Yalda gazed at his finely ridged skin, feeling suitably chastened and bamboozled. Then she began following the steps he had described for the simpler case, and the whole strange construction took on an eerie inevitability.
The true energy and momentum were linked by a circle, each simply rotating into the other. As the particle’s momentum grew from zero, its true energy began to fall—and at first, everything behaved very much like the earlier calculations, merely plotted upside-down.
But as the particle moved faster, its momentum could no longer increase without bounds. With the momentum levelling out, not only did the shells in momentum space cease growing so quickly, they became much thinner. At about two-thirds of the maximum total energy, the shells reached a peak in volume and began to shrink.
At that point, the effect of a change in energy on the number of possibilities open to the particle was reversed. A slow-moving particle could gain options by moving a bit faster… but a sufficiently fast-moving particle would lose options if it sped up. The ceiling on momentum made things cramped at the top.
The same thing showed up in the temperature, which switched sign when the shells’ volume peaked. And while negative temperatures on their own might merely have been the result of an idiosyncratic choice of conventions, Cornelio’s diagram made it clear that both negative and positive were real possibilities. You could always swap the labels for them by tinkering with the definitions, but you couldn’t banish the distinction itself.
Yalda said, “If everything in this room has a negative temperature, where are the positive ones?”
“On the surface of the sun,” Cornelio replied. “In our own burning stones.”
“I see.” A burning stone heated its surroundings, adding kinetic energy to them, so true energy would have to be flowing the other way, into the flame. Did that make sense? Cornelio had warned her that energy only flowed from the higher temperature to the lower if both had the same sign.
The mixed-sign case wasn’t hard to understand, though. A system with a positive temperature would gain possibilities if it gained energy. A system with a negative temperature would gain possibilities if it lost energy. Putting the two together, there was no subtle trade-off anymore—this was a win-win situation. Both systems could gain volume in momentum space from the same transaction.
So, any system with a negative temperature would lose true energy to any system with a positive temperature. That was why Cornelio had seen merit in calling ordinary objects “hotter than infinitely hot”; however high the positive temperature of a blazing sunstone, a “hotter than infinitely hot” cool breeze could still heap true energy upon it.
Yalda said, “But how can you know for sure that something has a positive temperature—and not just a large negative one? How do you know when things aren’t just ‘hot’ in the old-fashioned way?”
“Light,” Cornelio replied. “Whenever a system freely creates light—not in the orderly way a flower does it, but in the chaos of a flame—it’s turning true energy into something that didn’t exist before, opening up new possibilities. That’s the very definition of positive temperature.”
“So once an ordinary system with a negative temperature starts creating light,” Yalda ventured, “its temperature must change sign? Crossing infinity along the way?”
“Precisely,” Cornelio said. “Once it’s creating light, it’s lost to the ordinary world.”
Yalda couldn’t help stealing another glance at the workshop’s collection of energetically precarious concoctions. Above the shelves, the ceiling still showed signs of recent repairs.
“In the end,” Cornelio declared, “everything becomes heat and light. It’s not in our power to stop that. All we can do is slow it down a little and try to enjoy the ride.”
Yalda ended up staying in the chemistry department until dusk, then she caught a lift in the department’s truck back to the city campus, along with Cornelio and five of his students. As they drove across the dusty plain, Cornelio explained how the pressure of a gas could remain positive as its temperature changed sign, and finite as its temperature crossed infinity. The old ideal gas law—pressure times volume is proportional to temperature times quantity—was receding into the distance; it wasn’t even true within the flames of an ordinary lamp.
The back of the truck was open to the sky, so Yalda saw the Hurtler’s violet tip rushing toward them from the north, but then the driver panicked and slammed on the brakes, sending the vehicle lurching and skidding. When it came to a halt she could recall nothing but a whirl of color across a spinning bowl of stars.
Everyone clambered out, checking themselves for injuries, but it was soon clear that nobody had been hurt. Yalda was still clutching her light recording supplies; she examined the contents of the box in the starlight, but Cornelio had packed everything carefully and none of the vials appeared to have been damaged. She helped some of the students push the truck back onto the road, wasting no time fretting over the lost opportunity. At this rate, there’d be another Hurtler over Zeugma in a couple of stints.
“What do you think they are?” she asked Cornelio, as the truck lurched into motion again.
“Fragments from a big explosion,” he replied. “Something so distant that even the smallest differences in the speed of the debris could spread out its arrival over many years. My hunch is that successively later fragments will prove to be moving more slowly.”
“That’s an interesting idea.” Yalda tapped the box of goodies appreciatively. “Hopefully I’ll be able to test it soon.” A crisp image of a Hurtler’s light trail, captured at a single moment, might enable her to measure its asymmetry and finally quantify the object’s speed.
It was dark when they reached the city. At the university, Yalda bid farewell to Cornelio, stashed her new supplies in the optics workshop, then braved Ludovico’s wing of the department to see if Tullia was still around. But the place was empty. Tullia might have caught some observations of the Hurtler, then, on her way to her apartment or the Solo Club.
At the Solo, Yalda found Daria and Lidia; they hadn’t seen Tullia, but they persuaded Yalda to join them in a game of six-dice. To everyone’s amazement, Yalda won, so she stayed for a second game. Lidia beat her this time, but it was close.
Yalda was tired now, but she decided it was worth stopping by at Tullia’s apartment; it would be good to share the highlights of her trip to Amputation Alley. Tullia was planning to head up to Mount Peerless in a few stints; she could probably make use of Cornelio’s invention there herself.
When she arrived at the apartment, Yalda found the entrance unbarred but the curtain closed. She called out softly a few times, but received no reply. Tullia didn’t usually sleep so early, but if she’d dozed off after a hard day it would be unfair to wake her.
Yalda turned and started toward the stairs, but then she changed her mind; it wouldn’t hurt to sneak in quietly and check that everything was all right. She walked back, parted the curtain and stepped into the apartment.
Tullia was lying on the floor near the window. Yalda called her name but there was no response. She approached and knelt to examine her; Tullia was limbless, and her skin displayed a strange sheen. For one panicked moment Yalda thought of her grandfather, but then she realized that the patches of light she was seeing were just distorted reflections of the flowers above.
Yalda took her friend by the shoulders and shook her gently; her skin felt strange—tight, almost rigid—and she did not react at all. There was a furrow down the middle of her chest: a deep, narrow fissure, the first line of a symbol that Tullia would never have written by choice.