Vikram zoomed in on the diagram. “All phase shifts ultimately come from interactions—intersections of one world line with another. In the Kumar model, every network of world lines has a finite weave. At each intersection, there’s a tiny phase shift that makes time jump by about ten-to-the-minus-forty-three seconds… and it’s meaningless to talk about either a smaller phase shift, or a shorter time scale. So if you try to blue-shift a wave indefinitely, eventually you reach a point where the whole system no longer has the resolution to keep reproducing it.” As the wave packet spiraled in, it began to take on a smeared, jagged approximation of its former shape. Then it disintegrated into unrecognizable noise.
Cordelia examined the diagram carefully, tracing individual components through the final stages of the process. Finally she said, “How long before we see evidence of this? Assuming the model’s correct?”
Vikram didn’t reply; he seemed to be having second thoughts about the wisdom of the whole demonstration. Gisela said, “In about two hours we should be able to detect quantized phase in the experimental beams. And then we’ll have another hour or so before—” Vikram glanced meaningfully at her—privately, but Cordelia must have guessed why the sentence trailed off, because she turned on him.
“What do you think I’m going to do?” she demanded indignantly. “Collapse into hysterics at the first glimmering of mortality?”
Vikram looked stung. Gisela said, “Be fair. We’ve only known you three days. We don’t know what to expect.”
“No.” Cordelia gazed up at the stylized image of the beam that encoded them, swarming now with everything from photons to the heaviest mesons. “But I’m not going to ruin the Dive for you. If I’d wanted to brood about death, I would have stayed home and read bad flesher poetry.” She smiled. “Baudelaire can screw himself. I’m here for the physics.”
Everyone gathered round a single window as the moment of truth for
the Kumar model approached. The data it displayed came from what was essentially a two-slit interference experiment, complicated by the need to perform it without anything resembling solid matter. A sinusoidal pattern showed the numbers of particles detected across a region where an electron beam recombined with itself after traveling two different paths; since there were only a finite number of detection sites, and each count had to be an integer, the pattern was already “quantized,” but the analysis software took this into account, and the numbers were large enough for the image to appear smooth. At a certain wavelength, any genuine Planck scale effects would rise above these artifacts, and once they appeared they’d only grow stronger.
The software said, “Found something!” and zoomed in to show a slight staircasing of the curve. At first it was so subtle that Gisela had to take the program’s word that it wasn’t merely showing them the usual, unavoidable jagging. Then the tiny steps visibly broadened, from two horizontal pixels to three. Sets of three adjacent detection sites, which moments ago had been registering different particle counts, were now returning identical results. The whole apparatus had shrunk to the point where the electrons couldn’t tell that the path lengths involved were different.
Gisela felt a rush of pure delight, then an aftertaste of fear. They were reaching down to brush their fingertips across the weave of the vacuum. It was a triumph that they’d survived this far, but their descent was almost certainly unstoppable.
The steps grew wider; the image zoomed out to show more of the curve. Vikram and Tiet cried out simultaneously, a moment before the analysis software satisfied itself with rigorous statistical tests. Vikram repeated softly, “That’s wrong.” Tiet nodded, and spoke to the software. “Show us a single wave’s phase structure.” The display changed to a linear staircase. It was impossible to measure the changing phase of a single wave directly, but assuming that the two versions of the beam were undergoing identical changes, this was the progression implied by the interference pattern.
Tiet said, “This is not in agreement with the Kumar model. The phase is quantized, but the steps aren’t equal—or even random, like the Santi-ni model. They’re structured across the wave, in cycles. Narrower, broader, narrower again…”
Silence descended. Gisela gazed at the pattern and struggled to concentrate, elated that they’d found something unexpected, terrified that they might fail to make sense of it. Why wouldn’t the phase shift come in equal units? This cyclic pattern was a violation of symmetry, allowing you to pick the phase with the smallest quantum step as a kind of fixed reference point—an idea that quantum mechanics had always declared to be as meaningless as singling out one direction in empty space.
But the rotational symmetry of space wasn’t perfect: in small enough networks, the usual guarantee that all directions would look the same no longer held up. Was that the answer? The angles the two beams had to take to reach the detector were themselves quantized, and that effect was superimposed on the phase?
No. The scale was all wrong. The experiment was still taking place over too large a region.
Vikram shouted with joy, and did a backward somersault. “There are world lines crossing between the nets! That’s what creates phase!” Without another word, he began furiously sketching diagrams in the air, launching software, running simulations. Within minutes, he was almost hidden behind displays and gadgets.
One window showed a simulation of the interference pattern, a perfect fit to the data. Gisela felt a stab of jealousy: she’d been so close, she should have been first. Then she began to examine more of the results, and the feeling evaporated. This was elegant, this was beautiful, this was right. It didn’t matter who’d discovered it.
Cordelia was looking dazed, left behind. Vikram ducked out from the clutter he’d created, leaving the rest of them to try to make sense of it. He took Cordelia’s hands and they waltzed across the scape together. “The central mystery of quantum mechanics has always been: why can’t you just count the ways things can happen? Why do you have to assign each alternative a phase, so they can cancel as well as reinforce each other? We knew the rules for doing it, we knew the consequences—but we had no idea what phases were, or where they came from.” He stopped dancing, and conjured up a stack of Feynman diagrams, five alternatives for the same process, layered one on top of the other. “They’re created the same way as every other relationship: common links to a larger network.” He added a few hundred virtual particles, crisscrossing between the once-separate diagrams. “It’s like spin. If the networks have created directions in space that make two particles’ spins parallel, when they combine they’ll simply add together. If they’re anti-parallel, in opposing directions, they’ll cancel. Phase is the same, but it acts like an angle in two dimensions, and it works with every quantum number together: spin, charge, color, everything—if two components are perfectly out-of-phase, they vanish completely.”
Gisela watched as Cordelia reached into the layered diagram, followed the paths of two components, and began to understand. They hadn’t discovered any deeper structure to the individual quantum numbers, as they’d hoped they might, but they’d learnt that a single vast network of world lines could account for everything the universe built from those indivisible threads.
Was this enough for her? Her original, struggling for sanity back in Athena, might take comfort from the hope that the Dive clone had witnessed a breakthrough like this—but as death approached, would it all turn to ashes for the witness? Gisela felt a pang of doubt herself, though she’d talked it through with Timon and the others for centuries. Did everything she felt at this moment lose all meaning, just because there was no chance to carry the experience back to the wider world? She couldn’t deny that it would have been better to know that she could reconnect with her other selves, tell all her distant family and friends what she’d learnt, follow through the implications for millennia.