Luminous

by Greg Egan

  She didn’t reply. I tore up the image and let the pieces flutter to the ground.

  I didn’t take the subway. I needed the cold air to clear my head. So I walked back into the city, making my way between the ruins of the incomprehensible past, and the heralds of the unimaginable future.

  THE PLANCK DIVE

  Gisela was contemplating the advantages of being crushed – almost certainly to death, albeit as slowly as possible – when the messenger appeared in her homescape. She noted its presence but instructed it to wait, a sleek golden courier with winged sandals stretching out a hand impatiently, frozen in mid-stride twenty delta away.

  The scape was currently an expanse of yellow dunes beneath a pale-blue sky, neither too stark nor too distracting. Gisela, reclining on the cool sand, was intent on a giant, scruffy triangle hovering at an incline over the dunes, each edge resembling a loose bundle of straw. The triangle was a collection of Feynman diagrams, showing just a few of the many ways a particle could move between three events in spacetime. A quantum particle could not be pinned down to any one path, but it could be treated as a sum of localised components, each following a different trajectory and taking part in a different set of interactions along the way.

  In ‘empty’ spacetime, interactions with virtual particles caused each component’s phase to rotate constantly, like the hand of a clock. But the time measured by any kind of clock travelling between two events in flat spacetime was greatest when the route taken was a straight line – any detours caused time dilation, shortening the trip – and so a plot of phase shift versus detour size also reached its peak for a straight line. Since this peak was smooth and flat, a group of nearly straight paths clustered around it all had similar phase shifts, and these paths allowed many more components to arrive in phase with each other, reinforcing each other, than any equivalent group on the slopes. Three straight lines, glowing red through the centre of each ‘bundle of straw’, illustrated the result: the classical paths, the paths of highest probability, were straight lines.

  In the presence of matter, all the same processes became slightly skewed. Gisela added a couple of nanograms of lead to the model – a few trillion atoms, their world lines running vertically through the centre of the triangle, sprouting their own thicket of virtual particles. Atoms were neutral in charge and colour, but their individual electrons and quarks still scattered virtual photons and gluons. Every kind of matter interfered with some part of the virtual swarm, and the initial disturbance spread out through spacetime by scattering virtual particles itself, rapidly obliterating any difference between the effect of a tonne of rock or a tonne of neutrinos, growing weaker with distance according to a roughly inverse square law. With the rain of virtual particles – and the phase shifts they created – varying from place to place, the paths of highest probability ceased obeying the geometry of flat spacetime. The luminous red triangle of most-probable trajectories was now visibly curved.

  The key idea dated back to Sakharov: gravity was nothing but the residue of the imperfect cancellation of other forces; squeeze the quantum vacuum hard enough and Einstein’s equations fell out. But since Einstein, every theory of gravity was also a theory of time. Relativity demanded that a free-falling particle’s rotating phase agree with every other clock that travelled the same path, and once gravitational time dilation was linked to changes in virtual particle density, every measure of time – from the half-life of a radioisotope’s decay (stimulated by vacuum fluctuations) to the vibrational modes of a sliver of quartz (ultimately due to the same phase effects as those giving rise to classical paths) – could be reinterpreted as a count of interactions with virtual particles.

  It was this line of reasoning that had led Kumar – a century after Sakharov, building on work by Penrose, Smolin and Rovelli – to devise a model of spacetime as a quantum sum of every possible network of particle world lines, with classical ‘time’ arising from the number of intersections along a given strand of the net. This model had been an unqualified success, surviving theoretical scrutiny and experimental tests for centuries. But it had never been validated at the smallest length scales, accessible only at absurdly high energies, and it made no attempt to explain the basic structure of the nets, or the rules that governed them. Gisela wanted to know where those details came from. She wanted to understand the universe at its deepest level, to touch the beauty and simplicity that lay beneath it all.

  That was why she was taking the Planck Dive.

