Greg Egan - The Arrows of Time

‘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.