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By Root 2067 0

brightness with its intrinsic brightness, we are measuring the dilution of the light’s intensity between emission (Figure 6.1a) and reception (Figure 6.1c), arising from its having spread out on a large sphere (drawn as a circle in Figure 6.1d) during the journey. By measuring the dilution, we determine the size of the sphere—its surface area—and then, with a little high school geometry, we can determine the sphere’s radius. This radius traces the light’s entire trajectory, and so its length equals the distance the light has traveled. Now the question that initiated this section pops up: To which of the three candidate distances, if any, does the measurement correspond?

During the light’s journey, space has continually expanded. But the only change this requires to the static cosmic map is a regular updating of the scale factor recorded in the legend. And since we have just now received the supernova’s light, since it has just now completed its journey, we must use the scale factor that’s just now written in the map’s legend to translate the separation on the map—the trajectory from the supernova to us, traced in Figure 6.1d—into the physical distance traveled. The procedure makes clear that the result is the distance now between us and the current location of the Noa Galaxy: the third of our multiple-choice options.

Figure 6.1 (a) Light from a distant supernova spreads as it travels toward us (we are situated in the galaxy on the map’s right-hand side). (b) During the light’s journey, the universe expands, which is reflected in the map’s legend. (c) When we receive the light, its intensity has been diluted through the spreading. (d) When we compare the supernova’s apparent brightness to its intrinsic brightness, we are measuring the area of the sphere on which it has spread (drawn as a circle), and hence also its radius. The radius of the sphere traces the light’s trajectory. Its length is the distance now between us and the galaxy that contained the supernova, so that’s what the observations determine.

Notice, too, that because the universe is continually expanding, earlier segments of a photon’s journey continue to stretch long after the photon has sped past. If a photo painted a line on space that traced its path, the length of that line would increase as space expanded. By applying the map’s scale factor at the time of reception to the light’s entire journey, the third answer directly incorporates all such expansion. This is the right approach, because the amount by which the light’s intensity is diluted depends on the size of the sphere over which the light now spreads—and this sphere’s radius is the length of the light’s trajectory now, including all post facto stretching.5

When we compare the intrinsic brightness of a supernova with its apparent brightness, we are therefore determining the distance now between us and the galaxy it occupied. Those are the distances the two groups of astronomers measured.6

The Colors of Cosmology

So much for measuring distances to faraway galaxies containing brilliant Type Ia supernovae. How do we learn about the rate of the universe’s expansion ages ago, when each of those cosmic beacons momentarily ignited? The physics involved isn’t much more complex than that at work in neon signs.

A neon sign glows red because when a current runs through the sign’s gaseous interior, orbiting electrons in the neon atoms are momentarily knocked into higher-energy states. Then, as the neon atoms calm, the excited electrons jump down to their normal state of motion, relinquishing the extra energy by emitting photons. The color of the photons—their wavelength—is determined by the energy they carry. A key discovery, fully established by quantum mechanics in the early decades of the twentieth century, is that atoms of a given element have a unique collection of possible electron energy jumps; this translates into a unique collection of colors for released photons. For neon atoms, a dominant color is red (or, really, reddish orange), which accounts for the appearance of neon signs. Other elements