Schild's Ladder

  Sarumpaet's quantum graphs were the children of spin networks, moving one step further away from general relativity by taking their own parents' best qualities at face value. They abandoned the idea of any preexisting space in which the network could be embedded, and defined everything—space, time, geometry, and matter—entirely on their own terms. Particles were loops of altered valence woven into the graph. The area of any surface was due to the number of edges of the graph that pierced it, the volume of any region to the number of nodes it contained. And every measure of time, from planetary orbits to the vibrations of nuclei, could ultimately be rephrased as a count of the changes between the graphs describing space at two different moments.

  Sarumpaet had struggled for decades to breathe life into this vision, by finding the correct laws that governed the probability of any one graph evolving into another. In the end, he'd been blessed by a lack of choices; there had only been one set of rules that could make everything work. The two grandparents of his theory, imperfect as they were, could not be very far wrong: both had yielded predictions in their respective domains that had been verified to hair's-breadth accuracy. Doing justice to both had left no room for errors.

  Livia said, “Conceptually, that argument is very appealing. But there could still be deviations from the rules—far too small to have been detected so far—that would change the outcome of your experiment completely.”

  “So it's a sensitive test,” Cass agreed. “But that's not why I've proposed it.” They were talking in circles. “If the rules hold, the graph I've designed should be stable for almost six-trillionths of a second. That's long enough to give us a wealth of observations of a space-time utterly different from our own. If it doesn't last that long, I'll be disappointed. I'm not doing this in the hope of proving Sarumpaet wrong!”

  Cass turned to Darsono, seeking some hint that he might share her exasperation, but before she could gauge his mood, Livia spoke again.

  “What if it lasts much longer?”

  Finally, Cass understood. “This is about safety? I've addressed the potential risks, very thoroughly—”

  “On the basis that the Sarumpaet rules are correct.”

  “Yes. What other basis should I have used?” Phoenician astrology? Californian lithomancy? Cass resisted the urge to lapse into sarcasm; there was too much at stake. “I've admitted that there's no certainty that the rules hold in every last untested circumstance. But I have nothing better to put in their place.”

  “Nor do I,” Livia said gently. “My point is, we mustn't over-interpret the success of the Sarumpaet rules. General relativity and quantum field theory confessed from the start that they were just approximations: pushed to extremes, they both yielded obvious nonsense. But the fact that QGT doesn't—the fact that there is no fundamental reason why it can't be universally applicable—is no guarantee that it really does stretch that far.”

  Cass gritted her teeth. “I concede that. But where does it leave us? Refusing to perform any experiment that hasn't been tried before?”

  Rainzi said, “Of course not. Livia is proposing a staged approach. Before attempting to construct your graph, we'd move toward it in a series of experiments, gradually bridging the gap.”

  Cass fell silent. Compared to outright rejection this was a trivial obstacle, but it still stung: she'd worked for thirty years to refine her own proposal, and she resented the implication that she'd been reckless.

  “How many stages?”

  “Fifteen,” Livia replied. She swept a hand through the vacuum in front of her, and a sequence of target graphs appeared. Cass studied them, taking her time.

  They'd been well chosen. At first one by one, then in pairs, then triples, the features that conspired to render her own target stable were introduced. If there was some undiscovered flaw in the rules that would make the final graph dangerous, there could be no more systematic way to detect it in advance.

  “It's your choice,” Rainzi said. “We'll vote on whichever proposal you endorse.”

  Cass met his eyes. The openness of his face was an act of puppetry, but that didn't mean he was insincere. This wasn't a threat, an attempt to bully her into agreeing. It was a mark of respect that they were letting her decide, letting her weigh up her own costs, her own fears, before they voted.

  She said, “Fifteen experiments. How long would that take?”

  Ilene answered, “Perhaps three years. Perhaps five.” Conditions varied, and the Quietener wasn't perfect. Planning an experiment in QGT was like waiting for a stretch of ocean to grow sufficiently calm that a few flimsy barriers could block the waves and keep out the wildlife long enough to let you test some subtle principle of fluid dynamics. There was no equivalent of a laboratory water tank; space-time was all ocean, indivisible.

