“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.”
38
“Do you want to tell me what’s going on here?”
Tosco was halfway along the guide rope that crossed the chamber between the arborines’ cages; he must have entered while Carlo was in the storeroom. Carlo spent a moment contemplating his superior’s demeanor before deciding that there was no point in lying to him. He would not have been so angry unless he already knew at least part of the answer.