The Arrows of Time

by Greg Egan

  As she entered the observation chamber, she saw that at least six dozen people had shown up. The space couldn’t have held many more, but there were similar festivities taking place up and down the mountain’s rim. She squeezed her way through the crowd, moving aimlessly until someone called out to her.

  ‘Agata! Over here!’ It was Medoro’s sister, Serena. The whole family was gathered around a table by the edge of the dome.

  Agata approached, trying not to be distracted by the view before she’d greeted everyone. The lighting in the chamber was subdued, but she still needed to stare out at the sky to convince herself that she really was seeing it – that her vision wasn’t being blocked by reflections from the interior. All the long, orderly star trails she’d grown up with, the great meridional arcs that together filled half the sky, had shrunk into the kind of tiny, random lines of colour that she’d only ever known before as the signature of the orthogonal cluster. This was the ancestors’ sky. In less than a chime, the mountain would be at rest with respect to the home world. Apart from the effect of the Peerless’s displacement on the arrangement of the nearest stars, and apart from the absence of Hurtlers and the sister-world-turned-sun, Gemma, this was the view that anyone on the night side of the planet would be seeing right now.

  ‘Cira didn’t come?’ Medoro asked, feigning puzzlement.

  Agata wasn’t in the mood for jokes about her family – and apparently Medoro’s own relatives felt the same way: Gineto reached over and gave his nephew an admonitory thump on the arm, to Serena’s amusement. ‘Feel free to do that yourself whenever he annoys you,’ she suggested to Agata. ‘It’s the only way we manage to put up with him.’

  Vala said, ‘Agata and her mother have been through enough. Just let her enjoy the party.’

  Medoro cast Agata an imploring glance, as if he expected her to defend him.

  She said, ‘Don’t worry, nothing could spoil this day for me.’

  ‘Not even a Hurtler strike?’ he joked.

  Agata spread her arms and turned to face the sky. ‘Here we are, come and get us!’ For a day or two they’d be as vulnerable as the ancestors – but that felt more like a gesture of solidarity than a real source of danger.

  ‘Not even engine failure?’ Medoro persisted.

  ‘Our exhaust will be heading into the home cluster’s future,’ Agata replied. ‘That’s no different from the ancestors lighting a lamp, or the stars in the home cluster shining. There is no magical thermodynamic curse that can stop us making the turnaround. Or do you think Yalda and her friends couldn’t walk east when the Hurtlers’ arrow of time pointed west?’

  ‘And yet they were careful not to launch against the arrow,’ Medoro noted.

  ‘For which we should be grateful,’ Agata declared. ‘That let us observe the orthogonal cluster for six generations before losing sight of it. Better that than getting a surprise on the turn.’

  ‘Hmm.’ Medoro had run out of ways to needle her.

  Serena gestured at the food in front of them. ‘We’ve all been stuffing ourselves, so don’t be shy about catching up.’ Agata took a spiced loaf from the table. She hadn’t been able to eat with Cira in the apartment; every bite she took in her mother’s presence made her feel as if she were betraying her starving dead grandmother – who hadn’t actually starved for long, and whose co had helped her raise her machine-fathered daughter.

  Vala asked Agata how her research was progressing.

  ‘Still slowly,’ Agata confessed.

  Gineto hummed sympathetically. ‘What is it exactly that you’re doing? Medoro’s tried to describe it to us, but I’m not sure he really understands it himself.’

  ‘I’m just a humble instrument builder,’ Medoro said. ‘You can’t expect me to begin to comprehend Agata’s work.’

  Agata ignored his teasing, but Gineto seemed genuinely curious. And if he wasn’t, he was being too polite to be brushed off with ‘it’s complicated’.

  She said, ‘Do you know about Lila’s work?’

  ‘Vaguely,’ Gineto replied. ‘Didn’t she find a way to make gravity compatible with rotational physics?’

  ‘Exactly. Vittorio’s law of gravity assumed absolute time. Yalda must have known that it wasn’t rotationally invariant, but in those days the discrepancy wasn’t seen as important. People were busy enough trying to understand light.’

