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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.

9 thoughts on “Defining a universe — how many constants?

  1. As noted elsewhere, in 2019, venerable theoretical physicist Lee Smolin was busy promoting his latest book, Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum. He based a lecture on the book: Perimeter Institute online video > Lee Smolin Public Lecture.

    In his book Smolin discusses the foundations for the realist vs. anti-realist interpretations of quantum physics. I find his relational model interesting – “an object’s properties are not intrinsic to it — rather they reflect the relationships or interactions that object has with other objects.”

    While this Quanta Magazine article notes that “Smolin is considered a fringe figure in the field,” his sketch of a more complete cosmological theory has merit.

    Quanta Magazine > Insights Puzzle > “Solution: ‘Is It Turtles All the Way Down?’” by Pradeep Mutalik (March 27, 2020) – While the age-old chicken-and-egg paradox is easily answered, the question of infinite regress in physics is far from resolved.

    The question of how to solve the problem of infinite regress in physics elicited comments about modern theories that avoid some of the more paradoxical aspects of cosmology such as singularities.

    These theories do have the potential to enlarge our understanding of the beginning of the universe and its fate, but can they explain how the laws of the universe and universal constants and parameters took the form they did? … What’s required for this has been clearly stated by the cosmologist Lee Smolin. As Torbjörn commented, Smolin is considered a fringe figure in the field and has not had the compelling successes required for his theory of the evolution of the universe to become mainstream. However, in his book Time Reborn, Smolin uses philosophical principles to sketch out some of the qualities that an intellectually satisfactory and complete cosmological theory of the universe must have. I reproduce his criteria below (with some explanatory text in brackets):

    • It should contain what we already know about nature, but as approximations.

    • It should be scientific; that is, it has to make testable predictions for doable experiments [or experiments done by nature].

    • It should solve the Why these laws?

    • It should solve the initial-conditions problem.

    • It should be causally and explanatorily closed. Nothing outside the universe should be required to explain anything inside the universe.

    • It should satisfy the principle of sufficient reason, the principle of no unreciprocated action, and the principle of the identity of the indiscernibles.

    [Leibniz’s principle of sufficient reason states that there should be an answer to any reasonable question we might ask about why the universe has some particular feature.

    No unreciprocated action means that there should be nothing that affects the rest of the universe without being affected in return, which would rule out, for instance, Newtonian absolute time and absolute space.

    Identity of indiscernibles, another Leibniz principle, implies that two things that have the same relationships with everything else in the universe must actually be the same thing. This last principle precludes the existence of an infinite universe where every possible configuration and circumstance is repeated an infinite number of times: In that case, there would be no need to explain why something is the way it is!]

    • Its physical variables should describe evolving relationships between dynamical entities. There should be no fixed-background structures, including fixed laws of nature. Hence the laws of nature evolve [based on changing dynamical conditions within the universe in time].

    Other items mentioned in the article:

    • The pesky question: “Why is there something rather than nothing?”

    • The infinite regress problem for consciousness.

    • The question: “At what point in evolution does consciousness (internal experience) start, and with what experience?”

  2. A much simpler take than Ethan Siegel’s on defining a universe.

    A standard model of cosmology based on the Big Bang theory and research on the cosmic microwave background (CMB).

    • Science Focus > “The six numbers that define the entire Universe” by Prof Lyman Page (January 5, 2021) – In this edited extract from The Little Book of Cosmology, physicist Prof Lyman Page explains how our model of the Universe relies on just six parameters.

    With these six parameters in hand, we can compute the characteristics not only of the CMB but of any cosmological measurement we’d like to make. We can, for example, compute the age of the Universe: 13.8 billion years (give or take 40 million years).

    It means we can be proved wrong – not by different arguments, but by a better quantitative model that describes more aspects of nature.

    • “The amount of normal matter, or atoms, in the Universe, and it says that atoms account for just 5 per cent of the Universe.”

    • The amount of dark matter (25%) – “some type of new fundamental particle that we do not yet understand.”

    • The cosmological constant aka dark energy – “70 per cent of the Universe’s total matter and energy budget.”

    Optical depth – “how opaque the Universe was to the photons travelling through it.” [Re the epoch of reionisation of the universe and measurement of the polarisation of the CMB.]

    Primordial power spectrum – “the fluctuations in the density of the Universe in three-dimensional space.” [Density function / field over space.]

    Scalar spectral index – “how the [amplitudes of] primordial fluctuations, the tiny energy variations that were present in the infant Universe, depend on angular scale.”


    1. How is the amount of dark matter derived from our measurements of the minute temperature fluctuations in the cosmic microwave background radiation?

    2. How is the presence of dark energy directly measured through the cosmic acceleration?

  3. A quick recap of the history and standing of the cosmological constant: “dark energy is simply a placeholder describing some unknown anti-gravity substance.”

    The universe’s expansion rates in different directions is not uniform?

