“Of course.” Yalda set her anxieties aside. If Cornelio really had created what she’d asked him for, it was well worth the risk of being here.
“Let me show you.” Cornelio led her to a bench at the side of the workshop. In lieu of a heliostat, he’d set up a pair of manually adjustable mirrors that brought sunlight into the room and directed it into a box three spans or so wide.
He opened the side of the box, revealing a prism mounted within that split the beam into a spectrum that fell on a white screen. “Note the locations of the various hues, if you will,” he suggested to Yalda.
“Noted.” After witnessing three Hurtlers over Zeugma, Yalda could memorize the position of a spread of colors against any backdrop in an instant.
Cornelio covered the aperture that admitted the sunlight into the box with a card pierced by a far smaller hole. The spectrum remained visible, but it was much dimmer now. Then he slid a second, entirely opaque card into another slot, parallel with the first one, blocking the light completely.
Next, he took what appeared to be a stiff sheet of paper from a cupboard below the bench, and fastened it in place over the screen where the spectrum had been seen. Then he produced a small vial that had been divided partly in two, with one half containing an orange powder, the other a green resin. He attached the vial to a loop of cord that dangled into the interior of the box through its top face.
Cornelio closed the side of the box, carefully checking that there were no gaps along the edges. “This needs to be entirely sealed against the light,” he said. “Not a crack.”
Yalda was surprised by his diligence, but it was a good sign. “I understand.”
“First, you shake the vial,” Cornelio explained, taking hold of the cord where it protruded from the top of the box and jiggling it slightly. “That lets the ingredients react, and the gas that’s produced activates the paper.”
“Activates?”
“Sensitizes it to light. But only for a few pauses, until the gas disperses, so I shouldn’t delay—”
Cornelio pulled the opaque card most of the way out of its slot, then pushed it back in immediately.
“What’s wrong?” Yalda asked.
“Nothing,” he assured her. “That was the necessary exposure to the light: about a flicker.”
The spectrum from the smaller aperture had barely been visible, yet one flicker was long enough to cause a reaction?
Cornelio said, “The gas should have dispersed of its own accord now, but I’m thinking of adding a bellows to ensure that it’s expelled completely. Maybe we should wait a couple of pauses longer to be sure though, if you don’t mind.”
“Believe me, my patience has not been tested yet.” Yalda had seen a demonstration of an earlier version of the same idea; it had required an exposure of at least three bells to capture even the brightest star trails—after which the paper had needed to be treated with a resin that, as often as not, caused it to burst into flames.
“I think…” Cornelio opened the box, fumbling with the clasps. He peered in, then stood aside and let Yalda take a look.
The paper had been darkened very visibly in three places; three narrow black strips marked the locations of—if Yalda’s memory served her—shades of red, yellow and blue. It hadn’t captured the whole spectrum, but the very fact that the reaction was not an indiscriminate, panchromatic response would make it all the more valuable. A smudge of black that covered the entire trail of a star or a Hurtler would have been useless. This system could capture the precise locations of three specific hues at one instant, finally making it possible to quantify details of the Hurtlers that were presently just the subject of fleeting impressions.
“This is wonderful!” she declared ecstatically.
“I’m glad it meets your approval,” Cornelio said modestly.
“Does the paper ever…?”
“Start burning? No. This is a completely different reaction from the old one.”
“Then it’s perfect. I don’t know what to say.”
Cornelio had already assembled a box full of the treated paper and a rack of the activating vials. “These are yours. When you need more, just let me know.”
“Thank you.”
Yalda could already picture the device she’d build to capture data on the Hurtlers, but it would be rude to snatch up this generous gift and rush away.
She said, “I don’t know if the light recorder has occupied all of your time, but I’d be interested to hear how any of your other research is progressing.”
“I’ve been doing some theoretical work as well,” Cornelio replied. “Rotational physics vindicated our earlier measurements of chemical energy differences, but the implications need to be developed much further. In fact, we’re having to reinvent most of thermodynamics.”
Yalda was surprised. “That sounds a bit extreme.”
Cornelio said, “If I told you that your theory implies that everything in this room is hotter than infinitely hot, would that justify rewriting the textbooks?”
“Infinity is my least favorite temperature,” Yalda confessed. “If you’re serious, I might have to recant.”
Cornelio buzzed softly. “Let’s call them negative temperatures, then; that’s formally correct, though the first way of speaking has its merits too.”
Yalda found the second way much more agreeable. “True energy has the opposite sense to kinetic energy, so to be consistent I suppose you could just declare all temperatures to be negative. Since a hot gas has less true energy than a cold gas, its temperature should be less… no?”
Cornelio was regarding her with an exasperated expression, but he was too polite to articulate precisely what he was feeling.
“I’m a physicist, show some mercy!” Yalda pleaded. “Thermodynamics is your domain. All I ever studied was the ideal gas law.”
“Temperature is not a synonym for energy,” Cornelio said sternly. “It’s about the proclivity of energy to pass from one system to another, not the quantity of energy that either one contains.”
“I’m willing to believe that,” Yalda said. “But how do you make such a ‘proclivity’ precise?”
“First,” Cornelio said, “think about the range of different ways in which one system can possess the same energy. Start with a single particle of gas, under the old physics.”
He summoned a diagram onto his chest. “The particle’s kinetic energy is proportional to its momentum squared. Pick a few examples of the energy the particle might have, but don’t pin it down precisely; just say that the energy lies in some small interval. From the plot on your left, you can read off a corresponding range for the momentum in each case.”
Yalda examined the diagram. “So you follow the horizontal lines for energy across until they hit the curve, then drop them down to the momentum axis?”
“That’s correct,” Cornelio said. “But then, recall that momentum is a vector. The energy has given us a range of sizes for that vector, but no information at all about its direction. The particle might be traveling north, west, up, down; we don’t know. So, take an arrow whose length you know, more or less, and swing it around freely, without any constraints. The tip of the arrow traces out a sphere—or rather, because the length isn’t fixed exactly, a spherical shell. The volume of that shell in ‘momentum space’ represents all the possibilities open to the particle, while still having an energy that lies within the given range.”
Yalda said, “So you’ve sketched parts of these shells, and plotted their volume against the kinetic energy… which turns out to be the same kind of curve as the momentum itself.”
“In this case, yes,” Cornelio said, “but that’s not true in general! So forget the resemblance, and just concentrate on the right-hand curve on its own terms. What does it tell you?”
“The volume in momentum space gets larger as you increase the kinetic energy,” Yalda said. “That makes sense. A faster particle has its momentum lying on a bigger sphere; the shells do get thinner as the momentum grows, but the larger surface area of the sphere more than compensates for that.”
“So the volume grows,” Cornelio agreed, “but when does it grow most rapidly?”
“At the start,” Yalda said. “When the energy is low, the volume shoots up; after that, it grows ever more slowly.”
“Precisely.”