  In terms of separation from her friends, five years was nothing compared to the centuries she'd already lost. Still, Cass found the prospect daunting. It must have shown on her face, because Bakim responded, “You could always return to Earth immediately, and wait for the results there.” Some of the Mimosans had trouble understanding why anyone who found life in the station arduous would feel obliged to be here in person at all.

  Darsono, empathetic as ever, added quickly, “Or we could give you new quarters. There's a suitable cavity on the other side of the station, almost twice as large; it's just a matter of rerouting some cables.”

  Cass laughed. “Thank you.” Maybe they could build her a new body, too, four whole millimeters long. Or she could abandon her scruples, melt into software, and wallow in whatever luxuries she desired. That was the hazard she'd face every day, here: not just the risk that she'd give in to temptation, but the risk that all the principles she'd chosen to define herself would come to seem like nothing but masochistic nonsense.

  She lowered her gaze toward the illusory meadow, laserpainted on her retinas like everything around her, but her mind's eye conjured up another image just as strongly from within: the Diamond Graph, as she saw it in her dreams. She could never reach it, never touch it, but she could learn to see it from a new direction, understand it in a new way. She'd come here in the hope of being changed, by that knowledge if by nothing else. To flee back to Earth out of fear that she might test her own boundaries more rigorously here, in a mere five years of consciousness, than if she'd spent the same three-quarters of a millennium at home, would be the greatest act of cowardice in her life.

  “I'll accept the staged experiments,” she declared. “I endorse Livia's proposal.”

  Rainzi said, “All in favor?”

  There was silence. Cass could hear crickets chirping. No one? Not Livia herself? Not even Darsono?

  She looked up.

  All seven Mimosans had raised their hands.

  Chapter 2

  Riding her ion scooter the million kilometers to the Quietener, Cass found herself reveling in the view for the first time in years. The scooter was doing one-and-a-quarter gees, but the couch pressed against her back so gently that she might have been floating. Floating in dark water, beneath an alien sky. Even at half a light-year, Mimosa punched a dazzling violet hole in the blackness, a pinprick ten times as bright as a full moon. Away from its glare, the stars were far too plentiful to suggest constellations; any stick-figure object that she began to sketch between them was soon undermined by an equally compelling alternative, then a third, then a fourth—like a superposition of graphs, each with a different choice of edges between the same nodes. When she'd first arrived, she'd homed in on her own star, watching with a mixture of fear and exaltation as it hovered at the edge of visibility to her thousandth-scale eyes. Now, she'd forgotten all the cues she'd need to find it, and she felt no urge to ask her navigation software to remind her. The sun was no beacon of reassurance, and she'd be seeing it close-up again soon enough.

  Each time one of Livia's staged targets had been achieved, Cass had dispatched a small army of digital couriers to pass on the news to seven generations of her ancestors and descendants,
as well as all her friends in Chalmers. She'd received dozens of messengers herself, mostly from Lisa and Tomek, full of inconsequential gossip, but very welcome. It must have grown strange for her friends as the years had passed, and they no longer knew whether or not there was any point continuing to shout into the void. If she had traveled embodied, as a handful of ancients still did, she could have caught up with centuries of mail on the return voyage. Reduced to a timeless signal en route, though, she'd have no choice but to step unprepared into the future. Her homecoming was going to be the hardest thing she'd ever faced, but she was almost certain now that her time here would prove to have been worth it.

  Half an hour before arrival, Cass rolled onto her stomach and poked her head over the edge of the couch. Her engine's exhaust was a barely perceptible flicker, fainter than a methanol flame by daylight, but she knew that if she reached down and placed her hand in the stream of plasma, she'd rapidly lose any delusion that her Mimosan body was indestructible.

