The exhibit spun them around with the reference frame. Then, its disembodied hand moving with them, it placed a particle on the outer slope of the ridge; unsurprisingly, it fell directly away from the center. A second particle, placed on the inner slope, fell straight into the well.
"No stable orbits." Orlando picked up the particle that was rolling away and tried to balance it precisely on the ridge, but he couldn't position it accurately enough. Paolo saw a flash of fear in his eyes, but he said wryly, "At least that means no Lacertas. Everything that's going to fall together would have done it long ago."
They walked on to the next exhibit, a model of the macrosphere's cosmological evolution. As matter clumped together under mutual gravitational attraction from the initial quantum fluctuations of the early macrosphere, rotational motion either cut in at some point and blew the condensing gas cloud apart, or the process "crossed over the ridge" and the collapse continued unchecked. Star systems, galaxies, clusters and superclusters, all stabilized by orbital motion, were impossible here. But the fractal distribution of the primordial inhomogeneities meant that the end products of the collapse process had a wide spectrum of masses. Ninety percent of matter ended up in giant black holes, but countless smaller bodies were predicted to form, sufficiently isolated to survive for long periods, including hundreds of trillions with a stability and energy output comparable to stars.
Orlando turned to Paolo. "Stars without planets. So where will the Transmuters be?"
"Orbiting a star, maybe. They could stabilize an orbit with light sails."
"Built out of what? There'll be no asteroids to mine. Maybe they created a lot of raw materials with the singularity when they first crossed through, but for anything new they'd have to mine the star itself."
"That's not impossible. Or they could live on the surface, if they chose. That's where any native life is expected to be found."
Orlando glanced back at the model, which included something like a Hertzsprung-Russell diagram, plotting the evolving distribution of stellar temperatures and luminosities. "I wouldn't have thought many stars would he cool enough. Except for brown dwarves, and they'd freeze completely in no time at all."
"You can't really compare temperatures. We're used to nuclear reactions being orders of magnitude hotter than chemical ones, making them inimical to biology. But in the macrosphere they both involve similar amounts of energy."
"Why?" Orlando's gestalt still betrayed a sense of unease, but he was clearly hooked now. Paolo gestured at an exhibit further along, beneath a rotating banner reading PARTICLE PHYSICS.
The macrosphere's four-dimensional standard fiber yielded a much smaller set of fundamental particles than the ordinary universe's six-dimensional one. In place of six flavors of quarks and six flavors of leptons there was just one of each, plus their antiparticles. There were gluons, gravitons, and photons, but no W or Z bosons, since they mediated the process of quarks changing flavor. Three quarks or three antiquarks together formed a charged "nucleon" or "antinucleon," similar to an ordinary proton or antiproton, and the sole lepton and its antiparticle were much like an electron and positron, but there was no combination of quarks analogous to a neutron.
Orlando scrutinized the table of particles. "The lepton is still much lighter than the nucleon, the photon still has zero rest mass, and the gluons still act like gluons… so what shifts the chemical energy closer to the nuclear?"
"You saw what happened with the gravity wells."
"What's that got to do with it? Ah. Same thing happens in an atom? Electrostatic attraction also goes from inverse-square to inverse-fourth, so there are no stable orbits?"
"That's right."
"Hang on." Orlando screwed his eyes shut, no doubt dredging ancient memories of his flesher education. "Doesn't the uncertainty principle keep electrons from crashing into the nucleus? Even if there's no angular momentum, the attraction of the nucleus can't squeeze the electron's wave too tightly, because confining its position just increases its momentum."
"Yes. But increases it how much? Confining a wave spatially has an inverse effect on the spread of its momentum. Kinetic energy is proportional to the square of momentum, making that inverse-square. So the effective 'force,' which is the rate of change of kinetic energy with distance, is inverse-cube."
Orlando's face lit up for a moment with the sheer pleasure of understanding. "So in three dimensions, a proton can't ever make an electron crash, because the uncertainty principle is just as good as centrifugal force. But in five dimensions, that's not good enough." He nodded slowly, as if coming to terms with the inevitability of it. "So the lepton's wave shrinks down to the size of the nucleon. Then what?"
"Once the lepton's inside the nucleon, it's kink—pulled inward by the portion of the charge that's closer to the center than it is itself, which is roughly proportional to the fifth power of the distance from the center. That means the electrostatic force stops being inverse-fourth-power, and becomes linear. So the energy well isn't bottomless; outside the nucleon it's too steep for the lepton to 'brace itself' against the sides, the way an electron does in three dimensions, but inside the nucleon the sides curve together and meet in a paraboloid."
They moved on to the first chemistry exhibit, which showed the paraboloid bowl at the bottom of the well, with a translucent electric-blue bell-shape superimposed over it: the lepton wave in its lowest-energy, ground state. Orlando reached in and touched it; it flickered into an excited state, breaking apart and deserting the center to form two distinct lobes, one of them color-coded red to indicate an inverted phase. After a few tau the whole wave flashed green, spontaneously emitting a photon, and fell back to its lowest energy level.
"So this is the macrosphere's equivalent of a hydrogen atom?"
Paolo prodded the wave himself, trying to get it to the next highest level. "More like a cross between a hydrogen atom and a neutron. There are no neutrons in the macrosphere, but a positive nucleon with a negative lepton buried in it to cancel its charge makes a rough imitation of one. Blanca called it a 'hydron.' If you try to join two of them together to make a 'hydron molecule' you end up with something more like deuterium." The exhibit, overhearing him, obligingly provided an animated demonstration.
Orlando exhaled heavily. "I don't know how you can take this so calmly. Do you really trust anyone in C-Z to build an entire working polis according to these rules?"
"Maybe not, but if they get it wrong we won't even know about it. I can't see us shipwrecked in the macrosphere with the hardware disintegrating slowly beneath us. It'll be all or nothing: a working polis, or a cloud of random molecules."
"You hope. How are they even going to make molecules, if every chemical bond triggers nuclear fusion?"
"Not every bond does. If you throw enough hydrous together, the leptons fill up all the energy levels where they're confined tightly within the nucleus, so the outermost ones end up protruding sufficiently to be able to bind two atoms together with a respectable separation between the nuclei. You have to fill up the first two levels completely, which takes twelve leptons—so every stable molecule needs to contain a few judiciously placed atoms of number 13 or higher. Atom 27 can form fifteen covalent bonds; it's the closest thing in the macrosphere to carbon." The exhibit showed them a three-dimensional shadow of a five-dimensional, sixteen-atom molecule: one atom of 27, joined to fifteen hydrons. Paolo said, "Think of this as a souped-up version of methane. If you knock off any of these hydrons and substitute a side branch, you can build all kinds of elaborate structures."