"Diaspora" - читать интересную книгу автора (Иган Грег)9. Degrees of freedomCarter-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, trying 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 he 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 sciences, 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 he?" "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 time 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." It erased the hourglass-shaped tunnel, leaving the two holes disconnected again, then pasted a narrow strip between the left-hand side of the top rim and the right hand side of the bottom rim. As before, it extended the strip all the way around both circles, always connecting opposite sides of the rims, creating a pair of cones meeting at a point between the wormhole mouths. "This solution has positive mass. In fact, if GR held true at this scale, it would just be a pair of black holes sharing a singularity. Of course, even for the heaviest elementary particles the Schwarzschild radius is far smaller than the Planck-Wheeler length, so quantum uncertainty would disrupt any potential event horizons, and perhaps even smooth away the singularity as well. But I wanted to find a simple, geometrical model underlying that uncertainty." "So you expressed it by adding extra dimensions. If Einstein’s equations in four dimensions can’t pin down the structure of space-time on the smallest scale, then every "Exactly." The avatar gestured at the diagram, and it was subtly transformed: the translucent sheet became a mass of tiny bubbles, each one an identical perfect sphere. This was a heavily stylized view—rather like drawing a cylinder as a long line of adjoining circles—but Blanca understood the convention: every point in the diagram, though fixed in the two dimensions of the sheet, was now considered to be free to position itself anywhere on the surface of its own tiny sphere. "The extra space each point can occupy is called the The avatar created a fist-sized sphere floating above the main diagram, and covered it with a palette of colors that varied smoothly over the whole surface. "How does giving every point a 2-sphere to move in get around the singularity? Suppose we approach the center of the wormhole from a certain angle, and let the extra dimensions change like this." The avatar drew a white line down the sphere from the north pole toward the equator, and a colored line appeared simultaneously on the main diagram: a path leading straight into the top cone of the wormhole. The path’s colors came from the line being sketched on the sphere; they signified the values of the two extra dimensions being assigned to each point. As the line on the sphere crossed the equator, the path crossed between the two cones. "That would have been the singularity, but in a moment I’ll show you what’s become of it." The avatar extended the meridian toward the south pole, and the path through the worm hole continued on through the lower cone, and emerged in the bottom region of ordinary space. "Okay, that’s one geodesic. And in the classical version, all geodesics from one wormhole mouth to the other would converge on the singularity. But now…" It drew a second meridian on the sphere, starting again from the north pole, but heading for a point on the equator 180 degrees away. This time, the colored path that appeared on the wormhole diagram approached the top mouth from the opposite side. As before, when the meridian crossed the equator of the sphere, the path through the wormhole crossed between the two cones. Since the tips of the cones only touched at a single point, the second path had to pass through the same point as the first—but the avatar produced a magnifying glass and held it up to that point’s standard fiber for Blanca to see. The tiny sphere had two colored dots on opposite sides of its equator. The two paths never actually collided; the extra dimensions gave them room to avoid each other, even though they converged on the same point of ordinary space. The avatar gestured at the diagram, and suddenly the whole surface was color-coded for the extra dimensions. Far from the wormhole mouths the space was uniformly white—indicating that the extra dimensions were unconstrained, and there was no way of knowing any point’s position on the standard fiber. Within each cone, though, the space gradually took on a definite hue—red in the top cone, violet in the bottom—and then, close to the meeting point, the color began to vary strikingly with the angle of approach: vivid green on one side of the top cone, sweeping round to magenta 180 degrees away—a pattern that emerged inverted on the cone below, before melding smoothly into the surrounding violet, which in turn faded to white. It was as if every radial path through the wormhole had been lifted "up" out of the plane of this two-dimensional space to a slightly different "height" as it approached, allowing them all to "cross over" at the center without fear of colliding. The only real difference was that the extra-dimensional equivalent of "height above the plane" had to occur in a space that looped back on itself, so that a line rotated through 360 degrees could change "height" smoothly all the way, and still end up exactly where it began. Blanca gazed at the diagram, trying to see it from a fresh perspective despite the numbing familiarity of the concepts. "And a 6-sphere generates a whole family of particles, because there’s room to avoid the singularity in different ways. But you said you started with a 2-sphere. Do you mean later, when you were working with three-dimensional space?" "No." The avatar seemed somewhat bemused by the question. "I started exactly as you see here: with two-dimensional space, and a 2-sphere for the standard fiber." "But why a 2-sphere?" Blanca duplicated the diagram, but used a circle as the standard fiber instead of a sphere. Again, no two paths through the wormhole were the same color at the cross-over point; the main difference was that they took on different colors straight from the whiteness of the, surrounding space, because there were no "north and south poles" now from which they could spread out. "In two-dimensional space, you only need one extra dimension to avoid the singularity." "That’s true," the avatar conceded. "But I used a two-dimensional standard fiber because this wormhole possesses two degrees of freedom. One keeps the geodesics from colliding at the center. The other keeps the two mouths of the wormhole itself apart. If I’d used a circle as the standard fiber, then the distance between the mouths would have been fixed at precisely zero—which would have been an absurd constraint, when the whole point of the model was to mimic quantum uncertainty." Blanca felt vis infotrope firing up, frustrated but ever hopeful. They’d reached the