General · Language

Defining a universe — how many constants?

[Draft] [“Building a ‘verse” series]

Reference: “How Many Fundamental Constants Does It Take To Explain the Universe?” by Ethan Siegel (Nov 23, 2018).

Quite a large number of fundamental constants are required to describe reality as we know it …

The fundamental constants … describe the strengths of all the interactions and the physical properties of all the particles. We need those pieces of information to understand the Universe quantitatively, and answer the question of “how much.” It takes 26 [dimensionless] fundamental constants to give us our known Universe, and even with them, they still don’t give us everything.

As a metaphor, imagine trying to build something and not knowing how any of the materials or parts interact. For example, whether two pieces might stick together (or how strongly they do so). Whether some pieces will melt or crack due to temperature. Whether we can substitute one material for another without a problem. How long can we expect a part to last? How heavy are the raw materials (especially if our goal is to minimize weight)?

In an ideal world, at least from the point of view of most physicists, we’d like to think that these constants arise from somewhere physically meaningful, but no current theory predicts them.

If you give a physicist the laws of physics, the initial conditions of the Universe, and these 26 [dimensionless] constants, they can successfully simulate any aspect of the entire Universe. [2]

… our greatest hopes of a unified theory — a theory of everything — seek to decrease the number of fundamental constants we need. In reality, though, the more we learn about the Universe, the more parameters we’re learning it takes to fully describe it.

  • 1 The fine-structure constant (one of Feynman’s favorite mysteries) [3]
  • 2 The strong coupling constant
  • 3–17 The masses of the six quarks, six leptons, and three massive bosons (currently not derivable from anything more profound)
  • 18–21 The quark mixing parameters
  • 22–25 The neutrino mixing parameters
  • 26 The cosmological constant


[1] Notice what’s not in the above list of constants? Some that you probably learned in high school science (if not earlier): speed of light (c), gravitational constant (G), charge of an electron, mass of an electron, permittivity of free space, Planck’s constant. Hmm … That’s because a narrower definition is being used, as noted in this Wiki article:

The term fundamental physical constant is normally used to refer to the dimensionless constants, but has also been used (primarily by NIST and CODATA) to refer to certain universal dimensioned physical constants, such as the speed of light c, vacuum permittivity ε0, Planck constant h, and the gravitational constant G, that appear in the most basic theories of physics. Other physicists do not recognize this usage, and reserve the use of the term fundamental physical constant solely for dimensionless universal physical constants that currently cannot be derived from any other source.

[2] “Even with this, there are still four puzzles that may yet require additional constants to solve.” These are:

  • The problem of the matter-antimatter asymmetry.
  • The problem of cosmic inflation.
  • The problem of dark matter.
  • The problem of strong CP-violation.

[3] “Ask Ethan: What Is The Fine Structure Constant and Why Does It Matter? — Forget the speed of light or the electron’s charge. This is the physical constant that really matters” by Ethan Siegel (Jun 1, 2019)

Not only is there the coarse structure (from electrons orbiting a nucleus) and fine structure (from relativistic effects, the electron’s spin, and the electron’s quantum fluctuations), but there’s hyperfine structure: the interaction of the electron with the nuclear spin. The spin-flip transition of the hydrogen atom, for example, is the narrowest spectral line known in physics, and it’s due to this hyperfine effect that goes beyond even fine structure.

But the fine structure constant, α, is of tremendous interest to physics. Some have investigated whether it might not be perfectly constant. … These initial results, however, have failed to hold up to independent verification, …

A different type of variation, though, has actually been reproduced: α changes as a function of the energy conditions under which you perform your experiments. … at low energies, the virtual contributions from electron-positron pairs are the only quantum effects that matter in terms of the strength of the electrostatic force. But at higher energies, it not only becomes easier to make electron-positron pairs, giving you a larger contribution, but you start getting additional contributions from heavier particle-antiparticle combinations.