Schild’s Ladder

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.”

Tchicaya 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