The Eternal Flame

37

“You need to understand,” Carla pleaded. “This kind of research is more like exploration than engineering. It doesn’t always take you where you expected to go.”

Silvano was unmoved. “We’re grateful for your efforts, Carla, but with all due respect it’s not your role to decide where the research is taking us.” He turned and addressed his fellow Councilors. “The Object is as real and solid as this mountain. We’ve seen it, we’ve visited it, we’ve brought its trajectory into step with our own—and in doing so, we’ve proved beyond doubt that it’s composed of a material that can serve as a powerful fuel. But now this petitioner wants us to divert resources away from the program to make use of this extraordinary boon and invest them in a new kind of matter made entirely of light!”

“Temporarily,” Carla stressed. “And if you’ll forgive me for correcting you, Councilor, an optical solid isn’t made entirely of light; the light waves form the energy landscape, but we still put luxagens into the valleys. The point of using that kind of system is that it would let us vary the energy levels relatively easily, so we could see if a rebounder can be made to work, in principle. Once that’s been established we’ll know whether or not it’s worth trying to manufacture an ordinary substance with similar properties. It might sound profligate to perform these experiments on a ‘solid’ that needs sunstone to be burned just to maintain its existence from moment to moment—but there is no practical alternative.”

“Can you be certain there’s nothing in the mountain already that would do the job?” Councilor Giusta asked.

“Very nearly,” Carla replied. “We’ve gone through the spectra of every kind of clearstone, and tried to infer the energy levels. That’s not a foolproof process, but to test all the same materials directly would take a generation, and it would use up far more sunstone than the protocols I’m actually proposing.”

“You’ve asked for a very large amount,” Giusta said, glancing down at Carla’s application.

“We need to run the coherent light sources at a very high intensity, to make the energy valleys deep enough,” Carla explained. “But once we’ve mastered this—and once we can reproduce the effect in an ordinary solid—it will act as a net energy source. If we can get to that stage, the project won’t require any more sunstone at all.”

Giusta looked to Silvano, then the rest of her colleagues, but no one had any more questions for Carla. Even Councilors Massimo and Prospero—who’d been as merciless with Assunto on the hazards of dealing with the Object as they’d been with Carla at the previous hearing—seemed embarrassed by the alternative she was offering. The rebounder was already tainted by the inevitable comparisons with pre-scientific myths, but to claim that she could conjure her own Eternal Flame from a crystal of light sounded like the hyperbole of a stage magician: not even an appeal to genuine credulity so much as an invitation to share a joke.

“We’ll adjourn now,” Giusta said. “Thank you for your testimony.”

When the Councilors had left the chamber, Carla was alone with Assunto.

“If you change your mind, you’ll always be welcome on the orthogonal matter team,” he said.

“Thank you.” Carla had no ill feeling toward him; someone was always going to take over the project after she abandoned it, and she couldn’t blame Assunto for being a persuasive advocate for the cause. She’d benefited from his skills often enough, herself.

“I’ve had some thoughts about the Rule of One recently,” Assunto confided. “I’d be interested to hear what you think.”

“Of course.” Since the night with Patrizia and Romolo when they’d split the Rule of Two in half, Carla had had no success in explaining the simpler but equally mysterious principle that remained: once you took spin into account, you never found more than one luxagen in the same state.

“When we have a system of two luxagens,” Assunto began, “we need to think of it as a wave that depends on the positions of both particles. So if one particle is mostly here and another is mostly there, we need the wave to have a bump where the combination of positions spells that out.”

He sketched what he meant.

“Right,” Carla said. “That’s how I think of it too.”

“But there’s a problem,” Assunto claimed. “Suppose we compare that with another wave, where we swap the two particles.”

“That’s really the same thing,” Carla protested. “A luxagen is a luxagen; it makes no sense to say that it’s the ‘first luxagen’ in one location and the ‘second one’ in the other. Unless they have different spins, and you’re using that to tell them apart?”