    • > “What is the cosmological constant?” by Adam Mann (Feb 23, 2021)

    The cosmological constant is presumably an enigmatic form of matter or energy that acts in opposition to gravity and is considered by many physicists to be equivalent to dark energy. Nobody really knows what the cosmological constant is exactly, but it is required in cosmological equations in order to reconcile theory with our observations of the universe.

    connecting vacuum energy to the cosmological constant is not straightforward. Based on their observations of supernovas, astronomers estimate that dark energy should have a small and sedate value, just enough to push everything in the universe apart over billions of years.

    Yet when scientists try to calculate the amount of energy that should arise from virtual particle motion, they come up with a result that’s 120 orders of magnitude greater than what the supernova data suggest.


    Cosmological constant
    Friedmann Equation
    ΛCDM (Lambda CDM, where CDM stands for cold dark matter)

  4. Another useful recap by Paul Sutter – “baking” a universe (like whether really from scratch or not, eh).

    • > “How to make a universe” by Paul Sutter (June 8, 2021) – “Normal” stuff is optional.

    (quote) To get the cosmos we know, you need around 25% dark matter and 70% dark energy. Dark matter is some form of matter that is completely invisible; whatever it is, it doesn’t interact with light. We don’t know exactly what the dark matter is made of, but we do know it’s there through its gravitational machinations and interactions with everything else.

    We suspect that dark energy has something to do with the vacuum of space-time itself.

    – – –

    As far as “normal matter,” Sutter just mentions “baryonic” matter rather than speculating about a precursor quark-gluon fluid (or plasma). Or something sort of like “yeast” for the “dough” to expand, eh.

    But he does mention the “cosmic web” and cosmic voids, the CMB, etc.

  5. I am fascinated by the effort to reconcile ongoing discoveries about the geometry and arrangment and structure of the universe and that predicted by the Big Bang theory. Particularly for large structures, way beyond galactic clusters. Sort of writ large.

    The Big Bang theory is a model, sort of an idealized state, with a certain type of smoothness and symmetry. Which is then explosively carried forward. Using sort of uniformly evolving dynamics, which rule out certain nascent properties.

    Does “reverse engineering” of a dynamical fluidic system recover the original state? Even in principle? Like the classic example of recovering the initial state of a cup of coffee before cream was poured into it. Or before a Diet Coke and Mentos eruption (also known as a soda geyser), say, in microgravity using a floating sphere of soda.

    • > “Astronomers discover largest known spinning structures in the universe” by Charles Q. Choi (June 14, 2021) – They’re hundreds of millions of light-years long.

    (quote) Previous research suggested that after the universe was born in the Big Bang about 13.8 billion years ago, much of the gas that makes up most of the known matter of the cosmos collapsed to form colossal sheets. These sheets then broke apart to form the filaments of a vast cosmic web.

    The scientists noted they do not suggest that every single filament in the universe spins, but that spinning filaments do seem to exist.

    The big question is, “Why do they spin?” Libeskind [Noam Libeskind, a cosmologist at the Leibniz Institute for Astrophysics Potsdam in Germany] said. The Big Bang would not have endowed the universe with any primordial spin.

  6. Regarding the Big Bang and quark-gluon fluid, this article presents an overview of research at the LHC exploring primordial matter.

    • Earth Sky > “The 1st Microsecond Of The Big Bang” by Deborah Byrd (June 16, 2021) – The peer-reviewed journal Physics Letters B has published this new work online for its July 10, 2021, issue.

    (quote) You Zhou, together with his student Zuzana Moravcova, both at the Niels Bohr Institute at the University of Copenhagen, performed the work.

    On May 31, 2021, researchers said they used the Large Hadron Collider to investigate a specific kind of plasma present during the first millionth of a second – aka the first microsecond, or 0.000001 second – of the Big Bang. They said this plasma was the first matter ever to be present in our universe. And, they said, it had liquid-like properties [“constantly changing its shape over time”].

    Zhou commented: “For a long time researchers thought that the plasma was a form of gas, but our analysis confirm the latest milestone measurement, where the Hadron Collider showed that QGP was fluent and had a smooth soft texture like water.”

    The article includes a May 7, 2015, Fermilab YouTube video by Don Lincoln on Quark Gluon Plasma.

  7. As noted on my Famous Quotes page, “Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant … [as] a mystery ever since it was discovered.” [1]

    Wiki notes several interpretations of the fine-structure constant (α). See article for details of these.

    An essential interpretation (beyond spectroscopy) is based on the theory of quantum electrodynamics (QED):

    In quantum electrodynamics, α is directly related to the coupling constant determining the strength of the interaction between electrons and photons.”

    as a value plugged into the Standard Model:

    The theory does not predict its value. Therefore, α must be determined experimentally. In fact, α is one of the empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model.

    Some definitions are ratios of other pararemters [2]:

    > The ratio of two energies …

    > Using the Bohr model of the atom, the ratio of the velocity of the electron in the first circular orbit over the speed of light in vacuum. [Historically, the first physical interpretation.]

    > The two ratios of three characteristic lengths: the classical electron radius, the Compton wavelength of the electron, and the Bohr radius.

    Ethan Siegel discussed this constant in a June 1, 2019, article (as noted in another comment above).

    Here’s Paul Sutter’s take (article includes a video).

