“Suppose we obtained a large number of identical sources of any vibration, and arranged them in a line in a regular fashion, with a spacing roughly comparable to, but exceeding, the wavelength of the vibration itself.”
An image appeared on Nereo’s chest.
“If we ask in what direction the wavefronts from all these sources will come into agreement,” he said, “the answer is that, firstly, they will agree if you move orthogonally away from the line on which they lie. However, that’s not the only case. They will also agree at another angle, at a particular inclination to the central direction on either side.”
“Unlike the first direction, though, this one will depend on the wavelength of the vibration: as the wavelength grows, the angle from the center grows too.”
“The precise relationship between wavelength and angle is a simple trigonometric formula that will be familiar to all of you from Giorgio’s work; he dealt with two sources, and I am merely extending that idea. But increasing the number of sources does yield a powerful advantage: the passage of more light delivers a brighter, clearer pattern.”
Nereo gestured to an assistant, who pulled on a control rod for the blinds covering the skylight, plunging the theater into darkness. Before Yalda’s eyes had time to adjust, three brilliant patches of light appeared on a screen behind the now-invisible speaker. She recognized the central one as an almost unmodified image of the sun, captured by the heliostat on the theater’s roof. On either side of it were two dazzling streaks of color, distorted echoes of the primary image. Their inner rims, closest to the center of the screen, were deep violet, and they progressed in a rich, clear spectrum all the way to red. They were like star trails for the sun.
Nereo spoke from the darkness. “With the aid of my benefactor’s best machinists, I constructed a system of pantographs to etch precisely-spaced apertures in a sliver of calmstone: more than two dozen gross per scant. My measurements imply that vibrations of violet light come six dozen gross to the scant; the reddest light about three and a half dozen.” This was broadly in agreement with Giorgio’s results: a refinement, not a contradiction.
Yalda had seen a similar spectacle produced many times before, with clearstone prisms, but beyond the sheer beauty of Nereo’s crisper version she understood its significance. No one could give a detailed account of the underlying process by which a prism split light into its individual colors, so the angles at which different hues emerged from the slab of clearstone revealed nothing about the light itself. But Nereo’s barrier was not mysterious; every aperture’s location was known to him, every microscopic detail was there by his design. That light could be a vibration at all defied common sense—what was there to vibrate, in the void between the stars?—yet here was not only compelling evidence for that doctrine, but also a clear, unambiguous way to attach a wavelength to every hue.
The blinds were opened again. Yalda barely listened to the audience’s questions; the only thing she wanted to ask Nereo was how soon he could make another of these marvels. While Ludovico droned on about the “obvious” possibilities for reconciling Nereo’s experiment with the doctrine of luminous corpuscles, Yalda fantasized about pantographs. If Nereo could not supply them with a light comb, perhaps the university could make its own?
When the session ended, she moved quickly to the front of the theater; as one of Giorgio’s students it was her responsibility to help provide hospitality to his guest. Rufino and Zosimo were already hovering nearby, ready to escort Nereo to the food hall. But as the two great experimentalists chatted, Nereo’s rear gaze fell on Yalda. Her size made it hard for anyone to ignore her, and when their eyes met she seized the opportunity.
“Excuse me, sir, but I neglected to ask a question of you earlier,” she said.
Giorgio did not look pleased, but Nereo indulged her. “Go ahead.”
“The position of light within a star trail depends on its velocity,” she began. “If you fed successive slices from a star trail through your device, might that not allow you to build up a detailed picture of how the wavelength and velocity are related?” When Nereo did not reply straight away, Yalda added helpfully, “The university has an excellent observatory on Mount Peerless. A collaboration, combining the two instruments—”
Nereo cut her off. “If you took a sliver of a star trail narrow enough to characterize the light’s velocity, it would not make a bright enough source. The diffracted image with the wavelength information would be so dim as to be invisible.”
He turned back to Giorgio. Yalda cursed herself silently; she hadn’t thought through the practicalities.
As the five of them left the lecture theater and crossed the cobbled grounds, she struggled to find a way to salvage her proposal. The chemists were forever promising to devise a light-sensitive coating for paper that could record a telescopic image of the stars if subjected to a sufficiently long exposure. But their best offerings to date only responded to a narrow band of colors, and were prone to spontaneous combustion.
When they reached the food hall, Ludovico was waiting just inside the entrance. Zosimo bravely split off and approached him, improvising some diversionary nonsense about an administrative issue with his fees. Everyone welcomed debate about the merits of the wave and corpuscular doctrines, but Ludovico had crossed the line into monomania.
Yalda and Rufino went to fetch food from the pantry. “You must have sensitive eyes, Yalda,” Rufino teased her, “to aspire to measure the wavelength of a wisp of starlight.”
“There must be a way,” she retorted, extruding an extra pair of arms to deal with the choice of six seasoned loaves it was customary in Zeugma to offer to a guest.
The food hall wasn’t crowded; most people took lunch later, at the third bell. As Nereo and Giorgio sat eating, Yalda and Rufino stood by attentively; Zosimo was nowhere to be seen, but he must have stuck to his story and goaded Ludovico, as the department’s treasurer, into dragging him back to his office to check the payment records.
Contemplating the effort and skill that must have gone into the construction of Nereo’s marvel, Yalda realized that it would take the university years to develop the facilities to make their own light combs; the precision required was far beyond their present capabilities. If Nereo departed without an agreement to collaborate with them, they’d be left with nothing but the tables he’d doubtless publish in due course, assigning wavelengths to various subjectively judged hues. Being told how many vibrations of “red”, “yellow” or “green” light there were to a scant wasn’t utterly useless, but compared to being able to quantify the wavelength of an actual beam of light on an optical workbench it was a miserable second best. And to have any hope at all of making sense of light, they needed good numbers. Mathematics had been used to understand the vibrations of sound, the vibrations of solids, the vibrations of plucked strings—linking the properties of those diverse kinds of wave with the properties of the media that supported them. The medium that supported light was the most elusive of all, but if they could wrap the waves themselves in numbers, even this strange substance might yet be brought into the realm of comprehension.