  The messenger caught her eye again. It was radiating tags indicating that it represented Cartan’s mayor: non-sentient software that dealt with the maintenance of good relations with other polises, observing formal niceties and smoothing away minor points of conflict in those cases where no real citizen-to-citizen connections existed. Since Cartan had been in orbit around Chandrasekhar, ninety-seven light years from Earth, for almost three centuries – and was currently even further from all the other spacefaring polises – Gisela was at a loss to imagine what urgent diplomatic tasks the mayor could be engaged in, let alone why it would want to consult her.

  She sent the messenger an activation tag. Deferring to the scape’s aesthetic of continuity, it sprinted across the dunes, coming to a halt in front of her in a cloud of fine dust. ‘We’re in the process of receiving two visitors from Earth.’

  Gisela was astonished. ‘Earth? Which polis?’

  ‘Athena. The first one has just arrived; the second will be in transit for another ninety minutes.’

  Gisela had never heard of Athena, but ninety minutes per person sounded ominous. Everything meaningful about an individual citizen could be packed into less than an exabyte, and sent as a gamma-ray burst a few milliseconds long. If you wanted to simulate an entire flesher body – cell by cell, redundant viscera and all – that was a harmless enough eccentricity, but lugging the microscopic details of your ‘very own’ small intestine ninety-seven light years was just being precious.

  ‘What do you know about Athena? In brief.’

  ‘It was founded in 2312, with a charter expressing the goal of ‘‘regaining the lost flesher virtues’’. In public fora, its citizens have shown little interest in exopolitan reality – other than flesher history and artforms – but they do participate in some contemporary interpolis cultural activities.’

  ‘So why have these two come here?’ Gisela laughed. ‘If they’re refugees from boredom, surely they could have sought asylum a little closer to home?’

  The mayor took her literally. ‘They haven’t adopted Cartan citizenship; they’ve entered the polis with only visitor privileges. In their transmission preamble they stated that their purpose in coming was to witness the Planck Dive.’

  ‘Witness – not take part in?’

  ‘That’s what they said.’

  They could have witnessed as much from home as any non-participant here in Cartan. The Dive team had been broadcasting everything – studies, schematics, simulations, technical arguments, metaphysical debates – from the moment the idea had coalesced out of little more than jokes and thought experiments, a few years after they’d gone into orbit around the black hole. But at least Gisela now knew why the mayor had picked on her; she’d volunteered to respond to any requests for information about the Dive that couldn’t be answered automatically from public sources. No one seemed to have found their reports to be lacking a single worthwhile detail, though, until now.

  ‘So the first one’s suspended?’

  ‘No. She woke as soon as she arrived.’

  That seemed even stranger than their excess baggage. If you were travelling with someone, why not delay activation until your companion caught up? Or, better yet, package yourselves as inter-leaved bits?

  ‘But she’s still in the arrival lounge?’

  ‘Yes.’

  Gisela hesitated. ‘Shouldn’t I wait until the other one’s all here? So I can greet them together?’

  ‘No.’ The mayor seemed confident on this point. Gisela wished interpoli
s protocol allowed non-sentient software to play host; she felt woefully ill prepared for the role. But if she started consulting people, seeking advice, and looking into Athena’s culture in depth, the visitors would probably have toured Cartan and gone home before she was ready for them.

  She steeled herself, and jumped.

  * * *

  The last person who’d whimsically redesigned the arrival lounge had made it a wooden pier surrounded by grey, windswept ocean. The first of the two visitors was still standing patiently at the end of the pier, which was just as well; it was unbounded in the other direction, and walking a few kilodelta to no avail might have been a bit dispiriting. Her fellow traveller, still in transit, was represented by a motionless placeholder. Both icons were highly anatomical-realist, clothed but clearly male and female, the unfrozen female much younger-looking. Gisela’s own icon was more stylised, and her surface, whether ‘skin’ or ‘clothing’ – either could gain a tactile sense if she wished – was textured with diffuse reflection rules not quite matching the optical properties of any real substance.

  ‘Welcome to Cartan. I’m Gisela.’ She stretched out her hand, and the visitor stepped forward and shook it – though it was possible that she perceived and executed an entirely different act, cross-translated through gestural interlingua.

