[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 takes26[dimensionless]fundamental constantsto 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

Notes

[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) andfine structure(from relativistic effects, the electron’s spin, and the electron’s quantum fluctuations), but there’shyperfine 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 conditionsunder 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.

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.

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?”

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.

• “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 constantaka 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.”Questions1. 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?

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?

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

TermsCosmological constant

Einstein

Friedmann Equation

ΛCDM (Lambda CDM, where CDM stands for cold dark matter)

Quintessence

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

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

– – –

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.

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.

• Space.com > “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.

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.

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

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):

as a value plugged into 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).

• Space.com > “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.”

TermsElectron self-interaction

Quantum Hall effect

Anomalous magnetic moment of the electron

Atom interferometry

Notes[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)

[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.

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]

• Space.com > “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.

Notes[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.

Credit: Public domain (Wiki)