Greg Egan - The Arrows of Time

Azelio inclined his head, accepting her answer. But he remained sceptical. ‘And this measurement is going to tell you the shape of the cosmos?’

‘No – it’s necessary for that, but not sufficient. If I end up disproving Lila’s theory, then I won’t have much hope of working out the shape of anything. All my calculations linking energy to curvature depend on Lila being right.’

Azelio was confused. ‘Why couldn’t you adapt your work to Vittorio’s theory?’

Agata said, ‘If the results agree with Vittorio’s theory then I’ll have no choice but to accept that as a fact – but I’d have no idea how to integrate it into modern physics. Lila’s theory makes gravity consistent with the notion that everything should work the same way when we rotate our picture of it in four-space. If gravity doesn’t respect that, it would be the most shocking discovery since Yalda came down from Mount Peerless.’

‘Then you should hope for that shock,’ Azelio joked. ‘You’d be as famous as Yalda.’

‘And I’d have to throw out half a lifetime’s work and start again.’

‘Isn’t that the price of every scientific revolution?’

‘ Lila’s theory is the revolution!’ Agata countered. ‘It’s just been a quieter one than Yalda’s or Carla’s, because it’s been so hard to test. What the revolution will throw out isn’t my work, it’s Vittorio’s – and he didn’t live long enough to know or care that his beautiful ideas weren’t perfect.’

‘I won’t believe that space is curved until I’ve seen it with my own eyes,’ Azelio avowed. He wasn’t usually so invested in any of Agata’s purely theoretical claims, but he seemed to have found this impending empirical affront to his intuition too much to accept without protest.

Agata gestured at the screen. ‘You’ll see something, soon enough.’

‘No, all that will show us is that the light is bent. Which Vittorio’s theory predicts as well.’

Agata buzzed at his stubbornness. ‘Bent by a different amount – and for some colours, in the opposite direction! ’

Azelio said, ‘Honestly, don’t you think you’re trying to conclude too much from such slender evidence? Even if the bending is exactly what you predicted, couldn’t there be another explanation for it? Maybe the requirement for gravity to fit in with rotational physics implies certain angles of deflection for the light. But that could come from a tiny modification to Vittorio’s force law, couldn’t it? We’ve always known that gravity bends the paths of moving objects. Why not just refine that notion – instead of leaping to the conclusion that it’s actually bending space ?’

Agata didn’t know how to answer him. From the point of view of everyday experience, it probably did sound grandiose to make so much of such a small effect.

She thought for a while. ‘I’ll tell you why I’m going to believe that space is curved, unless I find overwhelming evidence to the contrary.’

‘Go ahead.’ Azelio was probably unswayable, but he was still interested in understanding her position.

‘If motion under gravity is due to curvature, rather than a force, it will obey an incredibly simple rule: the history of any object in free fall is just the shortest available path through four-space. In flat space, that’s a straight line. In the curved space around a star, it’s not.’

‘That’s simple in itself,’ Azelio allowed. ‘At the cost of making the geometry more complicated.’

‘But it’s more than just simple!’ Agata insisted. ‘It also fits perfectly with everything else we know about motion.’

‘In what way?’

‘When light moves from place to place,’ she said, ‘you need to add up contributions from different paths between its starting point and its destination. Paths where it spends about the same time travelling all add together, because the waves will have stayed more or less in step, with their peaks arriving simultaneously. Paths where the travel time varies rapidly mix up peaks and troughs, so they cancel each other out.

‘Imagine a kind of mathematical valley that stretches across the landscape of all paths, where the length of each path determines the height of the landscape. The shortest path becomes the lowest point: the bottom of the valley. If you change the path there slightly, you barely change its length, because the bottom of a valley is horizontal. But if you’re far up on the side of the valley instead, the path isn’t just longer, it’s at a point where the valley slopes much more, so any change would change the length more – making the waves slip out of phase.’

Agata sketched an example on her chest, and had the corset display it on her console.

Azelio frowned, but then he remembered something. ‘We used that principle in our optics class: you can find the law of reflection by looking for the angle that light makes with a mirror that lets it arrive all in phase.’

‘Right! So now apply the same logic to starlight moving past Esilio’s sun. Suppose the light does bend. If four-space is flat, then the light won’t be following the shortest path, since in flat space that’s always a straight line. It will be on a path up on the valley’s slopes, where any tiny variation changes the length and throws the light out of phase. There are ways around that: we can postulate some mechanism that messes with the phase in exactly the right manner to favour the bent path – but that’s complicated, because as well as explaining what happens with the light, it needs to explain the force on an orbiting planet.

‘If four-space is curved, though, that does the job for everything. Light waves and luxagen waves, it makes no difference: if they’re following the shortest path in four-space, they’ll arrive in phase. That’s enough to bend the beam, and enough to make a planet swing around in its orbit.’

Azelio pondered this, and found nothing he could object to. ‘It makes more sense than I thought,’ he admitted.

Agata was delighted. ‘So what’s your conclusion?’

‘My own prediction, now,’ he declared, ‘is that the light won’t bend at all. I can see why you think it would make things too complicated if you had to account for the bent paths of both light and matter, in flat space. So the simplest solution would be to keep space flat, but have light unaffected by gravity.’

Agata was on the verge of embarking on an account of how this would violate conservation of energy, but she stopped herself; she’d reached the point where it would be more economical to let the results speak for themselves. ‘Do you want to put two loaves on it?’ she suggested.

Azelio feigned shock. ‘The shape of the cosmos is at stake… and you want to swindle me out of my rations?’

‘Who’s swindling you? You can check all the data yourself. You can ask Ramiro to audit the software.’

Azelio considered the offer. ‘If the light goes straight, you pay me; if Lila’s predictions are confirmed, you win. Anything else – including Vittorio’s theory – is a draw.’

‘Agreed.’

‘Two loaves, then,’ Azelio confirmed. ‘You’re on.’

‘Is there something that needs monitoring while you’re waiting for the stars to align?’ Ramiro asked Agata. ‘I’m on watch all night – it wouldn’t be any trouble.’

‘There’s nothing like that,’ she replied.

‘Then why not get some rest?’

Agata looked up from her console. ‘I can’t just shut off my mind in the middle of this.’

Ramiro stretched his shoulders and swivelled around to face her. ‘The star trails will still be there when you wake. And we’ll be following the same orbit whether you’re sitting here fretting, or fast asleep in bed.’