Schild’s Ladder

Sophus said, "Tarek has looked into that, and even tried some experiments, but I believe it’s a dead end. For a start, we still don’t know what the bulk symmetries of this system are. I’ve more or less given up talking about the novo-vacuum; it’s too misleading. What vacuum? We don’t know that there’s state that lies in the null space of all annihilation operators for the Mimosan seed particles. And if there is such a state, we don’t know that it will obey anything remotely analogous to Lorentz invariance. Whatever’s behind the border might not even posses any kind of time-translation symmetry."

"You’re joking!"

"No. In fact, it’s looking more likely every day." Sophus glanced at Tchicaya meaningfully, as if he was waiting for the Preservationists' laudable openness to be acknowledged.

Tchicaya said, "That’s right. I watched one experiment myself, just a few hours ago." Mariama smiled at him, envious at this slight head start.

He smiled back at her, hoping his face wasn’t betraying his confusion. At the instant he’d seen her standing on the observation deck, he hadn’t consciously assumed anything about the faction she’d be joining; such ephemeral concerns had been swept from his thoughts entirely. Now that she’d casually revealed in passing that she’d come here to support the side that he would have sworn she’d be committed to opposing, the one part of his mind that resonated with this fact was the oldest, crudest model he had of her: someone whose only role in life was to confound and unsettle him. The original Mariama, who he had imagined would go to any lengths, not so much to spite him as to prove that he had no hope of pinning her down.

Tchicaya dragged his thoughts back to Sophus’s comments.

Kadir and Zyfete had been nowhere near as explicit, but then they’d not been in the friendliest of moods. Kadir’s despair made more sense now, though; it went beyond his growing fears for his home world, and one more ordinarily frustrating encounter with the border.

Time-translation symmetry was the key to all their hopes of predicting how the novo-vacuum would behave. In ordinary physics, if two people performed the same experiment, one starting work at midnight while the other began at noon, their separate versions could be compared, very easily: you merely added or subtracted half a day, and all their data could be superimposed. That sounded too obvious to be worth stating, but the fact that it was possible, and the fact that any laws of physics had to be compatible with this process of sliding the two sequences of events together, was a powerful constraint on the forms such laws could take.

Everything that happened in the universe was unique, on some level. If that were not true, there’d be no such thing as memory, or history; there’d be no meaningful chronology at all. At the same time, it was always possible to unpick some features of an event from the complicated tapestry of its context, and demand that this tiny patch of reality look the same as countless others, once you knew how to orient them all for the purpose of comparison. Taking a step north on Turaev on your eighteenth birthday could never be the same as taking a step west on Pachner four thousand years later, but in analyzing these two admittedly singular activities, you could safely abstract the relevant joints and muscles from the surrounding thicket of biographical and planetological detail, and declare that the applicable laws of mechanics were precisely the same in both cases.

It had been obvious since the accident that whatever the Mimosans had created in the Quietener did not possess the same symmetries as ordinary space-time, which allowed the unique location, time, orientation, and velocity of any physical system to be stripped away, revealing its essential nature. Still less had anyone expected the Mimosan vacuum to obey the "internal" symmetries that rendered an electron’s phase or a quark’s color as arbitrary as the choice of a planet’s prime meridian.

But everyone studying the novo-vacuum had been relying on the assumption that these familiar regularities had merely been replaced by more exotic ones. Mathematicians had long had a catalog of possibilities on offer that dwarfed those realized in nature: more or fewer dimensions, different invariant geometric structures, novel Lie groups for the transformations between particles. All of these things would be strange to encounter, but ultimately tractable. And at the very least, it had been taken for granted that there was some prospect of using the results of sufficiently simple experiments to deduce what would happen when those experiments were repeated. Once you lost that, prediction in the conventional sense became impossible. You might as well try to guess who you’d meet in a crowded theater on Quine by consulting the guest list for an opening night of Aeschylus.

Tchicaya said, "If you’re right, we’re wasting our time here."