by Greg Egan
“Yes, but that’s no reason for the tunnel to grow longer, just because the mouths are moved apart in external space.”
“Wait. There’s a tiny correction to the total energy that does depend on length. If the wormhole is shorter than the path through external space, then the energy of the virtual particles passing through it will be slightly higher than the normal vacuum energy. So if the wormhole is free to adjust its length to minimize that energy, the internal distance between the mouths will end up the same as the external distance.”
“But the wormhole isn’t free to do that! Kozuch Theory won’t allow it to grow longer than ten-to-the-minus-thirty-five meters; in the six extra dimensions, the whole universe is no wider than that!”
Gabriel said dryly, “It seems Kozuch Theory has a few problems. First Lacerta, still unexplained. Now this.” The gleisners had put a non-sentient probe into orbit around the Lacerta black hole, but it had revealed nothing about the cause of the neutron stars’ collision.
They sat in silence for a while, legs hanging over the canyon’s edge, watching the green mist cascading down. In terms of a pure intellectual challenge, Gabriel couldn’t have hoped for more: Kozuch Theory would have to be completely re-assessed, or even replaced, and the instrument he’d spent the last eight hundred years helping to build would be at the center of the transformation.
It was only as a short cut to the stars that the Forge had turned out to be a complete waste of time.
Blanca said, “You’ve brought us closer to the truth. That’s never a defeat.”
Gabriel laughed bitterly. “No? There’s already talk of cloning a thousand copies of Carter-Zimmerman and dispatching them all in different directions, to help us catch up with the gleisners. If the wormholes had been instantly traversable they would have bound the whole galaxy together; we could have moved from star to star as easily as we jump from scape to scape. But now we’re destined for fragmentation. A few clones of C-Z will fly off to the stars, centuries will pass ... and by the time any news comes back the other polises will be past caring. We’ll all drift apart.” He scooped a handful of dust forward, speeding its fall over the precipice. “I was going to build a network spanning the universe. That’s who I was: the citizen who’d put it all in the palms of our hands. Who am I now?”
“Instigator of the next scientific revolution.”
“No.” He shook his head slowly. “I can’t turn that corner. I can live with failure. I can live with humiliation. I can meekly follow the gleisners into space, slower than light, accepting that there’s no better way after all. But don’t expect me to take the thing that’s poisoned my dreams and embrace it as some kind of triumphant revelation.”
Blanca watched him staring morosely into the distance. Ve’d been wrong, for all these centuries: the elegance of Kozuch Theory had never been enough for Gabriel. So the chance to uncover and remove its flaws was no consolation to him at all.
Blanca stood. “Come on.”
“What?”
Ve reached down and took his hand. “Jump with me.”
“Where?”
“Not to another scape. Here. Over the edge.”
Gabriel regarded ver dubiously, but he rose to his feet. “Why?”
“It will make you feel better.”
“I doubt it.”
“Then do it for me.”
He smiled ruefully. “All right.”
They stood on the edge of the rock, feeling the dust swirl down around their feet. Gabriel said, surprised, “It makes me uneasy, just knowing that I’m going to give up control of my icon. Must be something vestigial. You know even winged exuberants had a strong reaction against free fall? Diving was often a useful maneuver for them, but they retained an instinctive desire to put an end to it as soon as possible.”
“Well, don’t panic and fly off, or I’ll never forgive you. Ready?”
“No.” Gabriel craned his neck forward. “I really don’t like this.”
Blanca squeezed his hand and stepped forward, and the laws of the imaginary world sent them tumbling down.
* * *
9
–
Degrees of Freedom
« ^ »
Carter-Zimmerman polis, interstellar space
58 315 855 965 866 CST
21 March 4082, 8:06:03.020 UT
Blanca felt obliged to visit the Hull at least once a year. Everyone in Carter-Zimmerman knew that ve’d chosen to experience some subjective time on the trip to Fomalhaut — despite Gabriel’s decision to remain frozen for the duration — and there was really only one acceptable reason for doing that.
