The Clockwork Rocket

ensure that every one of these people could make sense of the view around them using nothing but their eyes and their intuition.

She addressed the class again. “This drawing tells us something straight away, about the view we can expect from the Peerless. Any suggestions?”

Prospera said, “The violet light coming in from behind us has been tilted so far that it’s… gone past horizontal.” Her tone made it clear that she knew the change had to be significant, but she couldn’t quite see what it implied.

“So if you follow the light in toward us,” Yalda suggested, “what happens to its height?”

“It gets less, as you move in,” Prospera replied.

“Its height gets less. And what does height stand for, in this picture?”

“Time.” Prospera pondered this for a moment. “So the light would have to come from the future?”

“Exactly. It would have to be traveling back in time. Not for us—it’s still coming from our past—but for the star that emitted it. So what you’ve found tells us that no ordinary star that lies directly behind us—in the rear one-eighth of our view, or a bit beyond that—can appear to us in violet, because that would require the star to have emitted light into its own past.”

“But it would be different for an orthogonal star, wouldn’t it?” Fatima asked eagerly.

Yalda said, “Well, their time is horizontal in this picture, and their future is aligned with the direction in which we’re traveling, but—”

Fatima ran forward to the edge of the cave and peered down the slope of the mountain.

“—but unfortunately, the rock below us hides that part of the view.” Between the mountain and the haze from the engines, there was no chance at all of observing the orthogonal stars yet.

Yalda asked the students to draw the tilted pyramids from above. A few people became confused, or drew some preconception rather than the actual view, but after noticing the emerging consensus of their peers they looked again and refined their own versions.

She waited until everyone had the essential features correct.

“Each of the eight segments still represents an equal portion of our view,” she reminded them. “But their relationship with the surroundings has changed. Let’s start with the violet, the broader pyramid. Can someone tell me what’s going on?”

Ausilia spoke up. “At the front,” she said, pointing out the triangle on her chest, “the angle between the edges is much bigger than one-eighth now, seen from above.”

“Which means…?” Yalda pressed her.

Ausilia hesitated, but then followed through. “Our one-eighth of the view is taking in light from more than one-eighth of the stars?”

“Exactly!” Yalda approached her and had her turn so the whole class could see her sketch. “In the direction in which the Peerless is traveling, this slice of the view has a wider reach, so light from more stars gets crammed into it. We still see it as an equal eighth, but as far as our surroundings are concerned it’s much more.” She stepped away from Ausilia and gestured toward the zenith. “Focus on the violet ends of the trails. They started out scattered uniformly around us, before the launch; now they’re crowded together around the direction in which we’re traveling. And the reason is simple: when you take two lines that are a fixed angle apart— like the edges of that front triangle—the more you tilt them, the greater the angle between them will seem to be.”

She waited for the simple logic of it to mesh with the evidence before their eyes, then added, “In the opposite direction there’s an opposite effect. The mountain makes that harder to see—and we’ve already shown that there’s a region behind us where we won’t be getting violet light from the ordinary stars anyway—but in general, looking back the view is sparser.”

Fatima was standing closer to her than Ausilia now, so Yalda moved beside her and pointed to her drawing of the red pyramid.

“What about red light? If you compare the rear triangles in the two pyramids, it’s clear that the angle for the red light is even smaller than it is for violet—so we should see the red images behind us spread out across the sky more than the violet, pushed forward compared to the violet. And that difference persists as you move away from the rear. For any given star, the red light ends up further from the nadir. Does that sound familiar?” Yalda pointed to the vertical trails behind her, the red ends all higher than the violet.

“But what happens with the red light,” she continued, “when we look in the direction in which we’re traveling? There are only five triangles from the pyramid visible here. What’s going on with the three triangles that point to the front for us?”

Fatima helpfully added three lines that made the hidden triangles visible:

“They’ve ended up pointing backward,” Ausilia said.

“Yes!” Yalda raised her eyes to the zenith. “See those strange red ends of trails poking out the wrong way? They’re stars that are actually behind us! The pyramid shows us that in red light, we can’t see anything that’s in front of us—in the sense that an onlooker fixed to the stars would judge something to be ‘in front’. But our view isn’t empty of red in that direction; instead of seeing what’s in front of us, we’re seeing some of what’s behind us.”

“And all of it twice,” Fatima said, running a fingertip across the diagram toward the apex of the pyramid. “Every star we see behind us in red… we also see in front of us in red.”

“That’s right,” Yalda said. “But though it’s light from the same star—and it looks the same color to us—it’s not the same light.”

Fatima thought for a moment. “The red light we see, looking back, left the star at a greater angle than the angle it makes with us. So it left the star as faster-than-red light… but because we’re fleeing from it, it’s not gaining on us as quickly as it would if we were still. Our motion has changed the color from violet or ultraviolet to red.”

“Yes.” Yalda pushed her, “And the other light? The red light we see looking forward that came from the very same star?”

Fatima gazed down at the diagram, struggling. “From the angles, I think it must have left the star moving quite slowly. But if it’s moving so slowly, how could it ever catch up with us?”

Yalda said, “If you’re getting confused, just draw… whatever it is you need to draw.”

Fatima made a new sketch, paused, then added some annotations.

“The red light we see as coming from ahead,” she said, “must have left the star behind us long ago… but now we’ve caught up with it, we’re overtaking it. That’s why it strikes us from the front. The star is behind us, but the light was ahead of us.”

Fatima looked up at the zenith, then a fresh revelation struck her. “That’s why those upside-down star trails sputter out at green! However long ago the light left the star, the angle it made with our history could never end up greater than the angle for blue light. But blue would be the absolute limit—light from infinitely long ago. In real life we can’t expect to see that far back.”

She modified her diagram to show what she meant.