The Clockwork Rocket

died soon after she’d visited him in Red Towers—but she’d been longing to pursue his ideas about the interactions between light and matter.

“You explained it to me,” Valeria said, “three years ago, when I’d just started at the university. And you showed me the solution for a source consisting of a single point—a ‘luxagen’.”

“I remember.” Yalda had been trying to convey to her just how little was still known about the subject, while offering a glimpse of one crack in their ignorance that might yet be widened.

“Not long after that,” Valeria continued, “we were studying gravity. And I learned that the first thing Vittorio did after guessing the potential energy for a mass concentrated in a single point was to calculate what that meant for a mass arranged as a spherical shell.”

“Ah.” Yalda examined the sheet again, overcome with pride and delight. “And this is the equivalent, for the light field?”

“Yes.”

Yalda studied the results. “These sizes you’ve written, they’re the radius of each shell?”

Valeria said, “Yes. Vittorio showed that, outside the shell, the gravitational potential energy was exactly the same as it would have been if all the mass were just concentrated at the center, so I was hoping the light field would follow the same rule. When it didn’t, I thought I’d made a mistake, so I had to wait until I’d learned a different technique that I could use as a cross-check.”

Yalda was still trying to absorb the implications of what she was seeing. “For some sizes of shell… the external field vanishes completely?”

“That’s right,” Valeria confirmed. “That happens whenever the radius is a multiple of half the minimum wavelength. And when it’s an odd number of quarter-wavelengths, the interior field vanishes.”

Yalda would never have guessed that the undulating field from a myriad of point sources could cancel exactly over any extended region—let alone an infinite one, and from such a simple geometry. No wonder Valeria had doubted her first calculations; it was as if someone had claimed that a gross of clanging bells could be rendered inaudible merely by arranging them in a circle of just the right size.

“Have you shown Zosimo and Giorgio?”

Valeria said, “I wanted you to see it first.”

Yalda held the sheet aside and embraced her. “It’s a beautiful gift. Thank you.” Your mother should have been here to see this, she thought, but the words were too strange to speak aloud.

Lidia said, “I don’t want to risk annoying you both… but are these pictures of anything real?”

Yalda started to explain about the light field around the hypothetical particle Nereo had dubbed a luxagen, and how Valeria had added up that field for a multitude of luxagens arranged in a shell, but Lidia hushed her. “I meant something we can all see and touch.”

Yalda thought for a while. What did it mean that luxagens were normally surrounded by furrows in the light field, but in the right configuration the landscape around them could become perfectly flat?

She said, “How about something you can feel, but never see?”

“What, thin air?” Lidia joked.

“Exactly.” Yalda exchanged a glance with Valeria; she looked baffled for a moment, but then she understood.

“Nereo hoped that the light field might account for all the properties of matter,” Yalda explained. “Not just burning fuel and glowing petals, but how a rock holds together instead of crumbling, and how it resists being crushed down to a speck. Why dust is sticky, and fine dust even stickier… but an inert gas like air, which everyone thinks of as the finest dust of all, doesn’t stick to anything, not even itself.”

“And these pictures are the answer?” Lidia was bemused.

“Not to everything,” Yalda said, “but perhaps they’re a clue to the last puzzle. It’s not hard to see how solids could be built from luxagens: the particles would sit in the troughs of each others’ serrated fields, which would hold them a certain distance apart from each other in a kind of array. Two stones you pick up off the ground won’t stick to each other—even if you polish them flat—because with such vast numbers of particles you wouldn’t expect them to form a single, perfect array. But a speck of dust is lighter, and small enough for the internal geometry to be less of a mishmash; there’s more chance for everything to line up and make two specks adhere. So if gases are built from luxagens too—and are so fine as to be invisible—why don’t they stick together even more strongly?”

Lidia still didn’t see it; Yalda looked to Valeria for support.

“Suppose you arrange the luxagens in a spherical shell of just the right size,” Valeria said. “Then the force that makes most regular arrangements of luxagens sticky will vanish outside the shell. A shell like that won’t stick to anything—so maybe that’s what gases are made of.” She hesitated, then turned to Yalda. “I don’t think that quite works, though. If you look at the potential energy curves at the edge of the shells with no external field, they always slope in such a way as to produce an outward force—so wouldn’t that tear the shell itself apart?”

Yalda checked the diagrams. “Ah, you’re right,” she said. “So there must be something subtler going on.”

“See, we don’t have the answers here,” Daria joked. “We need the Peerless to go out and fetch them for us.”

“But this is close,” Yalda insisted. “If it’s not the whole story, it’s still a powerful hint.”

Yalda could have talked optics with Valeria all night, but that would only have made parting more difficult. “Have you seen your brother recently?” she asked.

“Two days ago,” Valeria replied. “I looked after the children while he went to the factory.”

“But you need to study!” Yalda hadn’t meant to blurt out a rebuke, but she couldn’t bear the thought of Valeria jeopardizing her own chances. “You can’t afford to do that all the time,” she added.

“I don’t; Valerio helps too. And Amelio has other friends as well.” Valeria was beginning to look uncomfortable; Yalda let it drop. Lidia and Daria would have helped with the children if Amelio had allowed it, but he was still angry with them for trying to persuade him and Amelia to wait. Yalda would never see Tullia’s grandchildren, but she suspected Amelio would relent in the end and heal the rift with his other honorary Aunts.

Lidia said, “I’m glad I missed the speeches, but I hope I haven’t missed all the food.” Yalda led them indoors, where Giorgio’s children were still running back and forth from the pantry, keeping everyone fed.

Yalda tried to keep the conversation from growing too solemn; she had no intention of making some kind of earnest declaration to each one of her friends, summing up and attempting to put right everything that had passed between them—as if they were business partners settling accounts. She had apologized often enough to Lidia for the unequal share she’d taken in the burden of raising the children, thanked Giorgio and Daria for their help at the times she’d received it, and offered encouragement to Valeria and Valerio whenever it had seemed likely to be well received. There was nothing more she could achieve with a few rushed words, and the last thing she wanted to do was sound like someone making death-bed reparations.

Around midnight, guests began making their excuses. Dozens of people from the university and the Solo Club—acquaintances with whom Yalda had played dice or argued some point of philosophy or physics—bid her good luck with the flight then departed without any fuss.

With the house almost empty, Giorgio approached her.

“Can we see you off at the station?” he asked.

“Of course.”

Yalda had no luggage; everything she owned was in Basetown already, and everything she’d need was in the mountain itself. The six of them walked together down the quiet streets, with Gemma high above them lighting the way.

On the platform, with just a lapse to departure, Valerio started humming and wailing. Yalda was bemused; they hadn’t been close since he was three. She bent down and embraced him, trying to quieten him before anyone else joined in.

“I’m not dying yet!” she joked. “Wait a year and a day, then you can mourn me. But don’t forget that I’ll have had a long life by then.”

Valerio couldn’t really make sense of this, but he recovered his composure. “I’m sorry, Aunty. Good luck with your journey.”

“Look after your brother,” she said. And try not to imitate him.