Assunto said, “No, no. Forget about spins for the moment, or just assume the spins are identical. Take it as given that we really can’t tell these luxagens apart.”

“Then the two situations are exactly the same,” Carla replied.

“So you’re saying there are two different waves that can be used to describe the same physical situation?”

“Yes,” Carla insisted. “It’s just a convention, a naming scheme: you have to make a choice, but the choice itself makes no difference.”

“All right,” Assunto agreed, though his assent sounded distinctly provisional. “But now suppose I want to compare the wave for this pair of luxagens with the wave for another pair that are in roughly the same positions. How exactly should I make the comparison? Which of the two waves should I use in each case? There are four possibilities in all. Half those possibilities give the two pairs of luxagens very similar waves… while the other half give them very different waves!”

Carla thought for a while. “Surely you just need to use the same scheme for both? I mean, it’s obvious that there ought to be some overlap between the two waves—and if you use different schemes there’s no overlap at all.”

“But if you can’t tell the luxagens apart,” Assunto pressed her, “how do you define ‘the same scheme’? How do you actually pick which luxagen of the pair gets its position assigned to which axis?”

“Hmm.” He’d forced her into a contradiction; she’d claimed the choice of schemes didn’t matter, but now she’d starting talking about the importance of selecting the right one, case by case.

“Do you have to peek at their locations first, then make sure you give the same axis to whichever particles are closest together?” Assunto was gently mocking her now.

“Hardly.” Carla stared at the four diagrams. She was starving, and she’d barely slept for the last three nights, but she wasn’t going to let him make a fool of her with this problem.

“You use both schemes,” she said finally. “Simultaneously. You add the wave where you use the first axis for the first particle to the wave where you use it for the second particle.”

She sketched the idea.

“The wave for the whole system is completely symmetrical,” she said. “It makes no difference if you swap the axes, or swap the particles. And when you compare two situations with two particles in roughly the same two places, you’re guaranteed to get a sensible result with some overlap between the waves.”

“I think you’re right,” Assunto said. He sounded pleased that they’d reached the same conclusion—but he wasn’t yet finished with the subject. “That’s one way of doing wave mechanics with identical particles.”

“One way?”

“It looks like the most natural choice,” he said. “But I don’t believe it’s the only one. What about this?”

“You subtract the waves instead of adding them?” Carla was confused. “But subtract them in what order? Aren’t you asking for the same problem again: which of two identical particles do you call the first?”

“No, because it makes no difference,” Assunto replied. “If you change the order, you just turn the whole wave upside down—and an overall change of sign like that has no effect on the physics of the wave.”

That was true. “But what’s the point?” Carla asked. “You end up with a wave with two bumps of opposite sign, instead of two identical bumps. The mathematics becomes a bit more complicated, but the final answers all turn out the same.”

“The final answers don’t depend on putting the particles in any particular order,” Assunto said. “But what makes you think they’re the same when you subtract the schemes as when you add them?”

Carla examined the diagram again. “If the particles get close together, the two waves you’re subtracting start to overlap.”

“Yes.”

“And if they’re in exactly the same state,” she realized, “you get nothing, zero.”

“Precisely.” Assunto buzzed softly. “Does that remind you of anything?”

“The Rule of One,” Carla said. “So you’re saying that you can never have two luxagens in the same state, because they follow this subtraction scheme, where the total wave for the pair would vanish?”

“Yes!”

“But why? Why can’t they follow the addition scheme?”

“It must be linked to the luxagen’s spin somehow,” Assunto said. “Think about the similarities! Take a luxagen, with spin of a half, and rotate it by a full turn: the rotation gives you the opposite of the original luxagen wave. A transformation that leaves most things unchanged leads to a change of sign. And now it turns out that we can get the Rule of One if we assume that swapping two luxagens in a pair—another transformation that might be expected to have no effect at all—also changes the sign of the overall wave.”

Carla remained silent, but she didn’t doubt his claim. These things could not be empty coincidences; Assunto was drawing close to a beautiful mystery.

