When you encounter the question of “how much,” you probably think of the force of gravity being determined by a universal gravitational constant, G, and of the “energy of a particle” being determined by its rest mass, such as the mass of an electron, me. You think of the speed of light, c, and for quantum mechanics, Planck’s constant, ħ. But physicists don’t like to use these constants when we describe the Universe, because these constants have arbitrary dimensions and units to them.
As it turns out, it takes 26 dimensionless constants to describe the Universe as simply and completely as possible, which is quite a small number, but not necessarily as small as we like. Here’s what they are.
1.) The fine-structure constant, or the strength of the electromagnetic interaction. In terms of some of the physical constants we’re more familiar with, this is a ratio of the elementary charge (of, say, an electron) squared to Planck’s constant and the speed of light. But if you put these constants together, you get a dimensionless number! At the energies currently present in our Universe, this number comes out to ≈ 1/137.036, although the strength of this interaction increases as the energy of the interacting particles rise.
2.) The strong coupling constant, which defines the strength of the force that holds protons and neutrons together. Although the way the strong force works is very different from the electromagnetic force or gravity, the strength of this interaction can still be parametrized by a single coupling constant. This constant of our Universe, too, like the electromagnetic one, changes strength with energy.
3–17.) This one is a bit of a disappointment. We have fifteen particles in the Standard Model: the six quarks, six leptons, the W, Z, and the Higgs boson, that all have a rest mass. While it’s true that their antiparticles all have identical rest masses, we were hoping that there would’ve been some relationship, pattern, or more fundamental theory that gave rise to these masses with fewer parameters. Alas, it takes fifteen constants to describe these masses, with the lone good news that we can scale these parameters to be relative to the gravitational constant, G, to wind up with 15 dimensionless parameters that have no need for a separate descriptor of the gravitational force’s strength.
18–21.) The quark mixing parameters. We have six different types of quarks, and because there are two subsets of three that all have the same quantum numbers as one another, they can mix together. If you’ve ever heard of the weak nuclear force, radioactive decay or CP-violation, these four parameters — all of which must be (and have been) measured — are required to describe them.
22–25.) The neutrino mixing parameters. Similar to the quark sector, there are four parameters that detail how neutrinos mix with one another, given that the three types of neutrino species all have the same quantum number. The solar neutrino problem — where the neutrinos emitted by the Sun weren’t arriving here on Earth — was one of the 20th century’s biggest conundrums, finally solved when we realized that neutrinos had very small but non-zero masses, mixed together, and oscillated from one type into another. The quark mixing is described by three angles and one CP-violating complex phase, and the neutrino mixing is described in the same way. While all four parameters have already been determined for the quarks, the CP-violating phase for the neutrinos is not yet measured.
If you give me the laws of physics and these 26 constants, I can throw these into a computer and tell it to simulate my Universe. And quite remarkably, what I get out looks pretty much indistinguishable from the Universe we have today, from the smallest, subatomic scales all the way up to the largest, cosmic ones.
The problem of the matter-antimatter asymmetry. The entirety of our observable Universe is made up dominantly of matter and not antimatter, yet we do not fully understand why this is so, or why our Universe has the amount of matter it does. This problem — the problem of baryogenesis — is one of the great unsolved problems in theoretical physics, and may require one (or more) new fundamental constants to describe its solution.
The problem of cosmic inflation. This is the phase of the Universe that preceded and set up the Big Seed has made many new predictions that have been verified observationally, but isn’t included in this description. Very likely, when we more fully understand what this is, additional parameters will have to be added to this set of constants.
The problem of dark matter. Given that it almost definitely consists of at least one (and maybe more) new type of massive particle, it stands to reason that more new parameters — potentially even more than one for each new particle type — will need to be added.
The problem of strong CP-violation. We see CP-violation in the weak nuclear interactions and expect it in the neutrino sector, but we have yet to find it in the strong interactions, even though it is not forbidden. If it exists, there should be more parameters; if it doesn’t, there is likely an additional parameter related to the process that restricts it.
Our Universe is an intricate, amazing place, and yet our greatest hopes of a unified theory — a theory of everything — ought to decrease the number of fundamental constants we need. But the more we learn about the Universe, the more parameters we’re learning it takes to fully describe it. While it’s important to recognize where we are and what it takes, today, to describe the entirety of what’s known, it’s also important to keep searching for a more complete paradigm that not only gives us everything the Universe has to give us, but makes it as simple as possible.