by Greg Egan
“All four curves use the same mass ratio, of about three to ten,” Patrizia explained. “You can find that straight away, from the maximum scattering angle! And then the only parameter left to determine is the vertical scale.”
Carla reached over and took the plot from her. With a judicious choice of just two numbers, Patrizia’s model had nailed every point. A pattern like this didn’t happen by chance. What these curves implied was that the light scattering off the luxagens was behaving exactly like a particle, about three times as heavy as the ones it was striking.
Except… this plot wasn’t showing the energy of a particle, it was showing the frequency of a wave. What they’d actually measured for that vertical axis had been the scattered light’s subsequent deflection through a prism, and then that had been converted to wavelengths and frequencies using the prism’s calibration against a light comb. So how did energy come into it? The energy in a light wave depended on its brightness—something they hadn’t even tried to measure.
“Tell me,” Carla asked, “what do you think’s going on here?”
Patrizia spoke tentatively. “Surely this means there’s some kind of particle, moving at the speed of the light itself? Not trapped in the wavefronts, like a luxagen would be, but actually traveling with the light.”
“And the luxagens we released from the mirrorstone scattered this particle?”
“Yes.”
“And then what?” Carla asked indignantly. “The light that had been pushing this mystery particle along decides to follow it? The laws of mechanics tell us how the particle alone should be moving after the collision… and the light wave accommodates that by adjusting its own speed, adjusting its frequency, to maintain the original relationship? Is the light supposed to be propelling this particle—or is the particle magically dragging the light around?”
Patrizia flinched. Carla hadn’t realized how sarcastic her tone had become. “I’m sorry,” she said. “I didn’t mean to be dismissive. I’m just confused. I don’t know how to make sense of this.”
Patrizia looked up and met her gaze; they both knew exactly what was making the conversation so difficult. She said, “I’ve been trying to think how we could explain the tarnishing experiment, making use of this result. Suppose there’s some reason why light waves have to be accompanied by these particles—let’s call them ‘luxites’, just to give them a name.”
Carla managed to stifle a derisive buzz. “Luxite” was the term that had been used by disciples of the ninth-age philosopher Meconio, the man who had first proposed—without a trace of evidence—that light was composed of “luminous corpuscles”. Giorgio had buried that notion with his double-slit experiment, and Nereo and Yalda had built a whole mountain of wave theory on top of the grave. Patrizia wasn’t to blame for Meconio’s failings, but the name carried too much baggage.
“Let’s call them ‘photons’,” Carla suggested. “Different root, same meaning.”
“If the light-makers are called luxagens, shouldn’t the particles that accompany light share the same root?”
“People might confuse the two,” Carla said. “This will be clearer, trust me.”
Patrizia nodded, indifferent. “The rule is, the photon moves at the speed of the light pulse,” she continued. “But for that to be true, to create light of a certain frequency means creating photons with a certain energy. So if a process generates a particular frequency of light, that imposes a peculiar constraint on the amount of energy involved: you can create one photon, or two, or three… but your choices are confined to whole numbers. You don’t get to make half a photon.”
“Wait!” Carla interjected. “What about the energy in the light wave itself? How is that connected to the energy of these particles?”
Patrizia gave an apologetic hum. “I’m not sure. For now, can we just say that it’s very small? That most of the energy in the light actually belongs to the photons?”
“It’s your theory,” Carla said. “Go ahead.”
Patrizia shifted anxiously on the guide rope. “Suppose the energy valleys for the luxagens in mirrorstone all have a certain depth. The luxagens would have a bit of thermal energy as well, raising them off the floor of the valley, but if that doesn’t vary too much there’ll still be a particular amount of energy that a luxagen would need to gain in order to climb out of the valley and into the void—leaving behind a tarnished surface.”
“That’s a reasonable starting point,” Carla agreed. Nereo’s theory implied that the luxagens should have climbed out of the valley on their own, eons ago—as their thermal vibrations generated light and ever more kinetic energy—but since nobody else had managed to solve the stability problem it would hardly be fair to expect Patrizia to deal with it.
“When you hit the mirrorstone with light of a single frequency,” Patrizia said, “the luxagens vibrate in time with the light, and create light of their own. But creating light means creating photons. Suppose a luxagen creates one photon; that will give it a certain amount of kinetic energy, but it might not be enough to get it out of the valley. Two might not be enough either, or three, but suppose four is sufficient. So once it’s made four photons, the luxagen escapes, the mirrorstone gets tarnished.”
Carla was following her now. “But if the light striking the mirrorstone has a lower frequency, that corresponds to a smaller energy for each photon, and there’ll come a point where it suddenly takes five to do the job. So that’s the first transition point we see in the tarnishing pattern: on one side four photons bridge the energy gap, on the other side you need five.”
Patrizia said, “Yes. All the nonsense I came up with before about the luxagens in the valleys being struck by different numbers of ‘wandering luxagens’ pushed around by the light… that’s all gone! The four and the five in the frequency ratio are just the numbers of photons that have to be created by the luxagens in order to escape from the valley.”
