“You could always stay away from the experiments,” Carla suggested. “Assunto’s trying to build a field theory for luxagens. Don’t you want to be a part of that?”
Patrizia said, “If there’s a luxagen field permeating the cosmos, I expect it will still be around next year.”
“That’s true. But what’s your big plan for the coming year?”
“What are you going to do?”
Carla spread her arms, taking in the empty classroom. “Was I such a bad teacher?”
“Never. But is that enough?”
“I’m too tired for anything else,” Carla admitted. The news that Carlo’s best attempts to end the famine now involved the prospect of inserting signals from a mating arborine into women’s bodies had crushed whatever small hope she’d once had that she might free herself from the hunger daze. “Maybe someone will look at the rebounder again when the politics is right.”
“Forget about the politics,” Patrizia said blithely. “You won’t need to go begging for sunstone if you can make this work in an ordinary solid.”
“We’ve looked at every kind of clearstone in the mountain,” Carla protested. “Are you going to try cooking up something new?”
“Not exactly,” Patrizia replied. “But I just read Assunto’s paper on multi-particle waves and the Rule of One.”
Carla hesitated, turning the non sequitur over in her mind in the hope that a connection would become apparent.
It didn’t.
“Go on,” she said.
“According to Nereo’s theory,” Patrizia began, “if you take two tiny spheres with source strength and set them spinning, one beside the other, if the ‘north poles’ are sufficiently close they’ll try to repel each other. That means the system will have its highest potential energy if you force those poles together. The circumstances in which that happens will depend on both the directions in which the spheres are spinning and their relative positions.”
She sketched two examples.
“It’s an odd effect, isn’t it?” Carla mused. “Two positive sources attract, close up, but the poles of these spheres work the other way: like repels like.”
“It’s strange,” Patrizia agreed. “And I can’t claim that it’s ever been verified directly. Still, everything we know suggests that it’s true—and that it ought to apply to spinning luxagens, in addition to the usual attractive force.”
Carla said, “I wouldn’t argue with that.” They’d found that the energy of a single luxagen in a suitably polarized field depended on its spin, and there was no reason to think that the analogy would suddenly break down when it came to two spinning luxagens side by side.
Patrizia continued. “The Rule of One won’t let you have two luxagens with identical waves and the same spin—but that still leaves open the question of what happens to the spin when the waves themselves are different. If you take this pole-to-pole repulsion into account for two luxagen waves in the energy valley of a solid, on average it gives a higher potential energy when the spins are identical. So if the spins start out being different the system will emit a photon and gain the energy to flip one of the spins and make them the same. In other words, though the paired luxagens with identically shaped waves must have opposite spins, the unpaired ones ought to end up with their spins aligned!”
Carla wasn’t sure where this was heading. “The energy differences from these pole-to-pole interactions would be very small, and we probably don’t have the wave shapes exactly right. Do you really think this is a robust conclusion?”
Patrizia said, “I don’t, which is why I didn’t raise it with you before. But then I read Assunto’s explanation for the Rule of One, and that changes everything.”
“It ruins the effect?”
“No,” Patrizia replied. “It strengthens it enormously!”
Carla was bewildered. “How?”
Patrizia buzzed with delight. “This is the beautiful part. Assunto claims that for any pair of luxagens we need the overall description to change sign if we swap the particles. If the spins are identical, in order to satisfy that rule you need to subtract the swapped versions of the waves. But if the spins are different, you use the spins instead of the waves to do the job of changing the overall sign when you swap the particles. So in that case, you find the positions of the luxagens by adding the swapped versions of the waves.”
She sketched an example.
“By adding the waves,” she said, “you end up with a high probability of the luxagens being close to each other. Now compare that with the case where the spins are the same and you need to subtract the waves to get the change of sign. There’s a much lower probability of the luxagens coming close.”
“All from the spins,” Carla marveled. “And by changing the distance between the luxagens…”
“You change their potential energy,” Patrizia concluded. “Not from the weak, pole-to-pole repulsion, but from the attractive force between the luxagens. Through Assunto’s rule, having identical spins forces the average distance between the luxagens to be greater, which means a higher potential energy. So we’re back at the original conclusion: unpaired luxagens really should be spinning in the same direction.”
Carla paused and ran through the whole analysis again in her head; there were just enough twists in the argument that she was afraid they might have lost track of one of them and proved the opposite of what they’d thought they’d proved. “That does makes sense,” she concluded. “But what does it have to do with the rebounder?”
Patrizia said, “In an optical solid we could use the polarization of the light to create the kind of field where each luxagen’s spin affects its energy—splitting the usual energy levels by a very small amount. The tiny jump between those closely spaced levels would be a perfect match for the tiny shift in energy for photons rebounding from an imperfect mirror. I’m sure we could have made that work—but wouldn’t it be better to do it in an ordinary solid?”
Carla understood the connection now. “Enough luxagens all spinning in the same direction ought to produce a similar kind of polarized field within an ordinary solid. But we never saw any sign of it in the spectra of the clearstone samples.”
Patrizia adjusted her grip on the rope. “The spins within each valley ought to be aligned—but once you go any further, the waves overlap far less and the force between the luxagens starts cycling back and forth between attraction and repulsion. So we can’t rely on Assunto’s rule to produce any kind of long-range order. Beyond a certain point, the directions of the spins will just vary at random—producing fields with random polarizations that largely cancel each other out.”
“Right.” Carla hesitated. “Which is unfortunate, but what can we actually do about it?”
“Maybe nothing,” Patrizia conceded. “But there’s one thing we could try. If the geometry, the energy levels and the number of unpaired luxagens are all favorable… I think we could ‘imprint’ the regularity of an optical solid onto a real solid. The field pattern traveling through the optical solids we’ve made so far isn’t moving all that rapidly. There’s no reason we couldn’t shoot a real solid through the light field at the same speed; that way it would experience a fixed pattern. If we can expose the material to an ordered, polarized field for long enough, we might be able to achieve a long-range alignment between all the unpaired spins.”