  ‘I’m Cordelia. This is my father, Prospero. We’ve come all the way from Earth.’ She seemed slightly dazed, a response Gisela found entirely reasonable. Back in Athena, whatever elaborate metaphoric action they’d used to instruct the communications software to halt them, append suitable explanatory headers and checksums, then turn the whole package bit by bit into a stream of modulated gamma rays, it could never have fully prepared them for the fact that in a subjective instant they’d be stepping ninety-seven years into the future, and ninety-seven light years from home.

  ‘You’re here to observe the Planck Dive?’ Gisela chose to betray no hint of puzzlement; it would have been pointlessly cruel to drive home the fact that they could have seen everything from Athena. Even if you fetishised realtime data over lightspeed transmissions, it could hardly be worth slipping one-hundred-and-ninety-four years out of synch with your fellow citizens.

  Cordelia nodded shyly, and glanced at the statue beside her. ‘My father, really …’

  Meaning what? It was all his idea? Gisela smiled encouragingly, hoping for clarification, but none was forthcoming. She’d been wondering why a Prospero had named his daughter Cordelia, but now it struck her as only prudent – if you had to succumb to a Shakespearean-names fad at all – not to put anyone from the same play together in one family.

  ‘Would you like to look around? While you’re waiting for him?’

  Cordelia stared at her feet, as if the question was profoundly embarrassing.

  ‘It’s up to you.’ Gisela laughed. ‘I have no idea what constitutes the polite treatment of half-delivered relatives.’ It was unlikely that Cordelia did, either; citizens of Athena clearly didn’t make a habit of crossing interstellar distances, and the connections on Earth all had so much bandwidth that the issue would never arise. ‘But if it was me in transit, I wouldn’t mind at all.’

  Cordelia hesitated. ‘Could I see the black hole, please?’

  ‘Of course.’ Chandrasekhar possessed no blazing accretion disk – it was six billion years old, and had long ago swept the region clean of gas and dust – but it certainly left the imprint of its presence on the ordinary starlight around it. ‘I’ll give you the short tour, and we’ll be back long before your father’s awake.’ Gisela examined the bearded icon; with his gaze fixed on the horizon and his arms at his side, he appeared to be on the verge of bursting into song. ‘Assuming he’s not running on partial data already. I could have sworn I saw those eyes move.’

  Cordelia smiled slightly, then looked up and said solemnly, ‘That’s not how we were packaged.’

  Gisela sent her an address tag. ‘Then he’ll be none the wiser. Follow me.’

  * * *

  They stood on a circular platform in empty space. Gisela had inflected the scape’s address to give the platform ‘artificial gravity’ – a uniform one gee, regardless of their motion – and a transparent dome full of air at standard temperature and pressure. Presumably all Athena citizens were set up to ignore any scape parameters that might cause them discomfort, but it still seemed like a good idea to err on the side of caution. The platform itself was a compromise, five delta wide – offering some protection from vertigo, but small enough to let its occupants see some forty degrees below ‘horizontal’.

  Gisela pointed. ‘There it is: Chandrasekhar. Twelve solar masses. Seventeen thousand kilometres away. It might take you a moment to spot it; it looks about the same as the new moon from Earth.’ She’d chosen their co-ordinates and velocity carefully; as she spoke, a bright star split in two, then flared for a moment into a small, perfect ring as it passed directly behind the hole. ‘Apart from gravitational lensing, of course.’

  Cordelia smiled, obviously delighted. ‘Is this a real view?’

  ‘Partly. It’s based on all the images we’ve received so far from a whole swarm of probes, but there are still viewpoints that have never been covered and need to be interpolated. That includes the fact that we’re almost certainly moving with a different velocity than any probe that passed through the same location, so we’re seeing things differently, with different Doppler shifts and aberration.’

  Cordelia absorbed this with no sign of disappointment. ‘Can we go closer?’

  ‘As close as you like.’