A stint ago, Carla would have called this new version twice as nonsensical as the first. If you could ping a rope as hard or as gently as you liked, making waves in it as strong or as weak as you liked, why should waves in the light field be so different, burdened with these strange restrictions and appurtenances? But if you were willing to treat the frequency of light as a surrogate for the energy of a particle moving at the same speed, Patrizia’s plot through the scattering data brought this hypothetical “photon” to life, showing it behaving in precisely the manner you’d expect when one particle collided with another.
Carla said, “Before we begin praising the genius of Meconio, can you think of any way we can test this idea?”
“I haven’t been able to come up with any wholly new experiment,” Patrizia admitted. “But there’s something in the original experiment that we haven’t measured yet.”
“Go on.”
“The time it takes for each part of the tarnishing pattern to appear.”
Carla could see the merit in looking at that more closely. “If it takes a certain amount of time to create each photon, then the extra time required for successive tiers to reach a given tarnishing density should be the same. We’d need to push it to a longer exposure, though, and get another tier at frequencies so low that it takes six photons to leave a mark.”
Patrizia said, “It might not take the same time to produce a photon at different frequencies. What if the light that’s driving the process has to go through a certain number of cycles?”
“Like… cranking the handle on those mechanical loaf-makers? It’s the number of turns, not the time you spend turning.” Carla had no idea what was required to crank out a photon, so there was no obvious way to decide between the two criteria. “The period of violet light is only one and a half times that of red light; we can make a long enough exposure to test both possibilities, and see if either of them fits the results.”
Patrizia emitted a chirp of delight. “So we’re really going to test this theory?”
“Of course,” Carla replied. “Isn’t tha
t what we’re here for?”
When Patrizia had left, Carla took the groundnuts from the cupboard and went through her ritual. As she savored the odor, she realized that she’d rushed through the discussion too quickly, leaving too many problems unchallenged.
How could a luxagen “know” how long it had been exposed to light? Whether it was meant to be counting cycles of the light or simply recording the passage of time, what physical quantity could play the role of timer? Not the luxagen’s energy, or the jumps in the tarnishing pattern would have been smoothed away. The success of Patrizia’s theory relied on the axiom that you couldn’t make half a photon, but unless something was keeping track of the process—if it could not, in some sense, be half done—then why should it take any particular amount of time to create one of these particles?
The scattering curves were beautiful. The link between energy and frequency was beautiful. But the whole theory still made no sense.
Carla put the groundnuts away, wondering how she was going to persuade Assunto—who doubted the existence of particles of matter—to give her six times as much sunstone as before so she could now go hunting for particles of light.
13
Silvano had an announcement for his friends. “I’ve decided to run for the Council.”
Carlo was caught unprepared. By the time it occurred to him that it would be polite to offer a few words of encouragement, he also knew that he’d left it too late to sound sincere.
“What’s in it for us?” Carla joked.
“Ah, that would depend on how much help I get with the campaign.” Silvano reached out and grabbed his son Flavio, who had drifted away from the guide ropes and started to flail around in midair. The family’s new apartment had weaker gravity than the last one, but Carlo could understand why Silvano had felt compelled to move.
Carla said, “I’ll tout for you six days a stint if you can take the pressure off my department’s sunstone allocations.”
“Hmm.” Silvano wasn’t willing to make rash promises, even in jest. “Wait and see what they find with the Gnat. If it turns out that we can run the engines on orthogonal rock, you’ll have all the sunstone you could wish for.”
Carlo said, “What will you be campaigning on?”
“Farm expansion,” Silvano replied.
“Expansion?” Carlo was bemused. “Do you think you can find a structural engineer willing to gamble on squeezing in another layer of fields?”
“No, no! Everyone agrees that’s reached its limit; we have to look for other opportunities.” Flavio was starting to squirm out of his father’s grip; he wanted to get back on the rope with his co. Silvano released him and let him drag himself clumsily away.
“Such as…?” Carla pressed him.
Silvano said, “When the Gnat visits the Object, what might it find? Either the Object will be made of something violently reactive, which we can use as part of a new kind of fuel, or it will turn out to be nothing but ordinary rock.”
Carlo exchanged a glance with Carla. She didn’t accept this list as exhaustive, but she was willing to let it pass for the moment.
“If it’s the first case,” Silvano continued, “we’ll be rebuilding the engines completely to make use of the new reaction, which should give us a chance to reclaim some of the feed chambers for agriculture. But the second case would be even more promising: we won’t have solved the fuel problem… but we’ll certainly have a lot more space.”
Carla caught his meaning first, and it forced a chirp of admiration from her. “You want to turn the Object into a farm?”
“Why not?” Silvano replied. “We should be prepared to make the best of whatever the Gnat finds. If the Object turns out to be ordinary rock, there’ll be nothing to stop us cutting into it, making some chambers, spinning it up—”
Carlo said, “But if it’s ordinary rock, the Gnat won’t be able to halt it.” The whole idea that they could capture the Object was based on the assumption that it was made of a substance that would react with calmstone as dramatically as the specks that had once lit up the Peerless’s slopes.