  ‘So . . . what changes?’ Gineto asked. ‘What does Vittorio’s inverse square law become?’

  ‘It’s trickier than that,’ Agata warned him. ‘In Lila’s theory, gravity isn’t a force at all, in the traditional sense: it’s a result of four-space being curved. You know how lines of longitude on a globe come together? Even though they start out parallel at the equator, they don’t remain the same distance apart.’

  ‘Right,’ Gineto agreed tentatively. There was nothing esoteric in the geometry she’d described, but he couldn’t quite see the connection.

  Agata said, ‘In Lila’s theory, gravitational attraction is the same kind of effect. When two massive bodies start out at rest with respect to each other – that is, with their histories parallel – they don’t stay the same distance apart, they accelerate towards each other. But you don’t need a force for that; all you need is curvature.’

  Gineto buzzed: he got it now. ‘That’s an elegant idea. Have the astronomers tested it?’

  ‘That’s the hardest part,’ Agata admitted. ‘The mathematics is beautiful, but we’re so far from any truly massive bodies that it’s almost impossible to devise a test.’

  ‘The ideal thing to study would be a planet orbiting close to its star,’ Medoro interjected. ‘Like the innermost planet in the home system. What was that called? Paolo? Peleo? I can never quite remember it.’

  Agata said, ‘Lila’s theory predicts that a close elliptical orbit would undergo “apsidal precession”: the near and far points of the orbit should move around the star, instead of staying fixed in space. So careful observations of a system like that could distinguish her theory from Vittorio’s.’ She sketched an example on her chest.

  ‘If there are other planets in the system it’s more complicated,’ she added. ‘The way they tug on each other will cause precession, too, so you have to separate out the various contributions. If we had copies of all the ancestors’ astronomical measurements we could hunt for some sign of Lila’s precession, but nobody thought to include that kind of thing in the library.’

  ‘And where does your own work fit into all this?’ Gineto pressed her.

  ‘My work’s about trying to understand entropy in the context of Lila’s theory,’ Agata replied. ‘According to Lila, the curvature of four-space depends on both the amount of matter present and the way it’s moving. If all the particles’ trajectories are neatly lined up, the curvature is different than when they’re moving around at random.’

  ‘Different how?’

  Agata said, ‘Ordered matter creates positive curvature along its time axis, so objects that start out at rest are drawn together. But sufficiently disordered matter produces negative curvature, with parallel histories spreading apart.’ She drew an illustration.

  ‘But when would the second case actually apply?’ Gineto wondered. ‘If you’re talking about a hot gas, won’t that always spread out into the void and become too thin to make any difference? Doesn’t the gravitational pull of a star come mostly from the rock beneath the fire – the solid part that actually stays put?’

  ‘That’s true, of course.’ Agata had underestimated him when she’d thought he might have just been making conversation. ‘In fact, Lila proved that a positive-temperature gas can’t be gravitationally bound – if the stars weren’t mostly rock, they couldn’t hold together at all! But on a large enough scale there might still be a disordered state that’s gravitationally significant. Our cluster moves one way, the orthogonal cluster another . . . and if you could step back far enough, you might see clusters moving in every direction in four-space. So it’s possible that something
analogous to a giant hot gas – with clusters of stars playing the role of particles – determines the overall curvature of the cosmos.’

  Serena said, ‘It’s getting close to the time.’

  All the partygoers were turning to face a screen mounted high on the chamber’s inside wall, showing an animation of an old-fashioned mechanical clock with its dials approaching the sixth bell. Hanging in the darkness behind the clock was an artist’s rendering of the home world. Medoro caught Agata’s eye, and he didn’t need to say a word for her to read his cynical mind: this was just the Council playing on their emotions. No doubt that was true, though to give them credit they hadn’t inserted any Hurtlers into the scene, poised to skewer the beloved planet.

  As the pause-dial on the clock neared twelve the chamber fell silent. To Agata the dial seemed to slow, each click forward taking longer than the last. But then the marks aligned and the room erupted with exuberant cheers. Medoro’s whole family were emitting deafening chirps – Medoro as enthusiastically as anyone. Agata felt her own tympanum thrumming, so she knew she was joining in, but the sound of the crowd was so overwhelming that she didn’t have a hope of discerning her own contribution to the din.

