Schild's Ladder (15 page)

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.

As this mood swept the room, Tchicaya felt gooseflesh rise along his spine. He couldn't claim to have anticipated the words he heard next, but they thoroughly merited his body's reaction.

“I believe there are no Sarumpaet rules,” Sophus proclaimed. “Not the originals, and not some grander, more perfect version that will explain what happened at Mimosa. But the world still looks so much like the way it would look if there were that we couldn't help but think such rules existed.”

In the silence that followed, Tchicaya turned to Mariama, wondering if she'd picked up more from Sophus's earlier remarks than he had, but she appeared to be equally stunned. Tchicaya was beaming with delight at the audacity of Sophus's claim. Mariama looked dismayed, almost fearful.

Sophus continued. “How can the Sarumpaet rules seem to be true, when they're false? How can our vacuum seem to be stable, when it isn't? I believe that the right way to answer these questions is virtually identical to the resolution of another paradox, one that was dealt with almost twenty thousand years ago. How can the universe appear to obey classical mechanics, when it really obeys quantum mechanics?

“What creates the illusion of classical mechanics is our inability to keep track of every aspect of a quantum system. If we can't observe the whole system—if it's too large and complex in itself, or if it's coupled to its surroundings, making
them
part of the system—we lose the information that distinguishes a genuine superposition, where alternatives coexist and interact, from a classical mixture of mutually exclusive possibilities.

“I believe the same effect is responsible for the Sarumpaet rules. How can that be? The Sarumpaet rules are quantum rules. They apply to systems that have
not
been rendered classical by decoherence. How can interaction with the environment explain anything
wholly quantum-mechanical
?”

Sophus smiled wearily. “It's been staring us in the face for twenty thousand years. An electron—a charged particle, which transforms the ordinary vacuum around it into an entirely different state—still obeys quantum mechanics in all of its
other
degrees of freedom. Its position is quantum-mechanical, its charge is classical. Even when we do our best to isolate an electron from its surroundings, we actually fail miserably at half of the task, while succeeding at the other half. So decoherence hides superpositions of different charge states from us, but
not
different position states. Our failure looks classical, our success is quantum-mechanical.

“We thought the Sarumpaet rules were pure quantum mechanics: the final story, the lowest level, the rules that held for a system in perfect isolation. Of course, we accepted the fact that,
in practice
, we could never isolate anything from its surroundings completely, but that wasn't the point. The universe itself, the total system, was assumed to be obeying the Sarumpaet rules—because whenever we did our best to examine any small part of it, separated out as scrupulously as possible, those were the laws that held.

“That was the wrong conclusion to reach. The electron shows how quantum and classical properties can coexist. The fact that you can demonstrate
some
quantum behavior in a system doesn't mean you've uncovered all that there is to be found.

“I believe that the Sarumpaet rules are
classical rules
. Part of the total state vector of any system obeys them, but not the whole. The part that does follow the Sarumpaet rules interacts with the environment one way: transforming its surroundings into what we think of as our own vacuum. But there are other parts that interact differently, creating other states. Because we can't begin to track what's really happening to the environment on the Planck scale, what we see is a single, certain, classical outcome: the Sarumpaet rules hold absolutely true, and our vacuum is absolutely stable.”

A member of the audience stood, and Sophus acknowledged the request. “Tarek?”

“You're claiming that the vacuum has been stabilized by something like the quantum Zeno effect?”

Tchicaya craned his neck to observe the questioner more closely. Tarek was the Preservationist who'd been trying to scribe Planck worms to devour the novo-vacuum, without waiting to discover what it was, or what it might contain. There was nothing fanatical about his demeanor, though; he merely radiated an impatience that everyone in the audience shared.

“It's similar to that,” Sophus agreed. “The quantum Zeno effect stabilizes systems through constant measurement. I believe that part of the total graph in which everything's embedded ‘measures’ the part we see as the vacuum, which also determines the dynamic laws that govern matter moving through that vacuum. It's like the vapor in a cloud chamber, condensing in droplets around the path of a subatomic particle. The particle only appears to follow a definite trajectory because each path is correlated with a particular pattern of droplets—and the droplets have too many hidden degrees of freedom to exhibit quantum effects themselves. But we know there are branches where the particle follows different paths, surrounded by different trails of droplets.”