The Arrows of Time

Having come so far, she ached to complete the story. She wanted to return to the Peerless with everything solved: the vacuum energy tied to the curvature of space and the topology of the cosmos – determining once and for all whether the entropy gradient that had enabled life was a stupendously improbable fluke, or simply an unavoidable consequence of a few simple principles.

When she lifted her gaze up from her desk, the prospect of the Surveyor’s planetfall was glorious and thrilling, the purpose of their journey finally to be fulfilled. But when she looked down at her unfinished calculations, she thought: glorious – but please, not yet.

Gathered with the rest of the crew around Tarquinia’s console, Agata compared the two images on the screen. One was a grey disc faintly mottled with reds and browns, weakly but uniformly lit, grainy and poorly resolved as the photodetectors struggled at the limits of their sensitivity. The other was a disc of the same size, and two-thirds of it lay in the deepest black night, but the crescent of dayside revealed an impossibly vivid landscape of jagged grey mountains, dusty red plains and twisted brown valleys, sharp enough to touch.

Esilio by the light of the home cluster’s stars, and Esilio by the light of its sun. Esilio as they’d see it with their own eyes, and Esilio through the time-reversed camera. Esilio as it had been a few chimes ago – and Esilio as it would be a few chimes in the future.

Tarquinia said, ‘The good news is, the temperature looks tolerable. Hotter than we’re used to, but not by much.’

Agata was surprised. ‘How did you measure the temperature?’

‘The density profile of the atmosphere. A hotter atmosphere will stretch up farther from the surface.’

‘Is that reliable?’ Agata had no problem with the general idea, but she suspected that the method would be fraught with uncertainties.

‘I’m not sure,’ Tarquinia confessed. ‘I’ve never had a chance to observe a planet before.’

Ramiro said, ‘If this world’s come all the way around the cosmos, shouldn’t it have had time to grow hotter?’

‘No plants, no fires,’ Azelio pointed out. ‘If there’s nothing making light, there’s just slow geochemistry to warm it up.’

‘Ah.’ Ramiro turned to Agata. ‘Temperature doesn’t change when you swap the direction of time, does it?’

‘Not as such,’ Agata replied cautiously. ‘Imagine reversing the motion of all the particles in a container of gas: it wouldn’t make any difference.’

‘But if “temperature as such” is unchanged, what about the implications?’ Ramiro pressed her. ‘Will heat still flow from hot to cold?’

‘That depends on exactly what you’re talking about.’ Agata wasn’t trying to be unhelpful, but the worst thing she could do was make a blanket pronouncement that ignored the subtleties of the problem. ‘We ought to be able to find examples on Esilio where two lukewarm objects start out with the same temperature, but then heat flows from one to the other – making one cooler and the other hotter.’

Ramiro hummed impatiently. ‘That’s obvious: inasmuch as we’re able to act purely as spectators, we can expect to see ordinary things happening in reverse. But when we touch something down there, some rock that’s colder than our hands… ?’

Agata said, ‘Why do you expect there to be a simple answer to that: a rule that will hold true in every case? We’re used to predicting heat flows on the basis that entropy will increase along one direction in time — and the same principle will have held on Esilio for most of its history, for its own notion of the future. But the two arrows point in opposite directions, so each side’s rule flatly contradicts the other. Those rules were never universal laws, and this is the place where we finally have to accept that.’

‘But couldn’t the Esilian rock pass some of its heat to us, even if it’s colder?’ Azelio suggested. ‘Its entropy goes down, as we see it, while ours goes up. So both sides get to follow their usual rules.’

‘That’s not impossible,’ Agata agreed. ‘But we can’t expect to be able to partition everything as neatly as that. While we’re still far apart we can talk about the two sides and their rules… but deep down, matter is just matter, it doesn’t come with allegiances. The real laws of physics treat all directions in time and space identically, and they’re the laws that every photon and luxagen obeys — without knowing or caring about anything called entropy, let alone what side it’s meant to be on in some clash of thermodynamic arrows.