Schild’s Ladder

"I’ll try not to fret." Tchicaya thought of the directions on a map. If the dynamic-law vectors were north and east, then the new, unbiased, law-momenta vectors would be north-west and north-east. Both had equal portions of the old directions — if you counted west as being the negative of east, and only cared about the size of things, not their sign — and they were at right angles to each other. In three dimensions or more you needed to introduce complex numbers to pull off the same balancing act, but from there you could keep on going to any number of dimensions. The amounts of the original vectors you combined were just a series of complex numbers that moved around a circle in the complex plane; to get different vectors, all orthogonal to each other, you just moved around the circle at different rates.

"Now picture a state vector which has equal components when written as superpositions of the old set, or the new."

In two dimensions, that was easy: north-north-east lay at the same angle to north as it did to north-east, and the same angle to east as it did to north-west. In terms of the quantum mechanics Rasmah was describing, it had equal uncertainty in the two complementary variables: it did not obey a precise dynamic law, but nor did it have any precise law-momentum. It split the difference and compromised, in the most symmetrical way.

Rasmah continued. "These are the states Yann wants to scribe, because if you create one on the border, and then arrange to measure the same kind of state coming back, they yield the highest attainable probability of returning with information about the interior."

" The highest attainable probability? That’s a resounding declaration of confidence." Tchicaya had been hoping for something more reliable. He knew what quantum mechanics was like, but if his own Qusp could pluck certainty from the haze, granting him the ability to make unique decisions, surely Yann could work some similar trick with the vastly more powerful abstract machine behind the border?

Rasmah emerged from her visualization. "I know how that sounds, but it really is the best we can hope for. We’re not arranged in the same way as the far side; we’re stuck in a dynamic-law eigenstate, and that’s always going to make things difficult."

"Yeah." Tchicaya was grateful for anything that took them beyond the current, artificial view of definite laws spread across the border, but it was sobering to realize how much stranger things became as the price of that advance. "I shouldn’t be disappointed, but I keep underplaying the problems in my head: sweeping all the hard parts off to one side, where I don’t have to look at them. If I faced the difficulties squarely, I’d probably just turn around and run."

Rasmah regarded him with a mixture of curiosity and affection. "You really do want to go through the border, don’t you?"

"I think so. What about you?"

"Absolutely. That’s what I came here to do." She hesitated, then added, "For a while, I thought I must have said something too extreme along those lines, and it put you off. But I don’t think that’s it. So what is it about me that you hate so much?"

Tchicaya shook his head vehemently. "Nothing."

"But we got halfway," she said, "and then you changed your mind." This wasn’t a question. Their bodies had ceased the silent exchange of pheromones, and that in itself would have dampened her feelings toward him, but it must have been clear to her that he was the one who’d halted the process.

"You’re very good company," Tchicaya said. "But you remind me too much of someone else, and I don’t feel right about that. I don’t want to confuse you with her; that wouldn’t be fair on either of us." He frowned apologetically. "Am I making any sense?"

Rasmah nodded uncertainly. "The other thing I thought was, maybe you and Yann were still, somehow — "

"No!" Tchicaya was taken aback. "Where did you hear about that?"

She waved a hand dismissively. "Everyone knows."

"Actually, I think Yann might have forgotten."

"But there is no one else, in the present? Just this nameless competitor from the past?"

Not exactly a competitor. And not wholly in the past. But Tchicaya didn’t want to explain any further. "That’s right."

"Okay." Rasmah stood, and Tchicaya rose beside her. In part, he was glad that she’d cleared the air, though at the same time he felt a surge of resentment, now that he’d been forced to put his reasons into words. He and Mariama would never be together. Why was he letting her shape his decisions at all?

"You’ll support Yann with this?" he asked.

Rasmah smiled. "Definitely. This is our best hope, and I’m sure I can sell it to the others. Suitably uglified."