The Eternal Flame (38 page)

She worked through the geometry more carefully, sketching the history of the mountain’s extremities and the light moving between them. The frequency measured for any given pulse of light depended solely on the relative velocity between the apparatus doing the measuring and the light pulse itself—which in turn came down to nothing more than the angle between their histories. Those angles were easy enough to find, and four of them told the whole story.

The mirror’s acceleration into the oncoming light would mean that the light struck it a little faster than the speed with which it had left the source. But the light source, in turn, would be accelerating
away from
the reflected light. By the time the light came back to the source, the relative velocity between the two would be reversed but otherwise unchanged—and the net result would be that there was no frequency shift at all.

In principle the blue shift could be measured by comparing the light at the base of the mountain with a reference beam produced locally by a second light source. But the ideal method would involve a direct comparison between the shifted light and the
original
beam. Carla hunted for a way around the problem, but the geometry always led back to the same result: the beam would suffer a blue shift traveling down the mountain, and a red shift traveling back up. And so long as the light was reflected unchanged, on a round trip the two effects would cancel out. It was just a form of conservation of energy.

What about Eulalia’s flight of fancy, then: a photon rocket? Would frequency shifts disrupt the light source there, or not? If a beam of light was powerful enough to be the
cause
of the mountain’s acceleration, it would be imparting momentum to the mirrors it struck, and losing some of its own. It would no longer be reflected unchanged; it would have to experience a red shift.

How much, though?

That depended on the mass of the object each photon effectively bounced against. In the experiments with free luxagens, the light had been scattered back with a huge red shift; because the individual luxagens were less massive than the photons that struck them, their recoil had carried off a lot of momentum. In the inferior grades of mirrorstone that could ruin a coherent light source, the luxagens were still mobile enough to recoil significantly before they transferred their momentum to the bulk of the material. In the highest quality mirrors, the luxagens were bound so tightly to their neighbors that each photon was effectively colliding with a significant portion of the mirrorstone—a portion heavy enough to be unmoved. But there were limits to this collective inertia: a single photon could never bounce off an entire mountain, as if it were a rigid, indivisible whole. So it would be the material properties of the mirror itself, not the acceleration of the mountain, that determined the frequency of the reflected light.

Carla had lost track of her surroundings. She paused, clinging to the guide rope, and looked around the corridor at the doors ahead and behind her. She had passed her apartment twice, she realized, and she was now a short way into a third circuit. The reminder that her food cupboard was only a few stretches behind her was enough to make her gut start twitching again, but she resolved to complete a couple more circuits in the hope that it would be enough to let her sleep.

She took up the thread of her argument once more. A poor quality mirror would reflect light with a small red shift, bouncing back photons that were no longer tuned to the gap between the energy levels that produced them. And perhaps a beam intense enough to be part of a photon rocket would exacerbate the effect, with the stronger light fields effectively “softening” mirrors that were perfectly adequate at a lower power. Was there any way around that? A red shift meant an increase in true energy: each reflected photon would be carrying too much energy to stimulate the emission of another photon from the original transition. But then, why not give it a different task? If its energy matched another gap between levels, maybe the whole system could be made to do something useful nonetheless.

Carla tinkered for a while, and came up with one possibility.

The luxagen started in the lowest of three levels; it would have to be pushed there by an external light source. From there, it jumped spontaneously to a higher level, emitting an infrared photon. Then it moved to a higher level still, emitting an ultraviolet photon.

Both photons were reflected back, red-shifted by their encounter with the mirror. But if the mirror’s properties and the spacing of the energy levels were related in just the right manner, the reflected IR photon would be able to push the luxagen back to the lowest level: exactly where it had started.

And then the cycle could begin again.

In each cycle, two photons were created and one was never recaptured. To balance that photon’s true energy, the clearstone and the mirrorstone would need to gain conventional energy; in principle, any mixture of kinetic, thermal and potential energy would do. But to balance the photon’s
momentum
, the device as a whole would need to accelerate, so the energy gained couldn’t be entirely in the form of heat. When a fuel met its liberator, the creation of light was accompanied by the creation of heat—and this device would certainly heat up to some degree. Over time, it might also suffer some degradation, some chemical change. But unlike burning fuel, it would not disintegrate in a flash, it would not turn to smoke.

To make light and not be consumed.
These were the properties of an Eternal Flame.

Carla paused, amused by her absurd conclusion, wondering where the mistake lay. As things stood, the photons wouldn’t really be produced all conveniently heading in the same direction, so the device would certainly need some refinements. Perhaps she could merge the recoiling mirror trick with her original design for a coherent source. But
this
source wouldn’t squander most of the energy from a blazing sunstone lamp; the red-shifted reflection of the IR photons it emitted itself would act as the main pump. After an initial flash to get the process started, it would only need a small amount of ongoing illumination to compensate for its imperfections and inefficiencies—and the beam it produced would far outshine that modest input.

It would not violate the conservation of energy or momentum. It would not violate any thermodynamic law: creating photons and waste heat amounted to an increase in entropy. But a photon rocket based on this design could run on a tiny fraction of the sunstone needed by any conventional engine. If it worked, it would solve the fuel problem.

