Anthology 2. Luminous [1998, 2010]

by Greg Egan

  Prospero was stunned. He looked around the room expectantly, as if waiting for someone to speak up in defence of the Ballad.

  No one made a sound.

  This was it: the end of diplomacy. Gisela spoke privately to Cordelia, whispering urgently: ‘Stay in Cartan! No one can force you to leave!’

  Cordelia turned to her with an expression of open astonishment. ‘But I thought …’ She fell silent, reassessing something, hiding her surprise.

  Then she said, ‘I can’t stay.’

  ‘Why not? What is there to stop you? You can’t stay buried in Athena—’ Gisela caught herself; whatever bizarre hold the place had on her, disparaging it wouldn’t help.

  Prospero was muttering in disbelief now, ‘Ingratitude! Base ingratitude!’

  Cordelia regarded him with forlorn affection. ‘He’s not ready.’ She faced Gisela, and spoke plainly. ‘Athena won’t last for ever. Polises like that form and decay; there are too many real possibilities for people to cling to one arbitrary sanctified culture, century after century. But he’s not prepared for the transition; he doesn’t even realise it’s coming. I can’t abandon him to that. He’s going to need someone to help him through.’ She smiled suddenly, mischievously. ‘But I’ve cut two centuries off the waiting time. If nothing else, the trip did that.’

  Gisela was speechless for a moment, shamed by the strength of this child’s love. Then she sent Cordelia a stream of tags. ‘These are references to the best libraries on Earth. You’ll get the real stuff there, not some watered-down version of flesher physics.’

  Prospero was shrinking the podium, descending to ground level. ‘Cordelia! Come to me now. We’re leaving these barbarians to the obscurity they deserve!’

  For all that she admired Cordelia’s loyalty, Gisela was still saddened by her choice. She said numbly, ‘You belong in Cartan. It should have been possible. We should have been able to find a way.’

  Cordelia shook her head: no failure, no regrets. ‘Don’t worry about me. I’ve survived Athena so far; I think I can see it through to the end. Everything you’ve shown me, everything I’ve done here, will help.’ She squeezed Gisela’s hand. ‘Thank you.’

  She joined her father. Prospero created a doorway, opening up onto a yellow-brick road through the stars. He stepped through, and Cordelia followed him.

  Vikram turned away from the gravitational wave trace and asked mildly, ‘All right, you can own up now: who threw in the additional exabyte?’

  * * *

  ‘Freeeeee-dom! ’ Cordelia bounded across Cartan Null’s control scape, a long platform floating in a tunnel of colour-coded Feynman diagrams that were streaming through the darkness like the trails of a billion colliding and disintegrating sparks.

  Gisela’s first instinct was to corner her and shout in her face: Kill yourself now! End this now! A brief side-branch, cut short before there was time for personality divergence, hardly counted as a real life and a real death. It would be a forgotten dream, nothing more.

  That analysis didn’t hold up, though. From the instant she’d become conscious, this Cordelia had been an entirely separate person: the one who’d left Athena for ever, the one who’d escaped. Her extended self had invested far too much in this clone to treat it as a mistake and cut its losses. Beyond anything it hoped for itself, the clone knew exactly what its existence meant for the original. To betray that, even if it could never be found out, would be unthinkable.

  Tiet said sharply, ‘You didn’t raise her hopes, did you?’

  Gisela thought back over their conversations. ‘I don’t think so. She must know there’s almost no chance of survival.’

  Vikram looked troubled. ‘I might have put our own case too strongly. She might believe the same discoveries will be enough for her, but I’m not sure they will.’

  Timon sighed impatiently. ‘She’s here. That’s irreversible; there’s no point agonising about it. All we can do is give her the chance to make what she can of the experience.’

  A horrifying thought struck Gisela. ‘The extra data hasn’t over-burdened us, has it? Ruled out access to the full computational domain?’ Cordelia had compressed herself down to a far leaner program than the version she’d sent from Earth, but it was still an unexpected load.

  Sachio made a sound of indignation. ‘How badly do you think I did my job? I knew someone would bring in more than they’d promised; I left a hundredfold safety margin. One stowaway changes nothing.’

  Timon touched Gisela’s arm. ‘Look.’ Cordelia had finally slowed down enough to start examining her surroundings. The primary beams, the infrastructure for all their computation, had already been blue-shifted to hard gamma rays, and the colliding photons were creating pairs of relativistic electrons and positrons. In addition, a range of experimental beams with shorter wavelengths probed the physics of length scales ten thousand times smaller – physics that would apply to the primary beams about a subjective hour later. Cordelia found the window with the main results from these beams. She turned and called out, ‘Lots of mesons full of top and bottom quarks ahead, but nothing unexpected!’