heart of the Distance Problem. The exaggerated size of the cones in the diagram was misleading; the gravitational curvature of ordinary space around an elementary particle was negligible, and contributed virtually nothing to the length of the wormhole. It was the way paths through the wormhole coiled around the extra dimensions of the standard fiber that allowed them to be slightly longer than they would have been if the two mouths had simply been glued together, rim to rim. Or in reality, much more than slightly. "Two degrees of freedom," Blanca mused. "The width of the wormhole, and its length. But in your model, each dimension shares those two roles from the start—and if they don’t share them equally it gives nonsensical results." Blanca had tried distorting the standard fiber to allow for longer wormholes, but that had been a disaster. Stretching the 6-sphere into a 6-ellipsoid of astronomical proportions allowed for hundred-billion-kilometer wormholes like the Forge had produced, but it also implied the existence of "electrons" shaped like pieces of string of astronomical length. And changing the topology of the standard fiber, rather than just its shape, would have destroyed the correspondence between wormhole mouths and particles. The avatar responded, somewhat defensively, "Maybe I could have done it your way, starting with a circle to keep the geodesics apart. But then I would have had to introduce a second circle to keep the mouth apart-making the standard fiber a 2-torus. If I’d taken that approach, by the time I worked my way up to matching the particle symmetries I would have found myself lumbered with twelve dimensions: six for each purpose. Which would have worked just as well, but it would have been twice as extravagant. And after the debacle of string theory, it was hard enough selling anyone on six." "I can imagine." Blanca responded automatically, before ve’d fully absorbed what the avatar had said. A moment later, it hit ver. Twelve dimensions? Ve’d felt so besieged by the realist backlash that ve’d never even considered doing more than defending Kozuch’s six against the charge of "abstractionism." Twice as extravagant? It certainly would have been in the twenty-first century, when no one knew how long wormholes really were. But now? Blanca shut down the avatar and began a fresh set of calculations. Kozuch herself had never said anything so explicit about higher-dimensional alternatives, but the avatar’s educated guess turned out to be perfectly correct. Just as a 2-torus was the result of expanding every point in a circle into another circle perpendicular to the first, turning every point in a 6-sphere into a 6-sphere in its own right created a 12-torus—and a 12-torus as the standard fiber solved everything. The symmetries of the particles, and the Planck-Wheeler size of their wormhole mouths, could arise from one set of six dimensions; the freedom of the wormholes to take on astronomical lengths could then arise from the remaining six. If the 12-torus was much larger in the six "length" dimensions than the six "width" ones, the two scales became completely independent, the two roles entirely separate. In fact, the easiest way to picture the new model was to split up the whole four-plus-twelve-dimensional universe in much the same way as the ten-dimensional universe of the original Kozuch Theory—but with three levels, instead of two. The smallest six dimensions played the same role as ever: every point in four-dimensional space-time gained six sub-microscopic degrees of freedom. But the six larger dimensions made more sense if the roles were reversed: instead of a separate six-dimensional "macrosphere" for every point in the four-dimensional universe… there was a separate four-dimensional universe for every point in a single, vast, six-dimensional macrosphere. Blanca returned to the avatar’s wormhole diagram. It was easier to interpret now if the space was unfolded and laid flat; it could then be thought of as one slice of many through a small—and hence approximately flat—part of the macrosphere. One slice through a stack of universes. Blanca replaced the single microsphere at the center of the wormhole with a long chain of microspheres arcing from one mouth to the other, stringing together virtual wormholes from the vacuum of adjacent universes. An elementary particle would be stuck with a constant wormhole length, fixed at the moment of its creation, but a traversable wormhole would be free to tunnel its way into detours of arbitrary size. For the femtomouths produced in the Forge, the verdict was clear: they’d stolen enough vacuum from other universes—they’d snaked out far enough into the macrosphere’s extra dimensions—to equalize their lengths with the external distance between their mouths. Of course, no one in C-Z would believe a word of this; it was abstractionism run riot. These hypothetical "adjacent universes"—let alone the "macrosphere" they comprised in their totality—would always be impossible to observe. Even if a wormhole could be made wide enough for a tiny robot to fly through, looking to the sides would reveal nothing but a distorted image of the robot itself, as light circled the wormhole’s cross-sectional sphere. The other universes, as ever, would remain 90 degrees away from any direction in which it was possible to look, or travel. Still, the Distance Problem was solved, with a model that merely extended Renata Kozuch’s work, discarding none of her triumphs. Let them try bettering that in Earth C-Z! Neither ve nor Gabriel were running versions there—they’d left behind snapshots only to be run in the unlikely event that the whole Diaspora was wiped out—but Blanca thought it over and reluctantly dispatched a bulletin homeward, summarizing vis results. That was the correct protocol, after all. Never mind if the work was laughed at and forgotten; ve could argue the case in Fomalhaut C-Z, once there was someone awake worth arguing with. Blanca watched the silver clouds circulating; there was a big quake coming soon, but ve’d lost interest in seismology. And although there were a thousand things yet to be explored in the extended Kozuch model—how the four-dimensional universes that played "standard fiber" to the macrosphere determined its own strange particle physics, for one—ve wanted to save something for Gabriel. They could map that real but unreachable world together, physicist and scape artist, mathematicians both. Blanca shut down the glassy plain, the orange sky, the clouds. In the darkness, ve built a hierarchy of luminous spheres and set it spinning beside ver. Then ve instructed vis exoself to freeze ver until the moment they arrived at Fomalhaut. Ve stared into the light, waiting to see the expression on Gabriel’s face when he heard the news. |
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