If you listen to enough fine tuning discussions it’s not hard to see that the main point of disagreement and really the main difficulty is really what is the best framework for assigning prior probability to it. The question really is: given that we have constants in our physical equations, what is the hypothesis that best explain their presence?

One naturalistic explanation is to say that they are simply a reflection of the inadequacy of our own scientific theories and if we did find better theories these constants might vanish. There’s no real way of actually knowing if that is a true proposition or not. Although it seems unlikely to us given that some of these constants are ratios between atomic weights of different particles or forces, and those really must not vary irrespective of which scientific theory one is using to describe them. The second, which is a kind of explanation of the first, is that these are only one set of constants in a multiverse in which all the possible constants are realized. There is some pristine eternal equation unencumbered by constants, but nature wants to use that equation in every possible manner that it can. Either that, or nature, in addition to every possible constant, also has every possible equation. Somewhere in the multiverse, there is a Universe based on the relationship “1=1”. The problems with this are first, the multiverse concept itself is highly debated even within the scientific community. Secondly because these are numbers, there are infinite possibilities of numbers and their fractions. Are we really talking about infinite combinations of infinities? What does that even mean. Is the fundamental nature of nature no more than a desire to randomize relationships between matter components? Mathematics is not substantial in the first place and so the mere presence of a randomizer at the fundamental level of reality does not explain the presence of substance itself.

Further, changing one constant has effects on other constants so these constants cannot possibly just be thrown up by a randomizer, as seems to be envisaged in this multiverse concept, there is a science to it. The phenomenon cannot both be random and Mathematical at the same time. The problem here is we’re not so quite what we are ascribing with the property off being able to produce all these universes and also what properties we are ascribing to it. That is something that’s in the multiverse theory, the cause of eternal inflation that is generating new universes, apparently eternally. This links into string theory which predicts a specific number of these universes which is 10⁵⁰⁰. Some scientists think that this is actually the number of string theories rather than the number of universes. And of course string theory clever as it is, is both not substantiated by evidence, and not complete. But what you’re left with at the end of all this is the picture of the universe-making machine as a random number generator that simply keeps throwing up every possibility regardless of whether it makes any scientific sense or not and somehow manages to be substantial at the same time rather than remain an abstraction, which is what numbers are.

On the theist side, the question asked is whether God would be likely to choose certain numbers that make life and the universe itself possible, were there a God. This hypothesis does away with the necessity of this extremely ill defined “universe making machine” which is one benefit. Even within the fine tuning there actually exists a range of possibilities for these constants that might yet permit life even though that range is admittedly pretty narrow, again difficult to define, and again involves estimating the effects of the change in one constant on the others.

For example the time it took you to get to work change it just has a knock on effect on everything else that you do during the day and this could have an effect on how that aspects of your life like relationships mental health physical health and literally everything, precisely because they are all interconnected. The constants in your life do not exist in exclusion of other constants in it. What’s more it is extremely difficult for us to actually know what values of constants would actually allow for life. For example if one were to be given the equations of the standard model of physics which is the best equation of reality that we have today and put in all the constants, no scientists could predict from this that life would arise. It is just impossible to look at a bunch of numbers and crosses and predict what will pop out of them terms of chemistry and biology. It is something like Looking at a chemistry book and predicting that H2O would feel wet. Equations simply do not have that kind of power. So much less can we make any predictions whether range of values of constants are different from what we know already. Also we cannot know that had carbon based life not evolved would like another some other form the possibility.

Luke Barnes Has shown that in the matter of quarks the two types of which entirely make up the atomic nuclei of literally all the matter in the universe, these have a very narrow range of weights within which they would even want to stick to each other. Lastly, in the case of the theistic hypothesis, it is also not necessary that the hypothesis end with the random-number-generator-equipped-universe-making-machine (RNGEUMM- pron. ring-ee-uhm), rather God could have created it.

Fine tuning as an argument for theism can be a deceptively difficult argument to get your head around. The science can be pretty tough too. Its not just that theists can misunderstand it, rather scientists struggle with the presence of these constants in nature too. This is a summary of how to approach the argument and lay it down, as I see it.

Even were it truly necessary that there be something rather than nothing, surely it cannot be necessary that there be “us”. Were this the case we would be asserting that our existing were somehow necessary, or that it were necessary that there were us rather than nothing. This would seem too strong a claim for science to bear. SO even were it necessary for some reason that there were something rather than nothing, that something could just have well have been some rubbish, or a jelly flood, etc.

But in order for there to be us, it seems necessary that certain constants of nature only take certain highly specific values. Intuitively it would seem unlikely that the Universe choose these values by random chance.

The main response if from the highly speculative and debated multiverse model based on eternal inflation in which our set of values is only one among a universe were every possible set is realised. The other response would be to say that the problem is not the unlikely values, rather it is with our calculations. Did we have the true “theory of everything”, these values might vanish. They are merely a reflection of our inability to calculate correctly.

I don’t really buy the latter response. Apart from the problem of question begging, the constants are not just values, rather they are related in the form of ratios to other values. They are more like ratios. the electron really is a certain number of times lighter than a proton. I don’t see how this difference would simply vanish in any future physics.

The presence of a deity might add some prior likelihood to there being personal agents as as part of what is there. Is it really likely that God “insert” values into mathematical equations that govern the laws of physics? What does that even mean?

Are theistic fine-tuning (TFT) proponents asserting that math is a tool and God sticks certain numbers into it to make our lives possible? Could God not simply have used a different math that did not require any constants to “fix it” in the first place?