“Blanca! You’re awake!” Enif had spotted ver already, and he bounded toward ver on all fours across the micrometeorite-pitted ceramic, sure-footed as ever. Alnath and Merak followed, at a slightly more prudent velocity. Most of the Osvalds used embodiment software to simulate hypothetical vacuum-adapted fleshers, complete with airtight, thermally insulating hides, infrared communication, variably adhesive palms and soles, and simulated repair of simulated radiation damage. The design was perfectly functional, but since each space-going clone of Carter-Zimmerman polis was barely larger than one of these Star Puppies, having the real things as passengers was out of the question. The Hull was just a plausible fiction, a synthetic scape melding the real sky with an imaginary spacecraft hundreds of meters long; thousands of times heavier than the polis, it could only have been real if they’d postponed the Diaspora for a few millennia in order to manufacture enough antihydrogen to fuel it.
Enif almost collided with ver, but he swerved aside just in time, barely maintaining his grip. He was always showing off his finely honed Hull-skills, but Blanca wondered what the others would have done if he’d misjudged the adhesion and launched himself into space. Would they have violated the carefully simulated physics and magicked him back down? Or would they have mounted a somber rescue mission?
“You’re awake! Exactly one year later!”
“That’s right. I’ve decided to become your vernal equinox, keeping you in touch with the rhythms of the home world.” Blanca couldn’t help verself; ever since ve’d discovered that the Osvalds’ outlook made them lap up any old astrobabble like this as if it was dazzlingly profound, ve’d been pushing the envelope in search of whatever vestigial sense of irony might have survived their perfect accommodation to the mental rigors of interstellar travel.
Enif sighed happily, “You’ll be our dark sun rising, a nostalgic afterimage on our collective retina!” The others had caught up, and the three of them began earnestly discussing the importance of remaining in synch with the Earth’s ancient cycles. The fact that they were all fifth generation C-Z homeborn who’d never been remotely affected by the seasons didn’t seem to rate a mention.
When Carter-Zimmerman polis was cloned a thousand times and the clones launched toward a thousand destinations, the vast majority of citizens taking part in the Diaspora had sensibly decided to keep all their snapshots frozen until they arrived, side-stepping both tedium and risk. If a snapshot file was destroyed en route without having been run since the instant of cloning, that would constitute no loss, no death, at all. Many citizens had also programmed their exoselves to restart them only at target systems that turned out to be sufficiently interesting, eliminating even the risk of disappointment.
At the other extreme, ninety-two citizens had chosen to experience every one of the thousand journeys, and though some were rushing fast enough to shrink each trip to a few megatau, the rest subscribed to the curious belief that flesher-equivalent subjective time was the only “honest” rate at which to engage with the physical world. They were the ones who required the most heavy-handed outlooks to keep them from going insane.
“So, what’s new? What have I missed?” Blanca showed verself on the Hull no more than once or twice a year, letting the Osvalds assume that ve was spending the rest of the time frozen. Since ve’d chosen to wake at all only on this, the shortest of the journeys, such
a watered-down approach to the Diaspora Experience must have struck vis fellow passengers as consistent, if not exactly laudable.
Merak rose up on her hind legs, frowning amiably, the veins in her throat beneath her violet hide still pulsing visibly after her sprint. “You really can’t tell? Procyon’s shifted almost a sixth of a degree since you were last here! And Alpha Centauri more than twice as much!” She closed her eyes, for a moment too blissed-out to continue. “Don’t you feel it, Blanca? You must! That exquisite sense of parallax, of moving through the stars in three dimensions ...”
Blanca had privately dubbed the citizens who used this outlook — most, but not all of them Star Puppies — “the Osvalds,” after the character in Ibsen’s Ghosts who ends the play repeating senselessly, “The sun. The sun.” The stars. The stars. When they weren’t speechless with joy over parallax shifts, they were mesmerized by the fluctuations of variable stars, or the slow orbits of a few easily resolved binaries. The polis was too small to be equipped with serious astronomical facilities, and in any case the Star Puppies stuck slavishly to their limited, mock-biological vision. But they basked in the starlight, and reveled in the sheer distance and time scales of the journey, because they’d reshaped their minds to render every detail of the experience endlessly pleasurable, endlessly fascinating, and endlessly significant.