He said, “I think we’re on the verge of explaining all the different properties of luxagens and photons. Photons are simply jumps between the energy levels in the light field, but with this clue I think there’s a chance we’ll find a way to see luxagens in the same terms. I used to believe that that was absurd, that the two things were completely incomparable… but look at the difference we can get from one small change in the way the wave is constructed! With photons, you add the different ways you can arrange them, so there’s no problem if a dozen photons are in the same state—it just means pushing one particular mode of the light field up a dozen energy levels. With luxagens, what we need to do is find the mathematical twist that stops you raising the energy of each mode once you’ve taken it to the first level—a way of guaranteeing that there’s either a single luxagen in that state, or none at all. Once we’ve translated the Rule of One into the language of fields, everything will be unified into a single picture.”

It was a glorious vision. And who with even a trace of curiosity in their soul wouldn’t wish to follow it: to see the deepest, simplest rules that governed light and matter finally spelt out?

Carla said, “If I joined you, what would happen to the rebounder?”

“Why not let that wait until the politics is more favorable?” Assunto suggested. “Silvano won’t be on the Council forever.”

“No?”

“Do you think we’ll see any real progress toward an engine based on orthogonal matter before the next election? Do you think we’ll see the old feeds dismantled to make way for new farms?”

“Probably not.” Carla regarded him with grudging admiration. “You’re just playing them, aren’t you? You don’t think an engine like that can be made to work at all.”

“Who knows what our descendants will achieve?” Assunto replied innocently. “But for now, this is the path of least resistance with the Council. So why not make the most of it? Whatever we can learn from experiments with orthogonal matter is sure to be worth knowing. If destroying two luxagens to make a pair of photons doesn’t give us insight into both kinds of particles, I don’t know what will. And you discovered that reaction, Carla! How can you not want to study it further?”

“I do,” she said. “But if I put the rebounder aside in the hope that the Council will eventually lose faith in the alternatives… I might not be around when they reach that position.”

“None of us are going to be around forever.” Assunto was probably six years older than her, which made his words a little less glib than they might have been. “Do you think either of us will live to see the Peerless decelerate, by any method?”

“Probably not,” Carla admitted.

“You’ve published your idea,” Assunto said. “It’s exciting and provocative; it certainly won’t be forgotten. If it can be made to work at all, you can be sure it will be put to use one day.”

“And you expect me to leave it at that?” Carla knew better than to try to force him to give his own verdict on the rebounder’s chances; the last time, all she’d managed to extract from him was an acknowledgment that it broke no laws in any obvious manner. “I know I’ll never see the home world, but it would still be something to know before I die that we’ve found a way to turn the Peerless around.”

“And what if you can’t prove that? What if you can’t make this thing work?” Assunto wasn’t goading her; there were a dozen ways she could end up facing that result, even if the basic idea was sound. “To live on the Peerless means handing half-solved problems on to our descendants. The ancestors had to accept that at the launch, but it’s no less true for this generation. There is no such thing for us as seeing an end to this. If you go looking for finality, you’re only going to be disappointed.”

The Councilors were returning. Carla didn’t try to read their faces as they entered the chamber; she turned her gaze to the floor. What had she been thinking—talking up the promise of the Object one day, declaring it redundant the next? The science was what it was, but she should have sought a way to shift the political momentum gradually—instead of standing in the path of Silvano’s blazing rocket, waving her arms and expecting him to change course.

Giusta announced the Council’s decisions. Assunto’s proposal had been accepted; the research into orthogonal matter would continue under his supervision.

“And Carla,” Giusta continued, “as intriguing as your idea was to the Council, we owe it to our descendants not to be reckless in our use of their legacy. If it turns out at some time in the future that we have less need to keep sunstone in reserve—a position to which Assunto’s project might well take us—then we would be prepared to reconsider your proposal. For now, though, we can’t risk disposing of such a large quantity of fuel for such an uncertain outcome.”