Since Paul Dirac first wrote about the subject of cosmic coincidences in 1937, many physicists have marveled at the specific values of natural constants, such as G, the constant in the law of gravity (6.673×10^-11 N m² kg^-2) — an extremely low number. This is an empirical value measured carefully in labs under controlled conditions; it is not derived from equations. One could imagine it taking a different value. 

But it is balanced between two catastrophes. If stronger, stars would burn hotter, and photosynthesis would be impossible, and life, if it could exist at all under the crush of gravity, would have to take refuge underground. If gravity were weaker, opposite problems ensue: stars would be unable to start fusion and form heavy elements, and would slowly burn out by convection giving off reddish light. We would say goodbye to a sun with the white-yellow light just right for photosynthesis. 

Amazing Coincidences

In his short book Children of Light (2018), Michael Denton explored the amazing coincidences between the solar spectrum, elemental abundances, and earth’s atmosphere that permit not just some life, but large, complex organisms like human beings (hear him discuss this on ID the Future). His previous book, The Wonder of Water (2017), described additional coincidences regarding the varied roles of water on earth. The blessings we get from light and water depend exquisitely on the values of physical constants. These constants make the laws of nature work.

The constants must also be finely tuned relative to one another. For instance, the constant of gravity for stable stars is tied to the constant of electromagnetism, which is about 10⁴⁰ times larger. The requirement that both constants must be “just right” constrains the possibilities even further. Speaking of the balance between radiative stars and convective stars, Guillermo Gonzalez and Jay Richards said, 

This dividing line is another razor’s edge, a teetering balance between gravity and electromagnetism. If it were shifted one way or the other, main-sequence stars would either be all blue or all red (convection resulting in red stars). Either way, stars in the main sequence with the Sun]’s surface temperature and luminosity would be rare or nonexistent. 

(The Privileged Planet, p. 204)

The gravitational and electromagnetic constants that affect stars are also linked to the strengths of the nuclear forces — the weak force and strong force. Tinkering with the values of these constants does not open up more possibilities; it reduces them drastically. Martin Rees and John Gribbin remarked,

If we modify the value of one of the fundamental constants, something invariably goes wrong, leading to a universe that is inhospitable to life as we know it. When we adjust a second constant in an attempt to fix the problem(s), the result, generally, is to create three new problems for every one that we “solve.” The conditions in our universe really do seem to be uniquely suitable for life forms like ourselves, and perhaps for any form of organic chemistry. 

(Cited in The Privileged Planet, pp. 206-207)

Another remarkable book about fine-tuning is by Geraint Lewis and Luke A. Barnes: A Fortunate Universe: Life in a Finely-tuned Cosmos (Cambridge, 2016). In this book (p. 110), and also in The Privileged Planet (p. 207), diagrams show the region of stable stars among possible values of electromagnetic and gravitational constants. The region occupied by the actual values we measure that permit our habitable universe represents a tiny spot on the graph. Lewis and Barnes show additional parameter spaces where the Goldilocks zones are even tinier.

Can the Constants Vary?

Several physical constants can be related to a dimensionless number called the fine-structure constant, also called the electromagnetic coupling constant, represented by the Greek letter alpha (α). This value, curiously measured to be almost precisely 1/137 (NIST), relates the elementary charge, the magnetic constant, the speed of light and Planck’s constant. In short, it relates electromagnetism to quantum mechanics.

A recent paper in the AAAS open-access journal Science Advances, by Michael R. Wilczynska and 16 others, using a spectrograph on the Very Large Telescope (VLT) in Chile, attempted to measure the value of α in the distant reaches of the cosmos (indicated by quasars with high redshift) and compare it to the terrestrial value, called α₀. They begin by stating that the fine-tuning question motivated their research.

What fundamental aspects of the universe give rise to the laws of Nature? Are the laws finely tuned from the outset, immutable in time and space, or do they vary in space or time such that our local patch of the universe is particularly suited to our own existence? We characterize the laws of Nature using the numerical values of the fundamental constants, for which increasingly precise and ever-distant measurements are accessible using quasar absorption spectra. [Emphasis added.]

