The Arrows of Time: Orthogonal Book Three (26 page)

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.’

‘That’s true.’

‘But . . . ?’

Agata said, ‘Why would I wait six years for the chance to do this, and then sleep through half of it?’

Ramiro buzzed. ‘Fair enough.’

‘I used to hold vigils outside the voting halls,’ Agata recalled. ‘I’d watch the people come and go, watch the tallies rising.’

He said, ‘So when you take something seriously, you try to make the most of it?’

‘Yes. Is that so strange?’ Agata tried to judge his mood, and decided to take a chance. ‘Isn’t that what you and Tarquinia are doing? Making the most of your
friendship?’ Ever since Azelio had confided his own suspicions about the pair’s activities to her, Agata had suffered bouts of curiosity, but she’d never had the courage to ask
the participants themselves about the experience.

Ramiro didn’t seem angered by the question, or embarrassed. ‘In a way,’ he said. ‘If I was back on the mountain, I’d be worried that I was doing the opposite:
taking the drive to raise children and wasting it on something trivial. Here, I can tell myself that I have no chance of becoming a father, so it’s not a waste at all.’

Agata said, ‘Everyone but the Starvers accepts that it makes sense to have children without fission – so why not refine the process even further and select precisely the effects we
want from it?’

‘Why not?’ Ramiro agreed. ‘As an abstract proposition, it sounds as sensible as separating out the parts of a plant instead of blindly eating the whole thing. We don’t
have to swallow the poisonous roots when it’s the stem that actually tastes good.’

‘But why as an abstract proposition?’ Agata pressed him.

Ramiro hesitated. ‘The trouble is, even when the body can’t put things back together, it never forgets how they used to be joined.’

‘What do you mean?’

‘It makes me want children more than ever,’ he said. ‘It takes that ache that might have faded with time, and reminds me, over and over again, that it’s never going to be
fulfilled.’

While they were in free fall the
Surveyor
could be oriented any way they liked, and Tarquinia had chosen to set the window facing the rim of the hemisphere of
home-cluster star trails. As Agata’s vigil stretched on, she left Ramiro in peace, ignored the clock on her console, and just stared out through the window, waiting for the first sign that
something solid and invisible had moved between her and the ordinary stars.

Despite the lights of the cabin, after a few lapses her eyes began picking out a faint grey disc against the deeper blackness of the dark hemisphere. Esilio’s sun scattered ordinary
starlight, so she could have checked its progress through the telescope without even switching to the time-reversed camera, but she was content to let the image remain elusive, coming and going as
her concentration faltered, or as Ramiro shifted in his harness and drew her focus back to the reflected interior.

When a bite appeared in the rim of the bowl, all ambiguity vanished from the scene. Agata felt a tingling of excitement, and beneath it a churning sense of disruption. When the
Surveyor
had altered its velocity the star trails themselves had stretched and shrunk, but she’d seen the same predictable deformation when the
Peerless
turned around, and in the end it
amounted to little more than holding up a distorting mirror to the sky. This was different: before her eyes, an orthogonal star was leaving its hemisphere and crossing the border, obscuring the
ancestors’ stars behind it.

The occulted region grew larger, slowly revealing with clarity and precision the shape she’d squinted and guessed at. Agata savoured the delay still to come: she’d chosen reference
points on the star trails well clear of the clutter of the rim, so it would be a bell or so before she could start making measurements.

Ramiro said, ‘I wonder what the settlers will call it: that day of the year when the sun starts its passage across the stars.’

Azelio and Tarquinia joined them, and the four of them ate breakfast together as they watched the black disc become whole. Then Agata turned to her console and summoned up the image through the
telescope.

She guided the software as it tracked the celestial markers she’d chosen. Some were transitions in the perceptually defined hue of a single star trail: the point where orange turned to
red, easy to find by eye though there was no discontinuity in the light’s actual wavelength. Others were points where two trails crossed, and were not so much fixed beacons as sites where she
expected some complicated but illuminating slippage. The colours of the two trails were never the same where they met, so two beams that were initially travelling side-by-side would be bent by
different amounts depending on their speed, leaving a slightly different pair of hues to meet up in their place.

Agata didn’t expect any telltale distortion to leap out at her from the screen; the changes would be measured in arc-flickers. All she could do was check that the software had latched on
to the correct features, and watch closely to ensure that nothing went awry as the black disc encroached on the field of view.

She did not take her eyes from the telescope’s feed until the last of the markers had vanished behind the sun. Then she summoned the analysis: a plot of measurements compared to
predictions.

‘Azelio?’ she called.

‘Yes?’

‘Prepare to skip lunch; I’ll be eating for both of us.’

Azelio dragged himself over to take a look at the results, soon followed by Ramiro and Tarquinia. The measurements with their spread of errors wove a course that hewed closely to Lila’s
predictions – and ruled out Vittorio’s theory entirely.