In our Universe, quantum transitions are the governing rule behind every nuclear, atomic, and molecular phenomenon. Unlike the planets in our Solar System, which could stably orbit the Sun at any distance if they possessed the right speed, the protons, neutrons, and electrons that make up all the conventional matter we know of can only bind together in a specific set of configurations. These possibilities, although numerous, are finite in number, as the quantum rules that govern electromagnetism and the nuclear forces restrict how atomic nuclei and the electrons that orbit them can arrange themselves.

In all the Universe, the most common atom of all is hydrogen, with just one proton and one electron. Wherever new stars form, hydrogen atoms become ionized, becoming neutral again if those free electrons can find their way back to a free proton. Although the electrons will typically cascade down the allowed energy levels into the ground state, that normally produces only a specific set of infrared, visible, and ultraviolet light. But more importantly, a special transition occurs in hydrogen that produces light of about the size of your hand: 21 centimeters (about 8¼”) in wavelength. Even as a physicist, you’d be well justified to call this the “magic length” of our Universe, as it just might someday unlock the darkest secrets hiding out in the deepest cosmic recesses from which starlight will never escape.

Backlit by the cosmic microwave background, a cloud of neutral gas can imprint a signal on that radiation at a specific wavelength and redshift. If we can measure this light with great enough sensitivity, we can actually hope to someday map out the locations and densities of gas clouds in the Universe thanks to the science of 21 cm astronomy. A dip in brightness temperature at redshifts of 15-20, observed in 2018, may be due to exactly the effect of 21-cm emission, although better instrumentation and better observational examples will be required to confirm such a claimed detection.

When it comes to the light in the Universe, wavelength is the one property that you can count on to reveal how that light was created. Even though light comes to us in the form of photons — individual quanta that, collectively, make up the phenomenon we know as light — there are two very different classes of quantum process that create the light that surrounds us: continuous ones and discrete ones.

A continuous process is something like the light emitted by the photosphere of the Sun. It’s a dark object that’s been heated up to a certain temperature, and it radiates light of all different, continuous wavelengths as dictated by that temperature: what physicists know as blackbody radiation. More accurately, because the different layers of the photosphere are at different temperatures, the solar spectrum acts like a series of blackbodies all summed together: an amalgam of continuous processes.

A discrete process, however, doesn’t allow for the emission of light of a continuous set of wavelengths, but rather only at extremely specific, or discrete (and quantized), wavelengths. A good example of that is the light absorbed by the neutral atoms present within the extreme outer layers of the Sun. As the blackbody radiation from the lower layers of the photosphere strikes those neutral atoms sitting at the surface, a few of those photons will have just the right wavelengths to be absorbed by the electrons within the neutral atoms they encounter. When we break sunlight up into its individual wavelengths, the various absorption lines present against the backdrop of continuous, blackbody radiation reveal both of these processes to us.

The visible light spectrum of the Sun, which helps us understand not only its temperature and ionization, but the abundances of the elements present. The long, thick lines are hydrogen and helium, but every other line is from a heavy element that must have been created in a previous-generation star, rather than the hot Big Bang.

Each individual atom has its properties primarily defined by its nucleus, made up of protons (which determine its charge) and neutrons (which, combined with protons, determine its mass). Atoms also have electrons, which orbit the nucleus at a distance determined by their charge-to-mass ratio, and each electron can only occupy a specific set of energy levels. In isolation, each atom will come to exist in the ground state: where the electrons cascade down until they occupy the lowest allowable energy levels, limited only by the quantum rules that determine the various properties that electrons are and aren’t allowed to possess.

Electrons can occupy the ground state — the 1s orbital — of an atom until it’s full, which can hold two electrons. The next energy level up consists of spherical (the 2s) and perpendicular (the 2p) orbitals, which can hold two and six electrons, respectively, for a total of eight. The third energy level can hold 18 electrons: 3s (with two), 3p (with six), and 3d (with ten), and the pattern continues on upward. In general, the “upward” transitions occur when a photon of a particular wavelength gets absorbed, while the “downward” transitions can occur spontaneously, and result in the emission of photons of the exact same wavelengths as are present within the atom’s absorption spectrum.

Electron transitions in the hydrogen atom, along with the wavelengths of the resultant photons, showcase the effect of binding energy and the relationship between the electron and the proton in quantum physics. The Bohr model of the atom provides the coarse (or rough, or gross) structure of these energy levels. Hydrogen’s brightest atomic transition is Lyman-alpha (n=2 to n=1), but its second brightest is visible: Balmer-alpha (n=3 to n=2), which emits visib