  She watched the Quietener growing beneath her, the silvery sphere glinting Mimosa-blue. Surrounding it was a swarm of smaller, twinned spheres, unevenly colored and far less lustrous. Tethers, invisibly slender, allowed the twins to orbit each other, while ion jets balanced the slight tug of the Quietener's gravity, keeping each pair's center of mass fixed against the stars.

  The Quietener made it possible to perform experiments that could never be carried out elsewhere. The right distribution of matter and energy could curve space-time in any manner that Einstein's equations allowed, but creating a chosen state of quantum geometry was a very different proposition. Rather than simply bending space-time in bulk, like a slab of metal in a foundry, it had to be controlled with the same kind of precision as the particles in a two-slit interference experiment. But the “particles” of geometry were twenty-five orders of magnitude smaller than atoms, and they could never be vaporized, ionized, or otherwise coaxed apart to be handled one by one. So the same degree of delicacy had to be achieved with the equivalent of a ten-tonne lump of iron.

  Refining the starting material helped, and the Quietener did its best to screen out every form of impurity. Ordinary matter and magnetic fields absorbed or deflected charged particles, while a shell of exotic nuclei, trapped by gamma-ray lasers in states from which they could not decay without absorbing neutrinos, mopped up a greater fraction of the billions wandering by than would have been stopped by a galaxy's-worth of lead.

  Gravitational waves passed through anything, so the only antidote was a second train of waves, tailored to cancel out the first. There was nothing to be done about sporadic cataclysms—supernovae, or black holes gorging on star clusters in the centers of distant galaxies—but the most persistent gravitational waves, coming from local binary stars, were cyclic, predictable, and faint. So the Quietener was ringed with countersources, their orbits timed to stretch space at the center of the device when the bodies they mimicked squeezed it, and vice versa.

  As Cass passed within a few kilometers of one of the counter-sources, she could see the aggregate rocky surface that betrayed its origins in Mimosa's rubble of asteroids. Every scrap of material here had been dragged out of that system's gravity well over a period of almost a thousand years, a process initiated by a package of micron-sized spores sent from Viro, the nearest inhabited world, at ninety percent of lightspeed. The Mimosans themselves had come from all over, traveling here just as Cass had once the station was assembled.

  The scooter's smooth deceleration brought her to a halt beside a docking bay, and she was weightless again. Whenever she was close enough to either the station or the Quietener to judge her velocity, it seemed to be little more than that of a train, giving the impression that in the five-hour journey she might have traveled the width of a continent on Earth. Not to the moon and back, and more.

  One wall of the bay had handholds. As Cass pulled herself along, Rainzi appeared beside her. The Mimosans had dusted projectors and cameras all over the walls of the places she visited in the Quietener, rendering guest and host mutually visible.

  “This is it!” Rainzi said cheerfully. “Barring untimely supernovae, we'll finally get to see your graph complete.” The software portrayed him with a jet pack, to rationalize his ability to follow her uneven progress up the wall without touching anything.

  Cass replied stoically, “I'll believe it when it happens.” In fact, from the moment Ilene had scheduled the run, twelve hours before, Cass had felt insanely confident that no more hurdles remained. Eight of the fourteen previous targets had been achieved at the first attempt, making the prospect of one more tantalizingly plausible. But she was reluctant to admit to taking anything for granted, and if something did go wrong it would be easier to swallow her disappointment if she'd been pretending from the start that her expectations had always been suitably modest.

  Rainzi didn't argue, but he ignored her feigned pessimism. He said, “I have a proposition for you. A new experience you might like to try, to celebrate the occasion. I suspect it will be against all your high-minded principles, but I honestly believe you'd enjoy it. Will you hear me out?”

  He wore a look of such deadpan innocence that Cass felt sure he knew exactly how this sounded in translation. If that was his meaning, the idea wasn't entirely absurd, or unwelcome. She'd grown fond of Rainzi, and if he'd never been quite as solicitous or as eager to understand her as Darsono, the truth was, that made him more intriguing. If they could find enough common ground to become lovers, it might be a fitting way to bid Mimosa farewell: sweeping away the mutually distorted views they had of each other. To remain loyal to the ideals of embodiment, here, she'd been forced to adopt a kind of asceticism, but that was definitely not a quality to which she'd ever aspired, let alone one for which she hoped to be remembered.