Blanca stayed for a few kilotau, allowing Enif, Alnath, and Merak to lead ver all the way around the imaginary ship, pointing out hundreds of tiny changes in the sky and explaining what they meant, stopping now and then to show ver off to their friends. When ve finally hinted that vis time was almost up, they took ver to the nose and gazed reverently at their destination. In a year, Fomalhaut hadn’t brightened noticeably, and there were no close stars to be seen streaming away from it, so even Merak had to admit that there was nothing much to single it out.
Blanca didn’t have the heart to remind them that they’d deliberately blinded themselves to the most spectacular sign of the polis’s motion: at eight percent of lightspeed, the Doppler-shift starbow centered on Fomalhaut was far too subtle for them to detect. The scape itself was based on data from cameras with single-photon sensitivity and sub-Angstrom wavelength resolution, so the sight was there for the asking, but the idea of cheating their embodiment to absorb this information directly, or even just constructing a false-color sky to exaggerate the Doppler effect to the point of visibility, would have filled them with horror. They were experiencing the trip through the raw senses of plausible space-faring fleshers; any embellishments could only detract from that authenticity, and risk leading them into the madness of abstractionism.
Ve bid them farewell until next time. They gamboled around ver, protesting noisily and pleading with ver to stay, but Blanca knew they wouldn’t miss ver for long.
* * *
Back in vis homescape, Blanca admitted to verself that ve’d actually enjoyed the visit. A brief dose of the Puppies’ relentless enthusiasm always helped shake up vis perspective on vis own obsession.
Vis current homescape was a fissured, vitreous plain beneath a deep orange sky. Mercurial silver clouds just a few delta from the ground rose in updrafts, sublimated into invisible vapor, then re-condensed abruptly and sank again. The ground suffered quakes induced by forces from the clouds that had no analogue in real-world physics; Blanca was beginning to get a feel for the patterns in the sky that presaged the big ones, but the precise rules, complex emergent properties of the lower-level deterministic laws, remained elusive.
This world and its seismology were just decoration and diversion, though. The reason ve’d elected to experience time on the voyage at all zig-zagged for kilodelta across the scape — and the trail of discarded Kozuch diagrams, failed attempts to solve the Distance Problem, would soon constitute the most significant feature of the plain, out-classing the fissures produced by even the strongest quakes.
Blanca hovered at the fresh end of the trail, taking stock of vis recent dismal efforts. Ve’d spent the last few megatau trying to patch an ugly system of “higher-order corrections” onto Kozuch’s original model, infinite regresses of wormholes-within-wormholes which ve’d hoped might sum to arbitrarily large, but finite, lengths — hundred-billion-kilometer fractals packed into a space twenty orders of magnitude smaller than a proton. Before that, ve’d tinkered with the process of vacuum creation and annihilation, ttying to get the space-time in the wormhole to expand and contract on cue as the mouths were repositioned. Neither approach had worked, and in retrospect ve was glad that they hadn’t; these ad hoc modifications were far too clumsy to deserve to be true.
After being used to create the antihydrogen to fuel the Diaspora, the Forge had been reclaimed by the small group of particle physicists in Earth C-Z not terminally disillusioned by the failure of its original purpose. Their experiments had now probed every known species of particle down to the Planck-Wheeler length, and so long as no traversable wormholes were produced the results remained perfectly consistent with Kozuch Theory. To Blanca, this strongly suggested that Kozuch’s original identification between particle types and wormhole mouths was correct, and whatever else needed to be overhauled or thrown out, that basic idea should remain intact as the core of a revised theory.
On Earth, though, there was a growing consensus that Kozuch’s whole model had to be abandoned. The six extra dimensions which allowed the wormhole mouths their diversity were already being described as “the mathematical fiction that misled physicists for two thousand years,” and theorists were urging each other to adopt a more “realistic” approach with all the puritanical vigor of scourge-wielding penitents.