    • > “Life as we know it would not exist without this highly unusual number” by Paul Sutter (March 24, 2022)

    Historically, physicist introduced other relational constants in physics [3]. But the fine-structure constant is unit-less: “There are no dimensions or unit system that the value of the number depends on.”

    The full explanation for the “fine structure” of the spectral line rests in quantum field theory, a marriage of quantum mechanics and special relativity. And one of the first people to take a crack at understanding this was physicist Arnold Sommerfeld. He found that to develop the physics to explain the splitting of spectral lines, he had to introduce a new constant into his equations — a fine-structure constant.

    In time, we came to recognize it as the fundamental measure for the strength of how charged particles interact with electromagnetic radiation. [In QFT, the interaction between two fields, the electron field and photon field (at low energies).]

    Today, we have no explanation for the origins of this constant. Indeed, we have no theoretical explanation for its existence at all. We simply measure it in experiments and then plug the measured value into our equations to make other predictions.


    Electron self-interaction

    Quantum Hall effect

    Anomalous magnetic moment of the electron

    Atom interferometry


    [1] I wonder whether there’s a higher dimensional geometric interpretation of the fine structure constant, related to interaction between topological knots and quantum vacuum.

    A Google search for “geometric interpretation of the fine structure constant” listed papers which explore its mystery. As a pure geometric number. Or using dimensional analysis. Or a mathematician’s take. Etc.

    As an example, this 2020 paper recaps its history and then discusses an interpretation “based on the vortex model and hydrodynamics” – a superfluid model (cf. Wilczek’s Grid?).

    The historical “The Structure of the Electron” section is interesting. In particular, the geometry of an electron’s extension in spacetime and “a physical relationship between flux and charge.”

    • Scientific Research (An Academic Publisher) > “A New Theory on the Origin and Nature of the Fine Structure Constant” by Nader Butto.

    (quote from abstract)

    The vacuum [is] considered to have superfluid characteristics and elementary particles such as the electron and Hydrogen molecule are irrotational vortices of this superfluid. In such a vortex, the angular rotation ω is maintained, and the larger the radius, the slower the rotational speed. The fine structure value is derived from the ratio of the rotational speed of the boundaries of the vortex to the speed of the vortex eye in its center. Since the angular rotation is constant, the same value was derived from the ratio between the radius of the constant vortex core and the radius of the Hall vortex. Therefore, the constancy of alpha is an expression of the constancy relation in the vortex structure.

    [2] In the definition(s), this measured constant is particularly interesting: the magnetic constant or permeability in vacuum or free space (µ sub 0) – from which are calculated the electric constant or permittivity in vacuum or free space (ε sub 0); and the vacuum impedance or impedance in free space (Z sub 0).

    Some equivalent definitions of α [approximately 1/137] in terms of other fundamental physical constants are:


    [3] Wiki notes:

    This constant was not seen as significant until Paul Dirac’s linear relativistic wave equation in 1928, which gave the exact fine structure formula.

  8. Here’s an article with a brief historical recap [1] and then some discussion of the “niggling suspicion” that “the gravitational constant isn’t quite as constant as scientists thought.” [2]

    • > “What is the gravitational constant?” by Keith Cooper (Sep 14, 2022) – The gravitational constant is the key to measuring the mass of everything in the universe.

    However, attempts to try and detect any significant variations in G in other parts of the universe have so far found nothing.


    [1] For example, the Cavendish experiment, as presented in this Harvard Natural Sciences Lecture Demonstration.

    [2] As noted above, the gravitational constant (universal dimensioned physical constant) is not in the posted list of fundamental physical dimensionless constants.

    Cavendish experiment
    Credit: Public domain (Wiki)

  9. Theory, predictions, observations.

    Here’s an article which summarizes research on general relativity. In particular, using statistical methods and a computer model based on key parameters: “the expansion of the universe, the effects of gravity on light and the effects of gravity on matter.” [1]

    • > “Something is wrong with Einstein’s theory of gravity” by Levon Pogosian [Professor of Physics, Simon Fraser University], Kazuya Koyama [Professor of Cosmology, University of Portsmouth] (11-20-2022) – Does the theory of general relativity need to be tweaked at large scales?

    Using a statistical method known as the Bayesian inference, we reconstructed the gravity of the universe through cosmic history in a computer model based on these three parameters [above]. We could estimate the parameters using the cosmic microwave background data from the Planck satellite, supernova catalogues as well as observations of the shapes and distribution of distant galaxies by the SDSS and DES telescopes. We then compared our reconstruction to the prediction of the LCDM model (essentially Einstein’s model).

    Our study also found that it is very difficult to solve the Hubble tension problem by only changing the theory of gravity. … we will have a lot more data from new probes in a few years.


    [1] An interesting point re the quantum vacuum:

    Quantum theory predicts that empty space, the vacuum, is packed with energy. We do not notice its presence because our devices can only measure changes in energy rather than its total amount.

    LCDM Accelerated Expansion of the Universe
    Credit: By Design Alex Mittelmann, Coldcreation, CC BY-SA 3.0

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