The Arrows of Time

‘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.’