  Gisela sent control tags to the platform, and they spiralled in. For a while it looked as if there’d be nothing more to see; the featureless black disk ahead of them grew steadily larger, but it clearly wasn’t going to blossom with any kind of detail. Gradually, though, a congested halo of lensed images began to form around it, and you didn’t need the flash of an Einstein ring to see that light was behaving strangely.

  ‘How far away are we now?’

  ‘About thirty-four M.’ Cordelia looked uncertain. Gisela added, ‘Six hundred kilometres, but if you convert mass into distance in the natural way, that’s thirty-four times Chandrasekhar’s mass. It’s a useful convention; if a hole has no charge or angular momentum, its mass sets the scale for all the geometry: the event horizon is always at two M, light forms circular orbits at three M, and so on.’ She conjured up a spacetime map of the region outside the hole, and instructed the scape to record the platform’s world line on it. ‘Actual distances travelled depend on the path you take, but if you think of the hole as being surrounded by spherical shells on which the tidal force is constant – something tangible you can measure on the spot – you can give them each a radius of curvature without caring about the details of how you might travel all the way to their centre.’ With one spatial dimension omitted to make room for time, the shells became circles, and their histories on the map were shown as concentric translucent cylinders.

  As the disk itself grew, the distortion around it spread faster. By ten M, Chandrasekhar was less than sixty degrees wide, but even constellations in the opposite half of the sky were visibly crowded together, as incoming light rays were bent into more radial paths. The gravitational blue shift, uniform across the sky, was strong enough now to give the stars a savage glint – not so much icy, as blue-hot. On the map, the light cones dotted along their world line – structures like stylised conical hourglasses, made up of all the light rays passing through a given point at a given moment – were beginning to tilt towards the hole. Light cones marked the boundaries of physically possible motion; to cross your own light cone would be to outrace light.

  Gisela created a pair of binoculars and offered them to Cordelia. ‘Try looking at the halo.’

  Cordelia obliged her. ‘Ah! Where did all those stars come from?’

  ‘Lensing lets you see the stars behind the hole, but it doesn’t stop there. Light that grazes the three-M shell orbits part-way around the hole befo
re flying off in a new direction – and there’s no limit to how far it can swing around, if it grazes the shell close enough.’ On the map, Gisela sketched half a dozen light rays approaching the hole from various angles; after wrapping themselves in barber’s-pole helices at slightly different distances from the three-M cylinder, they all headed off in almost the same direction. ‘If you look into the light that escapes from those orbits, you see an image of the whole sky, compressed into a narrow ring. And at the inner edge of that ring, there’s a smaller ring, and so on – each made up of light that’s orbited the hole one more time.’

  Cordelia pondered this for a moment. ‘But it can’t go on forever, can it? Won’t diffraction effects blur the pattern, eventually?’

  Gisela nodded, hiding her surprise. ‘Yeah. But I can’t show you that here. This scape doesn’t run to that level of detail!’

  They paused at the three-M shell itself. The sky here was perfectly bisected: one hemisphere in absolute darkness, the other packed with vivid blue stars. Along the border, the halo arched over the dome like an impossibly geometricised Milky Way. Shortly after Cartan’s arrival, Gisela had created a homage to Escher based on this view, tiling the half-sky with interlocking constellations that repeated at the edge in ever smaller copies. With the binoculars on 1000 X, they could see a kind of silhouette of the platform itself ‘in the distance’: a band of darkness blocking a tiny part of the halo in every direction.

  Then they continued towards the event horizon, oblivious to both tidal forces and the thrust they would have needed to maintain such a leisurely pace in reality.

  The stars were now all brightest at ultraviolet frequencies, but Gisela had arranged for the dome to filter out everything but light from the flesher visible spectrum, in case Cordelia’s simulated skin took descriptions of radiation too literally. As the entire erstwhile celestial sphere shrank to a small disk, Chandrasekhar seemed to wrap itself around them – and this optical illusion had teeth. If they’d fired off a beam of light away from the hole, but failed to aim it at that tiny blue window, it would have bent right around like the path of a tossed rock and dived back into the hole. No material object could do better; the choice of escape routes was growing narrower. Gisela felt a frisson of claustrophobia; soon she’d be doing this for real.