The subject of variable constants could be divided into two questions: do any of the constants vary from place to place in the universe, or do they vary over time from the birth of the universe till now? The terrestrial value, α₀, is a “here and now” measurement. Understandably, scientists would like to know the answer. Those interested in the details can follow the references in the open-access paper.

The quest to determine whether the bare fine-structure constant, α, is a constant in space and time has received impetus from the recognition that there might be additional dimensions of space or that our constants are partly or wholly determined by symmetry breaking at ultrahigh energies in the very early universe. The first proposals for time variation in α by Stanyukovich (1), Teller (2), and Gamow (3) were motivated by the large-number coincidences noted by Dirac (4, 5) but were quickly ruled out by observations (6). This has led to an extensive literature on varying constants that is reviewed in (7–11).

There are also interesting new problems that have been about extreme fine-tuning of quantum corrections in theories with variation of α by Donoghue (12) and Marsh (13). Accordingly, self-consistent theories of gravity and electromagnetism, which incorporate the fine-structure “constant” as a self-gravitating scalar field with self-consistent dynamics that couple to the geometry of spacetime, have been formulated in (14–20) and extended to the Weinberg-Salam theory in (21, 22). They generalize Maxwell’s equations and general relativity in the way that Jordan-Brans-Dicke gravity theory (23, 24) extends general relativity to include space or time variations of the Newtonian gravitational constant, G, by upgrading it to become a scalar field. This enables different constraints on a changing α(z) at different redshifts, z, to be coordinated; it supersedes the traditional approach (25) to constraining varying α by simply allowing α to become a variable in the physical laws for constant α. Further discussions relating spatial variations of α to inhomogeneous cosmological models can be found in (26, 27).

Surely there is value in going out and measuring things instead of speculating. So what did they find? Answers in physics are rarely precise. Usually, empirical measurements must take into account the degree of error — and there is much potential for error in measurements like these. After all, the astronomers are not taking measurements in situ at quasars, but here on Earth, where the light had to pass through billions of light-years of external influences, such as dust, gas, gravitational lensing, atmospheric distortion and other things. Moreover, the measurements are sensitive to the models used and the theories behind them. Physicists attempt to account for all known and potential sources of error, but are only human. There could be error in the assumptions and procedures used. One outlier can distort an average. Here is their answer:

Observations at z = 7:1 probe the physics of the universe at only 0.8 billion years old. These are the most distant direct measurements of α to date and the first measurements using a near-IR spectrograph. A new AI analysis method is employed. Four measurements from the x-shooter spectrograph on the Very Large Telescope (VLT) constrain changes in a relative to the terrestrial value (α₀). The weighted mean electromagnetic force in this location in the universe deviates from the terrestrial value by Δα/α = (αz − α₀)/α₀ = (−2:18 ± 7:27) × 10⁻⁵, consistent with no temporal change. Combining these measurements with existing data, we find a spatial variation is preferred over a no-variation model at the 3:9σ level.

For non-specialists, this means that the fine-structure constant didn’t appear to change over time, but it might vary from place to place just slightly. That’s at least according to the instrument used, and the models (and assumptions) used to interpret their measurements, and human error.

Here’s the Problem

The problem with belief in varying constants is that all the laws of nature need to cooperate with the change. Perhaps a self-consistent set of laws could be imagined with a slightly different α at another time or place, but the universe will crash and burn unless everything holds together in a way consistent with the existence of stars, planets, and people. Gonzalez and Richards quote astronomer Virginia Trimble, who commented on the debates about fine-tuning:

Efforts to avoid one problem by changing several of the constraints at once generally produce some other problem. Thus we apparently live in a rather delicately balanced universe, from the point of view of hospitality to chemical life. 

(The Privileged Planet, p. 206)

The video version of The Privileged Planet shows a universe-making machine with dials for each constant set appropriately for habitability. Disastrous consequences result when any one dial is turned a slight amount higher or lower. Would anyone be foolhardy enough to turn several dials simultaneously in a search for alternative universes that are habitable? The most parsimonious approach seems to be to take the fine-tuning we actually observe as a given, and deal with its philosophical and theological implications in as unbiased and straightforward manner as possible.

Photo: Pillars of Creation, Eagle Nebula, by NASA, ESA/Hubble and the Hubble Heritage Team.