No—more than that.
If it worked, the ancestors themselves might flee the home world in a swarm of photon rockets. If it worked, not only would the
Peerless
have gained the means to return home, it would have the right, it would have the reason. The purpose of its mission would have been fulfilled.

Carla moved slowly down the empty corridor, listening to the twang of the guide rope, waiting for the flaw she’d missed to reveal itself. When it finally hit her, she could buzz ruefully at her foolishness and drag herself back to bed.
What about cooling?
This rocket would still need a separate cooling system, burning fuel of its own… but there was no law that required the heat it generated to be as much as a conventional engine produced. And the right choices in the design could help: the faster the ultraviolet photons the device was able to emit, the less kinetic energy the mirror would need to remove from the other photons—which meant less energy ending up as heat.

Carla didn’t need to search for a clock to know that it was still early, but the only person in the mountain there’d be any point in waking was also the only one who’d understand why she couldn’t wait a few more bells to resolve this.

She reached the precinct easily enough, but she had to check the names on a dozen doors before she found the right one; she hadn’t paid a visit since Patrizia had started living apart from her co. Carla knocked tentatively, wondering belatedly if her behavior would appear completely deranged. But the door opened before she had a chance to change her mind and retreat.

“Good morning Carla.” Patrizia looked puzzled, but if she was annoyed at being woken she hid it well. “Come in, please!”

The apartment smelled of paper and fresh dye. There was a lamp burning in the front room, revealing walls stacked with books and tied bundles of notes. The gravity was very weak here, but Carla clung tightly to the guide rope.

“I won’t waste your time,” she said. “I’ve had a wild idea, and I need to hear your opinion.”

She described the basic principle of the mirror trick, then went on to explain how it might be used in a real device. When she’d finished speaking she braced herself for a barrage of objections, but Patrizia remained silent, gazing thoughtfully into the middle distance.

“So have I lost my mind?” Carla pressed her. She’d gently put Patrizia straight when the girl had fallen prey to her own kind of nonsense; it was time for Patrizia to return the favor.

“I don’t think so. Why would you even say that?”

“Because it can’t be this easy! The Eternal Flame—from a few mirrors and a slab of clearstone?”

Patrizia buzzed softly. “In the sagas, the Eternal Flame doesn’t
do
anything; it just sits there being cool and inscrutable. Your version would be more like the process plants perform every day: extracting energy from the production of light without incinerating themselves. Nature must have found a trick a lot like yours—shuffling luxagens around a closed cycle—even if it puts it to a very different use. Crossing the void with minimal fuel wasn’t something a flower was ever going to find helpful, but that doesn’t mean it’s impossible.”

Carla felt no sense of reassurance. If Patrizia had found a glaring flaw in the plan that would have settled the matter, but the fact that the idea had survived her brief scrutiny proved nothing. “And no one else thought of this? Not Yalda? Not Sabino? Not Nereo?”

“They all thought energy was continuous!” Patrizia protested. “Would this scheme work at all, without discrete energy levels?”

“I don’t know,” Carla admitted. Certainly the whole idea was easier to grasp when the luxagen could cycle repeatedly between a few fixed states.

“I think Yalda had hopes that we’d master the creation of light by studying plants,” Patrizia said. “And maybe that will give us the best insights into the process, eventually. But someone had to be the first to spell out the kind of steps that would make this possible. You’re the first, Carla. You’re not losing your mind, I promise you.”

“Thank you.” Carla did trust her to give an honest opinion, and not to indulge in flattery. “But I won’t believe I’m right until we’ve proved it.”

“So where do we begin?” Patrizia asked. “We’ll need to find varieties of clearstone with the right energy levels, but we’ll also need to calibrate mirrors for their red shifts.”

“This is going to be a whole new project,” Carla said. “I’ll have to go to the Council to get their approval for the change of plans.”

“Hmm.” Patrizia was impatient to get started. “Surely I can reanalyse a few absorption spectra without waiting for the Council? When Romolo and I went through them the last time, we were looking for very different properties.”

“That’s true.” The search for the perfect clearstone would start all over again, and there was a chance that once again it would succeed. But even the navigators’ modest needs would require the entire inventory of the clearstone Romolo had used in his visible light source. For this new application—

“It won’t be enough,” Carla realized. “Even if we can make this work in a demonstration rocket, there isn’t the slightest chance that we’ll have enough material to replace the engines.” The mountain’s stocks of exotically tinted minerals weren’t miserly, but the ancestors had only intended them to provide representative samples to be studied for the sake of materials science. They had never anticipated the possibility that one particular variety would become more valuable than sunstone.

Carla buzzed with grim satisfaction, glad that she’d caught her own mistake before making a fool of herself in front of the Council. “What was I thinking? Anything less than a full replacement for the engines would be worthless. If we can’t accelerate the
Peerless
at close to one gravity, it will take too much of the ancestors’ time for us to get back to them.” Returning to the home world a few years late—by the ancestors’ clocks—would mean arriving just as collisions with the orthogonal cluster began in earnest.