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.
Yatima glanced hopefully at the star they'd called Weyl. If it wasn't the last link in the chain, it had to be close. 'Eight and a half centuries later, the Diaspora reached Swift. From there, you know as much as I do.'
Paolo said, 'Forget Swift. What about Orpheus?'
'Orpheus?'
'Just because your clone didn't wake there—'
Yatima laughed. 'It's got nothing to do with that. Do you think an ancient, space-faring civilization will want to hear about every last novelty we've encountered in our travels?'
Paolo was unswayed. 'We wouldn't be here, if it wasn't for Orpheus. Orpheus changed everything.'
10
