20

As the Surveyor drew closer to Esilio’s sun, Agata willed the days to stop slipping away so quickly, robbing her of precious time to work.

It had taken her four years to reshape the foundations of field theory into a form that made sense to her: a kind of dissection of the behavior of fundamental particles into a series of simple diagrams. When a photon moved from one place to another, the first diagram of the series showed this happening entirely uneventfully. But in the second diagram, the photon was shown giving up its energy to the luxagen field to create a pair of disturbances with positive and negative source strength, which traveled for a while before recombining into a replacement for the original photon.

In a sense it was just like the old double-slit experiment that Yalda’s teacher, Giorgio, had used to convince people that light was a wave: light couldn’t be passing through one slit or the other, because the pattern of bright and dark lines it made could only be understood by adding contributions due to the light taking paths through both slits. But in Agata’s version the set of “paths,” included, not only a variety of routes, but all manner of transmogrifications along the way.

She had balked at this, at first: a lone photon couldn’t turn into a pair of luxagens—each with just a third of the photon’s mass—because whatever the velocities of those luxagens, it would be impossible to satisfy the laws of conservation of energy and momentum. But she’d finally understood that each of the diagrams on its own was just a kind of fiction, expressing a narrow sliver of the true history, and any characters that came and went without being present at the start and end of each story were mere flights of fancy, subject to very different rules compared to those that endured. Every part was needed to make up the whole, but only the totality was real.

With any process the variations were endless, but the more complex the diagram the smaller its contribution, allowing the sum to remain finite. And in this scheme, the vacuum itself was simply the sum of all diagrams that started and ended with no particles at all, its energy due entirely to disturbances that came and went of their own accord, with no connection to anything persistent.

Agata had been gratified to discover that, in flat space at least, these diagrams rendered the vacuum manageable. But if the vacuum energy curved space, then flat space was actually impossible—and if curvature modified the vacuum energy, the two could only be in harmony at some elusive fixed point that remained beyond the reach of her methods.

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 gray disk 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 disk 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 gray 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.

“Suppose we leave a piece of equipment behind on Esilio—say, a small spyglass. Over the eons, from our point of view, we’d expect it to become pitted by dust in the wind, and eventually break up completely and turn to sand. Our spyglass, our rules; that sounds fair, doesn’t it? But if that sand stays on Esilio, what origin will it have from Esilio’s point of view? Most likely, some ordinary Esilian rock will have broken down to make it—which to us, would look like erosion running backward. But then, in Esilian time the remnants of that rock will eventually form themselves spontaneously into a spyglass, which lies on the ground until we come along to retrieve it. So if you follow the history of the matter that makes up the spyglass far enough in both directions, it’s clear that it’s not committed to either side’s rules.”

Ramiro said, “That’s all very fascinating, but you still haven’t told me whether or not I’d burn myself by touching a cold rock.”

Tarquinia broke in. “No one will be touching anything until we’ve done enough experiments to know what’s safe and what isn’t.”

Ramiro gave up and dragged himself away, muttering about the uselessness of theoreticians.

Azelio caught Agata’s eye. “Your story about the spyglass was unsettling,” he said, “but I’ll tell you what disturbs me more.”

“What?”

“Swap the roles of Esilio and the Surveyor,” he replied, “then tell the same story again. If something from Esilio takes the place of the spyglass, it must be with us already. We must have been carrying it, or the things that will become it, from the very start. Because according to Esilio’s arrow of time we’ve already visited the planet, and it’s almost certain that something remained with us when we departed.”

“The black sun awaits your pleasure,” Tarquinia announced from the doorway.

Agata looked up, startled. “Already?”

“It’s now, or wait until we’re on our way back.”

“Of course.” Agata hesitated. “The telescope’s mine, until we switch orbits?”

“Absolutely,” Tarquinia replied. “But if you break it, you can grind a new lens.”

“From what?”

“The other part of your punishment will be hunting down suitable materials on Esilio.”

Agata could have done everything from her room, but that seemed selfish: the experiment belonged to all of them, and she wanted every member of the crew to feel free to look over her shoulder as she worked. So she dragged herself into the front cabin and strapped herself to her couch there.