  She said, “I'm listening.”

  “For special events like this, we sometimes go nuclear. So I thought I'd ask whether you'd like to join us.”

  Cass froze, and stared at him. “Nuclear? How? Has someone solved all the problems?” Femtomachines built from exotic nuclei had been employed as special-purpose computers ever since the basic design had been developed, six thousand years before. For sheer speed, they left every other substrate in the dust. But as far as Cass knew, no one could make a femtomachine stable for more than a few picoseconds; they could perform a great many calculations in that time, but then they blew themselves apart and left you hunting through the debris for the answer. Gamma-ray spectroscopy could only extract a few hundred kilobytes, which was orders of magnitude too small even for a differential memory—a compressed description of experience that could be absorbed by a frozen reference copy of the person who'd actually lived through it. Cass might have missed the news of a breakthrough while she'd been on her way here from Earth, but if word had reached Mimosa Station at all she should have heard by now.

  “Nothing's changed in the technology,” Rainzi said. “We do it freestyle. One-way.”

  Freestyle meant implementing your mind on a substrate that underwent quantum divergence. One-way meant none of the end products of any version of the computation could be retrieved, and transferred back into your usual hardware. Rainzi was asking her to clone herself into a nuclear abacus-cum-time-bomb that would generate a multitude of different versions of her, while holding out no prospect of even one survivor.

  Cass said haltingly, “No, I'm sorry. I can't join you.” So much for feeling smugly unshockable for daring to contemplate cross-modal sex. She joked, “I draw the line at any implementation where I experience detectable weight changes every time I learn something.” Femtomachines shuffled binding energies equivalent to a significant portion of their own mass; it would be like gaining or losing half a kilogram several times a second, from the sheer gravity of your thoughts.

  Rainzi smiled. “I thought you'd say no. But it would have been discourteous not to ask.”

  “Thank you. I appreciate that.”

  “But you'd see it as a kind of death?”
r />   Cass scowled. “I'm embodied, not deranged! If a copy of my mind experiences a few minutes' consciousness, then is lost, that's not the death of anyone. It's just amnesia.”

  Rainzi looked puzzled. “Then I don't understand. I know you prefer embodiment, for the sake of having honest perceptions of your surroundings, but we're not talking about immersing you in some comforting simulation of being back on Earth. Your experiment should last almost six picoseconds. Running on a strong-force substrate, you'd have a chance to watch the data coming in, in real time. Of course, you'll receive a useful subset of the same information eventually, but it won't be as detailed, or as immediate. It won't be as real.”

  He smiled provocatively. “Suppose the ghost of Sarumpaet came to you in your sleep, and said: ‘I'll grant you a dream in which you witness the decay of the Diamond Graph. You'll travel back in time, shrink to the Planck scale, and see everything with your own eyes, exactly as it happened. The only catch is, you won't remember anything when you wake.’ You say you don't believe that the dreamer would be dying. So wouldn't you still want the dream?”

  Cass let go of one handhold and swiveled away from the wall. There wasn't much point objecting that he was offering her a view billions of times coarser than that, of a much less significant event. It wasn't a ringside seat at the birth of the universe, but it was still the closest she could hope to get to an event for which she'd already sacrificed seven hundred and forty-five years of her life.

  She said, “It's not the fact that I wouldn't remember the experience. If you've lived through something, you've lived through it. What worries me is all the other things I'd have to live through. All the other people I'd have to become.”

  Cass dated the advent of civilization to the invention of the quantum singleton processor. The Qusp. She accepted the fact that she couldn't entirely avoid splitting into multiple versions; interacting with any ordinary object around her gave rise to an entangled system—Cass plus cloud, Cass plus flower—and she could never hope to prevent the parts that lay outside her from entering superpositions of different classical outcomes, generating versions of her who witnessed different external events.