Blanca accepted that it was possible that all of Kozuch Theory’s successful predictions were due to nothing but the “mirroring” of the logical structure of wormhole topology in another system altogether. The motion under gravity of an object dropped down a borehole passing through the center of an asteroid obeyed essentially the same mathematics as the motion of an object tied to the free end of an idealized anchored spring — but pushing either model too far as a metaphor for the other generated nonsense. The success of Kozuch’s model could be due to the fact that it was just an extremely good metaphor, most of the time, for some deeper physical process which was actually as different from extra-dimensional wormholes as a spring was different from an asteroid.
The trouble was, this conclusion fitted the prevailing mood in C-Z far too well: the recriminations over the failure of wormhole travel, the backlash against the other polises’ continuing retreat from the physical world, and the increasingly popular doctrine that the only way to avoid following them was to anchor C-Z culture firmly to the rock of direct ancestral experience, and dismiss everything else as metaphysical indulgence. In that climate, Kozuch’s six extra dimensions could never be more than the product of a temporary misunderstanding of what was really going on.
Blanca had originally planned to spend no more than twenty or thirty megatau on the problem, then sleep for the rest of the voyage, satisfied that ve’d struggled long and hard enough to understand exactly how difficult it would be to find a solution. Ve’d guarded against investing too much hope in the prospect of helping Gabriel out of his post-Forge depression, despite fanciful visions of greeting him when he woke with the news that his soul-destroying “failure” had been transformed into the key to the physics of the next two thousand years. But the fact remained that Renata Kozuch had invented a universe of unsurpassed elegance, ruled by a set of economical and harmonious laws — and the bulletins from Earth were beginning to portray this marvelous creation as some kind of hideous mistake, as disastrous as the Ptolemaic epicycles, as wrong-headed as phlogiston and the aether. Blanca felt that ve owed Kozuch herself a spirited defense.
Ve ran vis Kozuch avatar; an image of the long-dead flesher appeared in the scape beside ver. Kozuch had been a dark-haired woman, shorter than most, sixty-two years old when she’d published her masterpiece — an anomalous age for spectacular achievement in the scie
nces, in that era. The avatar wasn’t sentient, let alone a faithful re-creation of Kozuch’s mind; she’d died in the early years of the Introdus, and no one really knew why she’d declined to be scanned. But the software had access to her published views on a wide range of topics, and it could read between the lines to some degree and extract a limited amount of implicit information.
Blanca asked, for the thirty-seventh time, “How long can a wormhole be?”
“Half the circumference of the standard fiber.” The avatar, not unreasonably, injected a hint of impatience into Kozuch’s voice. And though it paraphrased inventively, the answer was always the same: about five times ten-to-the-minus-thirty-five meters.
“The standard fiber?” The avatar gave ver something approaching a look of exasperation, but Blanca pleaded stubbornly, “Remind me.” Ve had to go back to the foundations; ve had to re-examine the model’s basic assumptions and find a way to modify them that made sense of the Distance Problem, but left the fundamental symmetries of the wormhole mouths intact.
The avatar relented; in the end it always cooperated, whether Kozuch herself would have or not. “Let’s start with a two-dimensional spacelike slice through a Minkowski universe — flat and static, the simplest possible toy to play with.” It created a translucent rectangle, about a delta long and half a delta wide, then bent it around so that the two halves were parallel, a hand’s width apart, one above the other. “The curvature here means nothing, of course; it’s necessary in order to construct the diagram, but physically it has no significance at all.” Blanca nodded, feeling slightly embarrassed; this was like asking Carl Friedrich Gauss to recite multiplication tables.
The avatar cut two small disks out of the diagram, one in the top plane and the other directly beneath it. “If we want to connect these circles with a wormhole, there are two ways of doing it.” It pasted a thin rectangular strip into the diagram, joining a small part of the top hole’s rim to the matching segment of the bottom rim. Then it extended this tentative bridge all the way around both holes, spinning it out into a complete tunnel. The tunnel assumed an hourglass shape, tapering to a waist but never pinching closed. “According to General Relativity, this solution would appear to have negative energy in some reference frames, especially if it was traversable. The two mouths could still have positive mass, though, so I pursued some tentative quantum-gravity versions of this for a while, but in the end I could never make it work as a model for stable particles.”