Math, a set of symbols with supposed logical relation does not necessarily have any co-ordinate in reality, although some of it seems to have co-ordinates in part of our reality. In other words, it seems we can represent part of our reality through logically related symbols, on condition that we add the constants. TFT proponents are asserting that God makes it possible that these constants are the case in our reality.

Does this give the uncomfortable impression that math is some sort of pristine eternal relationship framework that God has to manipulate? I don’t think this is the correct view. God is three Persons which itself is the logical addition of single persons. That logical relationship applies to God eternally, and we could say co-eternally with him and there are no constants involved. Being the only plurality applicable to the Triune God, there are no other mathematical relations with regards to Him apart from simple unity.

Creation, on the other hand is defined by multiplicity and multiplicity entails mathematical relationships. No one can say a priori that no constants be admissible in the relationships between the multiple layered components when God creates. Does God have a master copy of the math involved in the Universe, one that is so pristine and advanced as to be transcendent and did not involve any use of constants? I think this is possible, I mean that when God created the temporal Universe, then the math involved in it was really known to him, but it is far beyond anything we can hope to comprehend (if we get there using quantum computing and AI, it will be far beyond anything we can comprehend anyway).

Perhaps it is true after all that God can see creation in pure logical relationships without the need for any cumbersome and incongruous decimal points in a manner that we cannot hope to comprehend. The other possibility is that God does see the cumbersome constants in our own reality. In the first case we only find it impressive that there are these constants due to our own shortcomings in mathematics in physics. In the second it seems that God has made only a particular mathematical possibility into a reality, for our sakes.

Temporality does entail a certain logical relationship between its layered moving parts. Which is unsurprising, but the noteworthy thing is that it is a certain particular relationship which is our reality. There being constants in temporality is not a slight on God’s omnipotence, it merely means that the mathematics of temporality requires certain constants, or constant ratios between its components in order that it be conducive to the emergence and sustenance of intelligent life.

There are constant ratios even in our own bodies, without which it would be impossible for us to be alive, like the weight of our brain to the rest of our bodies, the relative number of neurons, the total number of living cells, the blood levels of electrolytes and proteins like haemoglobin that we are all aware from laboratory tests can only inhabit a strict range compatible with life. Perhaps it is even correct to say that if not for the constants in nature, by the same math, we could also have no such constant ratios in our bodies, rather perhaps all things would exist in an exist in an amorphous 1:1 ratio, and no structure would ever form, beginning with galaxies.

So finally we are able to make some conclusions based on our foregoing ramblings. Temporality entails numerical relationships between the components that are in turn entailed by its complex nature, and this is mathematics. God on the other hand is a simple substance that does not entail mathematics as inherent to his nature. We will say that the presence of constants as integral to those relationships is more likely on the God hypothesis on a naturalistic hypothesis. It is an overly strong claim to state that every mathematical possibility is necessarily in actuality purely based on the fact that it is mathematically possible. It is also an overly strong claim Despite that not only is the range of possibilities include everything that mathematical equations can possibly predict but also everything that infinite multiples of infinite factors in those equations can predict. This requires to be whatever is at the foundation of existence to be the “Renguem” that we described.

The Fine Structure Constant

These are excerpts from the Wikipedia page that explain what it is:

Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887, Arnold Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure constant α was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the speed of light in the vacuum. Equivalently, it was the quotient between the minimum angular momentum allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfeld’s analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines. This constant was not seen as significant until Paul Dirac’s linear relativistic wave equation in 1928, which gave the exact fine structure formula.

With the development of quantum electrodynamics (QED) the significance of α has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term
α/2π is engraved on the tombstone of one of the pioneers of QED, Julian Schwinger, referring to his calculation of the anomalous magnetic dipole moment.

As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long fascinated physicists.

Arthur Eddington argued that the value could be “obtained by pure deduction” and he related it to the Eddington number, his estimate of the number of protons in the universe. This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not approximately but precisely the integer 137. By the 1940s experimental values for 1/α deviated sufficiently from 137 to refute Eddington’s arguments.

The fine-structure constant so intrigued physicist Wolfgang Pauli that he collaborated with psychoanalyst Carl Jung in a quest to understand its significance. Similarly, Max Born believed that if the value of α differed, the universe would degenerate, and thus that α = 1/137 is a law of nature.

Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:

There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won’t recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)

Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the “hand of God” wrote that number, and “we don’t know how He pushed His pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out – without putting it in secretly!

— Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 978-0-691-08388-9.
…Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community.

Initial Entropy Fine- Tuning

Fine tuning cane be taken to be of two types- that of the laws and constants of nature, and that of the initial conditions.

The Number N

Martin Rees describes the number as a measure of the smallness of the gravitional force compared to the other forces of nature, and it is 10 raised to 36 times smaller than the electrostatic force. This is why a planet like Jupiter can be as big as it is without imploding, same as the Sun in which the outward force it balanced by the gravitational force, but also the forces in the nuclei themselves where the forces of attraction between say the protons and neutrons are negligible compared to the electostatic forces so that atoms can form stable molecular bonds without collapsing into each other. Finally he describes how even the size of Black Holes is determined by this number so that 10 to 36 particles must collapse into the size of one particle in order to form a black hole.

The Nuclear force epsilon is 0.007 which is the energy released when the Hydrogen in the Son combines through fusion to give Helium. This number therefore determines the rate at which stars burn. Further as Hoyle himself argued, no Carbon based biosphere could even exist were e even 0.006 or 0.008.