The Clockwork Rocket

white-hot.”

“I thought we proved that solids were stable,” Ausilia interjected. “In our last class with Severa.”

Yalda said, “What you did, I think, was show that there are several geometries that an array of luxagens can assume in which Nereo’s force, acting between them, would hold them in place. Is that right?”

“That’s how I understood it,” Ausilia replied.

“So how does that work?”

“Every luxagen is surrounded by hills and valleys of potential energy,” Ausilia said. “If you have a number of them, you can drop them all into their neighbors’ valleys, making a nice, neat pattern in which they should all prefer to stay put.”

“That’s perfectly true,” Yalda said. “But there are a couple of problems Severa wouldn’t have raised, to avoid confusing you while you were still learning the fundamentals.”

She sketched a basic one-dimensional example.

“A luxagen can sit in its neighbor’s energy valley,” she said. “And I’ve put it in the first valley, rather than any of the more distant ones, which are shallower than the first. But is that really the deepest place there is?”

There was silence for a few pauses, then Prospera offered, “The pit would be deeper.”

“Of course,” Yalda replied. “The pit centered on the luxagen itself is bottomless, though I’ve only drawn it going down a short way. Once they’re close enough, two positive luxagens just keep attracting each other ever more strongly, until they collide. So why don’t all the luxagens in a piece of rock simply end up falling into each other’s energy pits, until the whole rock has shrunk down to a speck?”

“Isn’t that like asking why the world doesn’t crash into the sun?” Fatima suggested. “If there’s any sideways motion, the two luxagens wouldn’t actually collide. If they started outside the pit, they’d just skim around it and end up outside again. And even if they had the right amount of energy to stay in the pit, wouldn’t they just orbit each other, like Gemma and Gemmo?”

“You’re right,” Yalda said. “But if two luxagens end up orbiting each other, there’s something more to think about: a luxagen moving back and forth makes light. If the luxagens create light, they need to provide true energy to do that. But to provide true energy—to lose it themselves and turn it into light—they need to gain kinetic or potential energy. So why don’t they end up moving faster and faster, and breaking the whole solid apart?”

Silence again. Then Giocondo—a young man Yalda could only name from his tag—said, “What if the luxagens are moving too fast to make light?”

Yalda waited a pause to let the other students ponder that. “Go on,” she said.

“There’s a maximum frequency of light,” Giocondo began tentatively. “In the equation for light, the sum of the squares of the frequencies in the four directions must equal a fixed number—so none of the individual frequencies can have squares that are bigger than that number. If a luxagen is moving back and forth with a greater frequency than that… it can’t create light in step with its motion, because there’s no such thing.”

Yalda said, “That’s correct. And eventually we’ll work through the calculations for the amount of true energy that an oscillating luxagen passes to the light field, and we’ll show that when the frequency crosses the threshold Giocondo’s just described, the energy flow drops to zero.”

“Then why is there still a problem?” Ausilia asked. “Oh… why don’t all the luxagens end up orbiting in one single energy pit?”

Prospera said, “Because the peaks around the pit keep getting higher. Maybe a few luxagens are orbiting in the same pits, but the more of them you throw in together, the higher the energy barrier around them becomes.”

“Right,” Yalda said. “The more luxagens you have, as long they’re sitting in each other’s pits or valleys, the potential just keeps adding up: all the valleys become deeper and all the peaks get higher. So eventually the pit would become inaccessible, because it’s surrounded by insurmountable peaks.”

Fatima said, “So that keeps all the luxagens from falling together completely, and the rest just end up in each other’s valleys rather than each other’s pits?”

“Go on,” Yalda pressed her.

“I suppose they’d roll around in the valleys too, just like they orbit around the pits,” Fatima mused.

“And if they roll fast enough in the valleys,” Giocondo added, “they’d be stable there too. They wouldn’t emit light and end up tearing the solid apart.”

Yalda was delighted. “Bravo, everyone! A few lapses into the class, and we have solids rendered almost solid again.”

Ausilia said, “Almost? What’s the catch?”

“The idea that Giocondo raised is very appealing,” Yalda said, “and as far as our measurements can guide us, it seems to be true. The energy pits and valleys in real solids seem to be shaped in such a way that the natural frequencies of motion for the luxagens are greater than the maximum frequency of light.

“The only trouble is: if a luxagen isn’t going to make any light at all, there can’t be any wobbles to its orbit in the pit, or its rolling around in the valley. If there was even the tiniest imperfection in its motion that progressed at a sufficiently low frequency, then that would start to generate light.”

“Which would make the imperfection stronger,” Ausilia realized. “So it would lose true energy faster, grow stronger even faster… and the whole thing would get out of control.”

Yalda said, “Exactly. And the thing is, the shape of the potential energy that we get from Nereo’s equation doesn’t allow for perfect orbits, or perfect rolling in the valleys. The main cycle can have a high enough frequency to avoid creating light, but the potential has built-in flaws that guarantee that there’ll be lower-frequency motion as well. It seems to be unavoidable.”

“But solids don’t blow themselves apart,” Fatima proclaimed irritably. “Not without a liberator.”

“Of course,” Yalda said. “So although we seem to have most of the story, although it almost adds up… there must be something we’re missing, something that nobody yet understands.”

She let them ponder that for a moment, but then moved on swiftly. Being told that you’d reached the point where you could only make progress by breaking new ground was a daunting thing to hear for the first time.

“The second mystery,” Yalda continued, “is the structure of particles of gas. There are plenty of symmetrical polyhedrons where putting a luxagen at every vertex gives you a mechanically stable configuration—which seems to make them good candidates for the little balls of matter of which we expect a gas to be comprised. But those polyhedrons share the problem solids have: the luxagens rolling in their energy valleys will always have some low frequency components to their motion, so they ought to give off light and blow the whole structure apart.

“There’s another problem as well, though: tiny, pure fragments of solids are sticky, as Sabino’s experiments have shown. But the gases that make up air don’t seem to be sticky at all; it’s as if the field around them has somehow canceled out, almost completely.

“A young friend of mine back home, Valeria, showed that a spherical shell of luxagens of the right size would have no external field, so you might think that a polyhedron of a similar size could get close to that perfect cancellation. The trouble is, the need for mechanical stability gives you one size for the polyhedron, and the need to cancel the external field gives you a different size. It seems to be impossible to meet both criteria at once.”

Some of the students were beginning to look dismayed. Proving the mechanical stability of an icosahedron built out of luxagens had not been an easy exercise, and now they had to accept that all that hard work had been nothing but the first step into a larger, unknown territory.

“The third mystery,” Yalda said, “is the strangest, and the most dangerous. The Peerless is surrounded by fine dust that we believe is the same kind of material that we saw back home as Hurtlers, when it burned up in the solar wind at close to infinite velocity. But we’ve more or less matched its velocity now… so why should it behave any differently toward us than any other dust?”

Tamara, another near-stranger to Yalda, had heard the theory that had begun circulating a few days after the