  After crossing a dozen vasto-severances of void, the Peerless had reached the farthest point in its trajectory, halted for an instant and reversed. They weren’t fleeing any more; they were on their way home. For the ancestors, a mere two years had elapsed since the launch, and with luck the travellers would return in two more.

  They would not be too late, Agata believed; they would not find a world in flames. The journey would fulfil its purpose – and the generations who’d endured the isolation of the mountain, who’d suffered through famine and turmoil, who’d struggled and died with no reward, would not have lived in vain.

  Overcome, she sank to the floor on folded legs, her face down-turned, her rear eyes closed. She’d seen the ancestors’ sky, she’d stood motionless beside them. What more could she have hoped for in her lifetime?

  But these moments of connection would never be repeated. All she had left was the distant promise of the reunion, as remote to her now as the launch.

  Someone touched her shoulder. Agata looked up, expecting Medoro’s hand, but it was his mother’s. The noise was still too great for there to be any point in speaking, but Vala’s face was eloquent: she shared the same bitter-sweet feeling.

  Agata rose to her feet, hoping that she hadn’t embarrassed her friends too much, but the whole room was full of distraught people, torn between celebration and loss.

  Medoro approached and put an arm around her. ‘It’s enough,’ he said. ‘It has to be enough.’

  ‘Of course.’ Agata willed herself to accept that.

  ‘I know you don’t want grandchildren,’ he teased her, ‘but you can always tell your stories to my niece’s kids.’

  Stories of the spin-down, the exotic gravity, the shrunken stars. All her life, she’d ached to live through these tangible signs that the voyage really would have an end. But now that ache felt worse than ever. When her apartment’s floor was horizontal again, when the giant stairwells were tunnels and the star trails had stretched out into coloured threads that squeezed into half the sky, what could she look forward to?

  Serena joined them, standing beside her brother. ‘How are you feeling?’ Agata asked her.

  ‘I couldn’t be happier!’ Serena spread her arms. ‘I know, everyone’s emotional, everyone’s confused . . . but what can I say? Octofurcate me: we’re headed home!’

  Agata was ashamed. How many people had kept up the struggle when there’d been no end in sight? She still had her work, she still had her friends, and she’d always have her memories of this day. What more did she want?

  ‘We’re headed home,’ she agreed. ‘That’s enough.’

  5

  Seated at his console in the main control room, Ramiro watched the image feed from the camera out on the slopes. At his behest, a small tethered engine ran through a series of moves, tugging on a set of restraining springs and force gauges that allowed its thrust to be measured.

  To his astonishment, the rules that the test rig was obeying remained as simple and intuitive as he could have wished: he could point the engine’s outlet any way he liked, and when he powered up the engine it generated thrust in the opposite direction. No exceptions, no complications – and no dependence at all on the disposition of distant worlds.

  ‘That’s disturbing,’ he told Tarquinia. An inset showed her in her office near the summit; she’d carried out the tests herself before inviting Ramiro to repeat them.

  ‘What did you expect?’ she asked. She wasn’t mocking him; it was a serious question.

  ‘I don’t know,’ Ramiro replied. ‘Maybe part of me always imagined this outcome, but I shouted it down as naïve.’

  ‘I never knew what to think,’ Tarquinia admitted. ‘My gut feeling – when I was looking at the engine in isolation – was that there’d be thrust in all directions. But all I had to do to change my mind was picture the consequences of that: all the specks of dust and gas out in the void that would need to conspire to make it happen.’ She sent Ramiro a sketch via her corset; it appeared in miniature in a second inset. ‘But then all I had to do to change my mind again,’ she added, ‘was to think of the engine magically “knowing” that it wasn’t meant to work when it was pointed towards the wrong part of the sky. That was just as hard to swallow as the alternative.’