  ‘Good!’ Gisela felt the knot of guilt and anxiety inside her begin to unwind. Cordelia had chosen the Dive freely, just like the rest of them. The fact that it had been a hard decision for her to make was no reason to assume that she’d regret it.

  Timon said, ‘Well, you were right. I was wrong. She certainly tunnelled out of Athena.’

  ‘Yeah. So much for your theory of closed trapped memetic surfaces.’ Gisela laughed. ‘Pity it was just a metaphor, though.’

  ‘Why? I thought you’d be overjoyed that she made it.’

  ‘I am. It’s just a shame that it says nothing at all about our own chances of escape.’

  * * *

  Each orbit gave them thirty minutes of subjective time, while the true length and time scales of Cartan Null shrank a hundredfold. Sachio and Tiet scrutinised the functioning of the polis, checking and re-checking the integrity of the ‘hardware’ as new species of particles entered the pulse trains. Timon reviewed various methods for shunting information into new modes if the opportunity arose. Gisela struggled to bring Cordelia up to speed, and Vikram, whose main work had been the nanomachines, helped her.

  The shortest-wavelength beams were still recapitulating the results of old particle accelerator experiments; the three of them pored over the data together. Gisela summarised as best she could. ‘Charge and the other quantum numbers generate a kind of angle between world lines in the networks, just like spin does, but in this case they act like angles in five-dimensional space. At low energies what you see are three separate subspaces, for electromagnetism and the weak and strong forces.’

  ‘Why?’

  ‘An accident in the early universe with Higgs bosons. Let me draw a picture …’

  There was no time to go into all the subtleties of particle physics, but many of the issues that were crucial outside Chandrasekhar were becoming academic for Cartan Null anyway. Broken symmetries were being restored as they spoke, with increasing kinetic energy diluting differences in rest mass into insignificance. The polis was rapidly mutating into a hybrid of every possible particle type; what governed their future would not be the theory of any one force, but the nature of quantum mechanics itself.

  ‘What lies behind the frequency and wavelength of a particle?’ Vikram sketched a snapshot of a wave packet on a spacetime diagram. ‘In its own reference frame, an electron’s phase rotates at a constant rate: about once every ten-to-the-minus-twenty seconds. If it’s moving, we see that rate slowed down by time dilation, but that’s not the whole picture.’ He drew a set of components fanning out at different velocities from a single point on the wave, then marked off successive points where the phase came full circle for each one. The locus of these points formed a set of hyperbolic wavefronts in space-time, like a stack of conical bowls – packed more tightly, in both time and space, where the components’ velocity was greater. ‘The spacing of the o
riginal wave is only reproduced by components with just the right velocity; they trace out identical copies of the wave at later times, all neatly superimposed. Components with the wrong velocity scramble the phase, so their copies all cancel out.’ He repeated the entire construction for a hundred points along the wave, and it propagated neatly into the future. ‘In curved spacetime the whole process becomes distorted, but, given the right symmetries, the shape of the wave can be preserved while the wavelength shrinks and the frequency rises.’ Vikram warped the diagram to demonstrate. ‘Our own situation.’

  Cordelia took this all in, scribbling calculations, cross-checking everything to her own satisfaction. ‘OK. So why does that have to break down? Why can’t we just keep being blue-shifted?’

  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 spiralled in, it began to take on a blurred, jagged approximation of its former shape. Then it disintegrated into unrecognisable 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 quantised 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 stylised 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 at 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 travelling 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 ‘quantised’, 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 artefacts, 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 quantised, but the steps aren’t equal – or even random, like the Santini 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 quantised, 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 backwards 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, criss-crossing 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, colour, 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 he
r? 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.

  But the whole universe faced the same fate. Time was quantised; there was no prospect of infinite computation before the Big Crunch, for anyone. If everything that ended was void, the Dive had merely spared them the prolonged false hope of immortality. If every moment stood alone, complete in itself, then nothing could rob them of their happiness.

  The truth, of course, lay somewhere in between.

  Timon approached her, grinning with delight. ‘What are you pondering here by yourself?’

  She took his hand. ‘Small networks.’

  Cordelia said to Vikram, ‘Now that you know precisely what phase is, and how it determines probabilities … is there any way we could use the experimental beams to manipulate the probabilities for the geometry ahead of us? Twist back the light cones just enough to keep us skirting the Planck region? Spiral back up around the singularity for a few billion years, until the Big Crunch comes, or the hole evaporates from Hawking radiation?’

  Vikram looked stunned for a moment, then he began launching software. Sachio and Tiet came and helped him, searching for computational short cuts. Gisela looked on, light-headed, hardly daring to hope. To examine every possibility might take more time than they had, but then Tiet found a way to test whole classes of networks in a single calculation, and the process sped up a thousandfold.