Nereo stood and addressed the students. “The food was delicious; thank you.”
Desperate, Yalda blurted out an idea that had been lurking unvoiced in the back of her mind. “Sir, forgive me, but… what if you fed an entire star trail into your device? Properly focused, wouldn’t the spread of colors be recombined into an image that was bright enough to see?”
Giorgio said, “Please! Our guest is tired!”
Nereo raised a hand, requesting his forbearance, and responded to Yalda. “By the principle of reversibility, yes—but only if the way the colors were distributed by the two methods were in precise agreement, which I doubt would be the case.”
Yalda’s skin tingled with excitement. If the recombination of the colors was sensitive to the detailed way the light was brought together, all the better.
“What if the star trail was focused by means of a flexible mirror?” she suggested. “A band that could be adjusted to vary the angles at which the colors were delivered, all along its length. By changing the shape of that mirror until the combined system yielded a single, sharp image for the star… wouldn’t the final, successful shape embody information about the relationship between wavelength and velocity?”
Nereo fell into a thoughtful silence. Rufino stared at the floor, embarrassed. Giorgio stared directly at Yalda; she could tell that he was actually quite taken by the sheer audacity of her suggestion, if not by the clumsy way she’d raised it.
Nereo said, “It just might work. And if you blocked the center of the star’s image—the brightest part—your eyes would adapt to the lesser brightness of the remaining halo, allowing you more easily to judge when your adjustments had diminished it as much as possible.”
Yalda was momentarily lost for words. If Nereo was offering her ways to improve her methodology, that meant he was taking the whole thing seriously.
“So you think it’s a worthwhile experiment?” she asked.
“Absolutely,” Nereo assured her. “And better you than me on Mount Peerless! I’ve grown used to the presence of certain decadent comforts, such as air.”
Giorgio buzzed amusement.
Yalda had never been to the observatory, but she didn’t care what hardships it entailed. “You’ll let us borrow the light comb, sir?” The glittering key to the secrets of wavelength, bought with his patron’s incomparable wealth, would be borne up the mountain’s slope to meet the starlight… in her hands?
“I’ll let you borrow it for eight chimes,” Nereo replied, “before I have to leave to catch my train. That should be long enough for you to calibrate your best prism against it.”
“Prism? But—”
Nereo said, “Everything in your methodology should work just as well with a prism used to recombine the star trails; all you need in order to make that worthwhile is a conversion table that translates between the angles at which the same hue emerges from the different devices. Do you think you can manage that, before I depart?”
In the optics workshop a young student was using the heliostat for an experiment in polarization, but when Yalda asked if he could take an early lunch he obliged without a moment’s hesitation.
From the storage room, she chose a prism that she’d used before; the sides had been polished to near-perfect flatness, and were unblemished by chips or scratches. Equally, the clearstone from which it had been cut appeared to contain no internal flaws. She knew that it would separate the colors smoothly, however mysterious its method.
With the prism in place in the beam of sunlight that was brought down from the clockwork-driven mirror on the roof, Yalda locked Nereo’s comb onto a platform that could swivel through the emerging fan of colors, along with a slit for selecting a narrow range of the prism’s light. The slit could not be set too fine, though, or it would itself diffract the beam.
She placed a white screen half a stride beyond the comb, and set about recording the pairs of angles for a succession of hues: the angle at which the light had been bent by the prism, and the angle at which it was subsequently bent by the comb.
Yalda worked with scrupulous care, but after a while the process became mechanical, automatic. She glanced at the polarisers she’d taken off the bench: slabs of an exotic form of clearstone from Shattered Hill. Place one of them in a beam of light, and the beam’s brightness was diminished by one third. A second polariser aligned identically with the first had no effect, but if the two were “crossed”—their axes arranged at right angles to each other—the original brightness was diminished by a further third.
Giorgio had sought to explain this in terms of the wave doctrine. An elastic solid could experience shear waves, in which the medium suffered distortions perpendicular to the direction of the wave’s motion. A polariser, he argued, must somehow be inhibiting light’s equivalent of such waves when they lined up with the stone’s special axis. A horizontal polariser could rid a beam of sunlight of its left-to-right vibrations; a second, aligned vertically, would rid it of all waves that vibrated up and down.
A mystery remained, though. Along with shear waves, every solid carried pressure waves, which were much like the sound waves in air. The velocities of the two kinds of wave were due to distinct properties of the material, and pressure waves always traveled faster than shear waves. It would require both a truly bizarre material and an absurd coincidence to force the two to share the same speed.
When two crossed polarisers were held up to a star trail, if the light that emerged had traveled from the star at a different speed than the light that was blocked, some portion of the trail’s spread of velocities should have been favored over the rest. But in fact what was seen was a perfectly uniform dimming of the entire trail. Light waves that lacked polarity—supposedly the equivalent of a solid’s pressure waves—were no faster or slower than the rest.
Yalda could not believe that this was a coincidence—a perfect conspiracy of elastic moduli. Rather, what it suggested was that the whole analogy was flawed. Whatever carried light between the stars wasn’t actually being squeezed and stretched and sheared. Nereo had pinned down light’s wavelength, the distance at which each cycle repeated, but the truth was that no one yet had an answer to the question: cycles of what?