  Ramiro said, ‘Well, now you’ve settled it. Either way, something had to offend our intuition – so we should be grateful that the chosen offence happens far away and out of sight.’ He enlarged Tarquinia’s sketch, which drove home the point: eerie as it would have been to watch the engine selectively fail, if they could have witnessed the actual results in every detail that would have been at least as unsettling.

  Unless the engine’s outlet was aimed at the Peerless itself, every photon it pumped out would eventually strike some distant object: usually just a particle of gas or dust belonging to one of the clusters. Given the present motion of the Peerless, it was easy to arrange the geometry so that the light would be arriving from the dust’s future – which meant that according to its own arrow of time, the dust would be emitting the light, not receiving it. By that account, the engine’s whole exhaust beam was being spontaneously emitted by countless tiny sources scattered across the void, just as much as it was being emitted by the engine’s own rebounders.

  ‘So the final slowdown shouldn’t be a problem,’ Ramiro realised belatedly.

  ‘If this holds up – no, it shouldn’t,’ Tarquinia agreed.

  Ramiro leant back from the console, pondering the political consequences. Even the staunchest reunionists had assumed that they’d be leaving their descendants with the burden of finding a way to start decelerating on the approach to the home world. But the tiny engine Tarquinia had set straining against its springs had had no difficulty achieving thrust in exactly the direction that the Peerless itself would need for that last manoeuvre. The migrationists had lost their most powerful scare story.

  But physics had lost a story of its own. From the point of view of the ultimate recipients of the engine’s exhaust, its successful firing was the kind of absurd picture that came from imagining time running in reverse, with the fragments of some shattered object reassembling themselves into the whole.

  ‘So much for the law of increasing entropy,’ Ramiro said.

  Tarquinia was unfazed. ‘That was never going to last.’

  ‘No.’ If the cosmos really did loop back on itself in all four dimensions, nothing could increase for ever. ‘But what do we put in its place?’

  ‘Observation.’ Tarquinia nodded towards the image of the test rig.

  ‘So everything becomes empirical?’ Ramiro was happy to be guided by experiments, so long as some prospect remained that they could yield the same result twice in a row.

  ‘The cosmos is what it is,’ Tarquinia replied. ‘The laws of o
ptics and mechanics and gravity are simple and elegant and universal . . . but a detailed description of all the things on which those laws play out seems to be nothing but a set of brute facts that need to be discovered individually. I mean, a “typical” cosmos, in statistical terms, would be a gas in thermal equilibrium filling the void, with no solid objects at all. There certainly wouldn’t be steep entropy gradients. We’ve only been treating the existence of one such gradient as a “law” because it was the most prominent fact in our lives: time came with an arrow distinguishing the past from the future.’

  Ramiro said, ‘But isn’t there still a question of how brutish the brute facts are? We know that the home cluster’s entropy was much lower in its distant past, and the same was true of the orthogonal cluster. The most economical explanation is that both clusters shared a common past.’

  Tarquinia said, ‘So you want to cling to the notion of parsimony? A single region of low entropy is already stupendously unlikely, but even if we have no choice about that, you want to hold the line and refuse to allow two?’

  ‘You don’t think that’s reasonable?’

  Tarquinia thought it over. ‘I don’t know what’s reasonable any more,’ she said.

  Ramiro closed his eyes for a moment, raising some crude scrawls on his chest based on Tarquinia’s diagram, but keeping them private. ‘Forget about whether or not the clusters have a common past; forget about the orthogonal cluster entirely. Suppose the only thing we rely on is the fact that the home cluster had vastly lower entropy in the past.’

  ‘All right.’

  ‘So the state of the home cluster long ago is already “special”,’ he said, ‘compared to a random gas made of the same constituents. But now if we take it for granted that this state could, potentially, give rise to all kinds of situations analogous to the experiment we just did with the engine, which result would require the most “unlikely” original state? The result where none of those situations ever actually arise: no fast-moving object ever emits a burst of light in such a way that the light would need to be emitted, as well, by other objects scattered around the cluster? Or the result where such events do occur, with the original state guaranteeing coordinated action by all the different emitters? And you can’t say “neither”; it has to be one or the other.’