acorporeals were running the Quietener.”
“The Sarumpaet rules survived twenty thousand years of scrutiny!” Sophus marveled. “How flawed, how misguided, could they possibly be? So we began with the sensible, conservative approach: we'd find a new set of rules that extended the old ones, very slightly. The smallest change we could possibly make, the tiniest correction, or expansion, that would encompass all their past successes—but also explain what happened at Mimosa.
“Fine. That's a simple enough piece of mathematics; people solved the equations within days of hearing the news. Then we built the Rindler...and that minimal extension didn't quite fit what we found. So we tweaked the rules a little more. And a little more.
“In essence—and I know this is unfair to some of you, but I'm going to say it anyway—most of what's been done here has consisted of repeating that process, over and over, for a quarter of a millennium. We've raised ever more elaborate theoretical towers on the same foundations, and most of them have been toppled by the very first prediction they made.”
Sophus paused, frowning slightly. He looked almost apologetic, as if he'd been surprised by the tone of his own rhetoric. When he'd spoken to Tchicaya earlier, he'd appeared casually optimistic, but now his frustration was showing through. That sentiment was understandable, but it risked undermining the reception of whatever he said next: to claim any kind of fundamental new insight now would sound like arrogance, after so many people before him had struggled and failed. Still, if he honestly believed that they'd all been misguided, and that progress would come not from standing on their shoulders but from digging in the opposite direction entirely, there was a limit to how graciously that opinion could be expressed.
He collected himself and continued, loosening his posture, visibly striving to make light of his subject, however many worlds, and egos, were at stake.
“Sarumpaet was right about everything that happened before Mimosa. We have to hold on to that fact! And in one sense, we were right, to aim to tamper with his work as little as possible. But what we shouldn't have done was paint ourselves into a corner where we just kept building ever more baroque and elaborate ‘refinements’ of the original rules.
“What do the Sarumpaet rules really say?” Sophus looked around the theater, as if expecting volunteers, but he'd caught everyone off-balance, and there were no takers. “We can write them half a dozen ways, and they're all equally elegant and compelling. A combinatorial recipe for transition amplitudes between quantum graphs. A Hamiltonian we exponentiate to compute the way a state vector evolves with time. There's a Lagrangian formulation, a category-theoretic formulation, a qubit-processing formulation, and probably a hundred more versions cherished by various enthusiasts, who'll never forgive me for leaving out their favorite one.
“But what do they all say, in the end? They say that our vacuum is stable. And why do they say that? Because Sarumpaet required them to do so! If they'd implied anything else, he would have considered them to be a failure. The stability of the vacuum is not a prediction that emerges from some deep principle that had to be satisfied, regardless; it was the number one design criterion for the whole theory. Sarumpaet certainly found some simple and beautiful axioms that met his goal, but mathematics is full of equally beautiful axioms that don't get to govern everything that happens in the universe.”
Sophus halted again, arms folded, head inclined. To Tchicaya he seemed to be pleading for forbearance; what he'd just stated was so obvious and uncontroversial that half the audience had probably found it baffling, if not downright offensive, that he'd wasted their time spelling it out for the thousandth time.
“Our vacuum is stable: that was the hook on which Sarumpaet hung everything. So why did he have such unprecedented success, despite basing his entire theory on something we now know to be false?”
Sophus let the question hang in the air for a moment, then changed tack completely.
“I wonder how many of you have heard of ‘superselection rules’? I only learned the phrase myself a month ago, while doing some historical research. They're an arcane notion from the dawn of quantum mechanics, and they only persisted in the vocabulary for the first couple of centuries, before people finally got things straightened out.
“Everyone knows that it's an axiom of quantum mechanics that you can form superpositions of any two state vectors: if V and W are possible physical states, then so is aV + bW, for any complex numbers a and b whose squared magnitudes sum to one. If that's true, though, then why do we never see a quantum state with a fifty-percent probability of being negatively charged, and a fifty-percent probability of being positively charged? Conservation of charge is not the issue. Long after people could routinely prepare photons that were equally likely to be on opposite sides of a continent, why couldn't they manage to prepare a system that was equally likely to be an electron here and
a positron here”—Sophus held up his left hand, then his right—“or vice versa?
“For a hundred years or so, most people would have answered that question by saying: ‘Oh, there's a superselection rule for charge! You can usually combine state vectors...but not if they come from different superselection sectors of the Hilbert space!’ Apparently there were these strange ghettos that had been cordoned off from each other, and whose inhabitants were not allowed to mix. Cordoned off how? There was no mechanism, no system; it was just an inexplicable fact dressed up in some fancy terminology. But people went ahead and developed methods for doing quantum mechanics with these arbitrary borders thrown in, and the lines on the map became something to be memorized without too much scrutiny. If some innocent novice asked a jaded elder student, ‘Why can't you have a superposition of different charges?’ the reply would be, ‘Because there's a superselection rule forbidding it, you idiot!’”
Sophus lowered his gaze slightly before adding acerbically, “We're far more sophisticated now, of course. No one would tolerate mystification like that—and besides, every child knows the real reason. An electron and a positron in the same position would be correlated with vastly different states for the surrounding electric field, and unless you could track all the details of that field and incorporate them into your observations, you'd have no hope of recognizing the state as a superposition. Instead, the two different charge states would decohere, and you'd be split into two versions, one believing that you'd detected an electron, the other that you'd detected a positron. So although there are no superselection rules, the world still looks so much like the way it would look if there were that all the mathematics that revolved around the term lives on, in various guises.”
Tchicaya sensed a sudden change in the atmosphere around him. When he'd glanced at people before, most had seemed puzzled that they were being offered such mundane observations. Tolerant, and prepared to go on listening for a while, thanks to Sophus's reputation, but clearly not expecting much from yet another tortured reexamination of their field's basic assumptions. Now there was a shifting of bodies, a creaking of seats, as people felt compelled to transform their postures of indifference or mild disappointment into something altogether more vigilant.