Tarquinia had trained her to use the telescope’s software, but Agata still felt an illicit thrill when she invoked it from her own console and began passing it instructions through her corset. Since they’d shut off the engines the Surveyor had been sweeping in toward Esilio’s sun along a hyperbola, with the home cluster’s stars behind them. But as they swung around the sun in order to help them match velocities with Esilio, she’d finally have a chance to juxtapose the two kinds of stars, with the dark mass in the foreground perfectly suited to its role.

Agata used the navigation system to map out the expected path of the black disk against an ordinary-light image of the sky. Then she chose two dozen points on various star trails that were destined to pass behind the sun, and measured their current positions with as much precision as the instruments allowed. The idea that gravity might distort the appearance of these trails wasn’t all that shocking—if it could bend the path of a planet into an ellipse, why wouldn’t it be able to nudge a beam of light? What was astonishing was the prospect of being able to distinguish between a force tugging on the light and curving its trajectory, and the light merely following the straightest possible history through a space that was itself curved.

Azelio harnessed himself to the couch beside her. “How do you know you won’t just be measuring an optical effect from the sun’s atmosphere?” he challenged her.

“I’ll need to include that in the final calculations,” Agata conceded. “But there ought to be a point where the gravitational effects are showing up clearly, while the light’s still traveling far above the densest part of the atmosphere.”

“Really? You’ve always talked about starlight ‘grazing the disk,’” Azelio protested.

“I have, haven’t I?” She’d been trying to stress that the lack of glare from the time-reversed sun would allow her to follow the stars right up to the moment they disappeared behind it. “But there’s nothing special about the light passing just above the surface—the effect doesn’t suddenly increase there. It’s the distance from the center of the sun that counts, not the distance from its surface.”

Azelio inclined his head, accepting her answer, but he remained skeptical. “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 colors, 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 traveling 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 favor 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 swiveled 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 gray disk 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 savored 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 disk 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 colors of the two trails were never the same where they met, so two beams that were initially traveling 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 disk 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.

“Space is curved!” Tarquinia exclaimed delightedly. She’d taken no prior position on Lila’s theory, but the sheer strangeness of the notion seemed to please her now that it could finally be justified.

“Very slightly,” Azelio conceded. “It’s barely measurable.”

“This might seem like a tiny, obscure effect now,” Tarquinia replied, “but I guarantee that in a couple of generations, every astronomer will be making use of it somehow.”

Ramiro squeezed Agata’s shoulder. “Congratulations.”

She said, “It was Lila’s prediction, not mine.”

“And yet I don’t see Lila here making the measurements.”

“When I told her I was going to be doing this,” Agata recalled, “she said: ‘If the results aren’t what my equations dictate, all we can do is pity the poor cosmos—because true or not, the theory will be the more beautiful of the two by far.’”

“So you’ve proved that the cosmos is beautiful,” Azelio concluded. “But you still can’t tell us its shape.”

“The beauty is that it’s comprehensible,” Agata declared. “Even if its shape is unknown.”

“Unknown to you,” Ramiro said provocatively.

“Yes.” Agata frowned. “But why the distinction? Have you been working with Lila’s equations yourself, on all those long watches?”

“Ha! I wish I were that smart.”

“Then who…?”

“If the messaging system’s been operating on the Peerless since a year or so after we left,” Ramiro reasoned, “then Lila and her students will have had a year by now to think over all the results we bring back. So who knows how far they might have taken things?”

“That doesn’t bother me,” Agata said firmly. “I’ve stolen an advantage over everyone on the Peerless, squeezing three years into each year that passed for them. If they end up deriving some beautiful corollaries from my results by the time I return, that will give me the best of both worlds: I’ll get to see what other people make of my work—and I won’t even have to wait around while they do it.”

It was a nice idea in principle; maybe she really could live up to it. But whether or not her competitors had already had the last word, she was hungry to return to her calculations, reinvigorated by this proof that her efforts so far had not been wasted.

Tarquinia said, “Make sure everything’s secure in your cabins. I’ll need to run the engines hard for a while; we still have a lot of velocity to shed before we can go into orbit around the planet.”

Agata said, “Right.” The shape of the cosmos would have to wait; there was still the small matter of Esilio.