“That’s true,” Silvano agreed. “We’d need to follow up quickly with a second expedition, carrying enough fuel to do the job with a conventional engine. But think what it would mean: in the long run, we could easily quadruple the harvest.”
Carlo didn’t reply. He couldn’t declare that this plan was impossible. But the workforce that had carried out the same kind of transformation on Mount Peerless itself—with all the benefits of air and gravity, and a planet’s worth of resources behind them—had vastly outnumbered its present population.
Carla said, “No one could accuse you of thinking small.”
“We need something like this,” Silvano replied. “A big project of our own, in the service of a common goal that might actually be achieved in our lifetimes.”
“A project of our own?” Carla’s tone remained friendly, but she made no attempt to hide her irritation. “So now everything gets classified that way? Is it for us, or is it for them?”
“You know what I mean,” Silvano said, impatient with her umbrage. “Even if we all had the skills to work on some ingenious scheme for rescuing the ancestors, none of us has the slightest chance of living to see the pay-off. Maybe you’re happy pondering the deep reasons why mirrors get tarnished—and maybe that will lead somewhere, in an age or two—but the only way that most of us can stay sane is to think about doing something for our own children and grandchildren. The generations we can actually… empathize with.” It sounded as if he’d been on the verge of invoking a closer connection than mere empathy, but then recalled just in time that his interlocutor would not be cuddling her own grandchildren.
“Just be careful what you promise,” Carlo warned him. “The Object will give its own verdict on all of these plans, and if you’ve talked up the prospect of quadrupling the harvest you might have some disappointed voters to deal with.”
Silvano was puzzled. “I told you: the whole point of my candidacy will be to ensure that people benefit regardless. If we can’t farm the Object, solving the fuel problem would certainly be a big boost to morale—but we have to be prepared to find more space for agriculture, whatever the Gnat discovers.”
“Rocket fuel or rock, you win either way?” Carla was finding the whole thing amusing. “I can see the posters already.”
When they’d left the apartment, Carlo turned to her. “You think there’s a chance we’ll end up farming the Object?”
“Anything’s possible,” she said. “Though if the whole thing’s as inert as calmstone and we end up relying on it, the fuel problem won’t just be unsolved, it will be doubled.”
“Yeah.” As a child, when he’d first understood that the Peerless had been loaded up far beyond its capacity to return, Carlo had railed against the ancestors—and now here was Silvano, contemplating doing exactly the same thing. “Do you want to run for the Council on a No Expansion platform? ‘Forget about a bigger harvest, people! There’s no point getting used to a mountain of extra food, when we have no way to decelerate a mountain of extra rock!’”
Carla buzzed wryly. “Maybe not. I can’t really blame Silvano, though. He doesn’t want his son to have to do what he did.” When Carlo didn’t reply she glanced across at him. “Your solution would be better, but it’s harder for most of us to believe in. We all know that a flying mountain can be turned into a farm, but for well-fed women to start having two children sounds more like turning people into voles.”
“Western shrub voles, to be precise,” Carlo replied. “They’re the biparous ones. But they have no males, so that doesn’t really help—breeding still doubles their numbers. As far as anyone knows, there’s never been an animal population that was stable in the absence of predation, famine or disease.”
“Don’t get discouraged,” Carla said, reaching over and putting a hand on his shoulder. “That’s just the history of life for the last few eons. It’s not as if it’s a law of physics.�
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14
Tamara woke in the clearing as the wheatlight was fading. She brushed the straw and petals off her body, then lay still for a while, luxuriating in the sensation of the soil against her skin. She was spoilt as a farmer’s co, she decided; she didn’t know how anyone could sleep in the near-weightlessness of the apartments. She’d never had any trouble doing her work in the observatory, and she often spent the whole day close to the axis, but having to be held in place by a tarpaulin every night, trying to cool yourself in an artificial bed’s sterile sand, struck her as the most miserable recipe for insomnia imaginable.
She rose to her feet and looked around. Tamaro was standing a short distance away; her father was up, but she couldn’t see him.
“Good morning,” Tamaro said. He seemed distracted, the greeting no more than a formality.
“Good morning.” Tamara stretched lazily and turned her face to the ceiling. Above them, the moss was waking; in the corridors the same species shone ceaselessly, but here it had learned to defer to the wheat. “Have you been up long?”
“A lapse or two,” he replied.
“Oh.” She’d half-woken much earlier and thought she’d sensed his absence—in the yielding of the scythe when she’d brushed an arm against it—but she hadn’t opened her eyes to check. “I should get moving,” she said. She had no urgent business to attend to, but when Tamaro was distant like this it usually meant that he was hoping she’d leave soon, allowing him to eat an early breakfast. That was probably what her father was doing right now.
He said, “Can I talk to you first?”
“Of course.” Tamara walked over to him.
“I heard about Massima,” he said.
“Yeah, that was a shame.”
“You never mentioned it.”
Tamara buzzed curtly. “It wasn’t that much of a shame. I would have been happy to have her with us, but it won’t affect the mission.”
