Schild’s Ladder

"In part, it’s the history," she admitted, relaxing slightly. "The lineage of the ideas. If some alien civilization had handed us Quantum Graph Theory on a stone tablet — out of the blue, in the eighteenth or nineteenth century — I might not feel the same way about it. But general relativity and quantum mechanics were among the most beautiful things the ancients created, and they’re still the best practical approximations we have for most of the universe. QGT is their union. If general relativity is so close to the truth that only the tiniest fragment can be missing, and quantum mechanics is the same…how much freedom can there be to encompass all of the successes of both, and still be wrong?"

Kusnanto Sarumpaet had lived on Earth at the turn of the third millennium, when a group of physicists and mathematicians scattered across the planet — now known universally as the Sultans of Spin — had produced the first viable offspring of general relativity and quantum mechanics. To merge the two descriptions of nature, you needed to replace the precise, unequivocal geometry of classical space-time with a quantum state that assigned amplitudes to a whole range of possible geometries. One way to do this was to imagine carrying a particle such as an electron around a loop, and computing the amplitude for its direction of spin being the same at the end of the journey as when it first set out. In flat space, the spins would always agree, but in curved space the result would depend on the detailed geometry of the region through which the particle had traveled. Generalizing this idea, crisscrossing space with a whole network of paths taken by particles of various spins, and comparing them all at the junctions where they met, led to the notion of a spin network. Like the harmonics of a wave, these networks comprised a set of building blocks from which all quantum states of geometry could be constructed.

Sarumpaet’s quantum graphs were the children of spin networks, moving one step further away from general relativity by taking their own parents' best qualities at face value. They abandoned the idea of any preexisting space in which the network could be embedded, and defined everything — space, time, geometry, and matter — entirely on their own terms. Particles were loops of altered valence woven into the graph. The area of any surface was due to the number of edges of the graph that pierced it, the volume of any region to the number of nodes it contained. And every measure of time, from planetary orbits to the vibrations of nuclei, could ultimately be rephrased as a count of the changes between the graphs describing space at two different moments.

Sarumpaet had struggled for decades to breathe life into this vision, by finding the correct laws that governed the probability of any one graph evolving into another. In the end, he’d been blessed by a lack of choices; there had only been one set of rules that could make everything work. The two grandparents of his theory, imperfect as they were, could not be very far wrong: both had yielded predictions in their respective domains that had been verified to hair’s-breadth accuracy. Doing justice to both had left no room for errors.

Livia said, "Conceptually, that argument is very appealing. But there could still be deviations from the rules — far too small to have been detected so far — that would change the outcome of your experiment completely."

"So it’s a sensitive test," Cass agreed. "But that’s not why I’ve proposed it." They were talking in circles. "If the rules hold, the graph I’ve designed should be stable for almost six-trillionths of a second. That’s long enough to give us a wealth of observations of a space-time utterly different from our own. If it doesn’t last that long, I’ll be disappointed. I’m not doing this in the hope of proving Sarumpaet wrong!"

Cass turned to Darsono, seeking some hint that he might share her exasperation, but before she could gauge his mood, Livia spoke again.

"What if it lasts much longer?"

Finally, Cass understood. "This is about safety? I’ve addressed the potential risks, very thoroughly — "

"On the basis that the Sarumpaet rules are correct."

"Yes. What other basis should I have used?" Phoenician astrology? Californian lithomancy? Cass resisted the urge to lapse into sarcasm; there was too much at stake. "I’ve admitted that there’s no certainty that the rules hold in every last untested circumstance. But I have nothing better to put in their place."