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.
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 leveclass="underline" 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.