The Eternal Flame

Romolo was at a loss for words, so Carla intervened. “She’s joking! Any frequency shift would be extremely small. Even at one gravity there’s no chance at all it could stop the light source from operating.”

“I was joking,” Patrizia admitted. “But maybe we could design a system that’s deliberately sensitive to the shift, and use it as an accelerometer—as a kind of navigational aid.”

Carla couldn’t think of any objection to that in principle. “Why not?” she said. “Another project for our grandchildren.”

Romolo angled the reflected beam onto Patrizia’s chest. The red disk looked like a hole in her skin, revealing the realm of light within.

Carla woke, her gut in spasms. She turned to the clock by the bed and waited for her vision to come into focus. Breakfast was still more than two bells away.

She lay beneath the tarpaulin, humming softly. She wondered if it would help if she made some kind of promise to herself, to end her hunger if it became too much to bear. But end it how? She couldn’t take Silvana’s way out, even if she’d wanted to: Carlo was so convinced that he could rescue her from the famine that he’d rather fend her off with his ridiculous knife than cure her of her misery. She wasn’t going to go off holin, or step out of an airlock. There was nothing to be done but to endure it.

She tried to sleep again, but it was impossible. She pulled herself out of bed and left the apartment. If she followed the corridor around in a circle until she was too weary to continue, she could drag herself back to bed with some hope of losing consciousness.

The precinct was quiet, the moss-lit corridor deserted. What did other women do, she wondered, when their hunger became unbearable? Did they lie beside their cos and fantasize about the day it would finally end, until one by one they abandoned all the plans they’d made for their lives and gave in to that glorious vision?

Carla searched for something cheerier to occupy her thoughts. Romolo’s new light source was a striking vindication of the whole theory of energy levels… but when she thought about the journey the device would enable, the prospect filled her with dread. Without a deep understanding of the annihilation reaction, any plans for an engine that burned orthogonal matter would be nothing but whimsy. But was it really her duty to face the risk of becoming fuel for that fire herself, not just once, but over and over again?

If she refused, there would be plenty of volunteers to take her place. She could still work on the theory underlying the reaction, but she would probably slip behind the researchers with first-hand knowledge of the new results. If Patrizia flew on the second Gnat and returned with a triumphant discovery of her own, it would finally place her reputation unambiguously beyond Carla’s.

Would that be so intolerable, though? Would it be unjust? They had both made contributions, but the most powerful ideas had been Patrizia’s. Looking back, it seemed to Carla that the best thing she’d done had been to impose some discipline on Patrizia’s wilder speculations and then tidy up the details of those that worked out. So perhaps she should reconcile herself to that role. If it was to be her legacy, better to value it than resent it.

What was left for her, then? More tidying up? Turning throwaway lines about accelerometers into real devices? If she could come up with a design for a light-based accelerometer that actually worked, there’d be nothing dishonorable in that. On the scale of a small craft like the Gnat it might be fanciful, but over greater distances there’d be more time for the acceleration to reveal its effect.

How long would it take the slowest detectable infrared light to run the full length of the Peerless, from the tip of the mountain to the base, and back? Still just a fraction of a flicker. In which time, at one gravity’s acceleration, the velocity of the mountain would have changed by… a few parts in the fifth power of a gross.

Carla dragged herself faster along the guide rope, determined to complete her first circuit of the corridor and get past her apartment while she was still distracted. As she pondered the problem she realized that she’d been careless: it was reasonable to assume that the light’s frequency would be unchanged when it bounced off the mirror that sent it back toward its source—that was the definition of a good mirror, after all—but she’d ignored the fact that the mirror would be accelerating along with the Peerless. On the finicky level of detail required to keep track of the tiny effects she was hoping to measure, that would be enough to change the result.

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.