There are a number of “constants” used in physics, such as the speed of light, the Planck constant, elementary charge and so forth. Some of these constants are bare, meaning they do not have a dependency on other constants, and some are derived from other constants, like vacuum permittivity (which is an exact formula of the speed of light and vacuum permeability, the latter being dependent on the definition of ampere).
Now these constants appear in certain formulas, and these formulas are derived by arguments, the lists of premises of which are very long and contain both observation and (ultimately) metaphysical premises. For instance, all use math, which is not observational. The constants “fall out” of these formulas, and are estimated via experiment. Their values are not deduced directly as, say, the value of π is in mathematics (there are many formulas for calculating the value of π, all based on argument).
If in any of these physics formulas a constant’s value can be derived, it is no long really a constant, but an assumed true (given the prior argument) value.
Though experiment can assist in estimating constants, conditional on the arguments which imply the constants’ existence, what follows is nobody knows why these constants take the values they do (nobody knows why π takes the value it does, either, though we can compute its value). Since constants are not derived, it could be that they are not real, in the sense they are not really part of the universe; it may be that they are estimating or summarizing groups of effects, that because the formulas which imply them might be incomplete, the constants are only parameterizations, in the same sense of probability models, or of encapsulating more fundamental processes as yet unknown. Or it could be they are real, in which case their values might be deduced. But it’s only “might” because it does not follow that we will ever know the right and true premises which lead to their deduction.
If the constants are only parameterizations, then arguments based on “choosing” constants, as is Penrose’s anthropic-like entropy argument, rely on false premises.
But, like most physicists do, I think the constants are real: they are the Way Things Are. And that means they were caused to be the way they are. They were made to take the values they did. The question then becomes why these values and not others.
It turns out, physicists like Penrose say, that assuming the arguments in which the constants appear are true, that if the certain values of these constants were to vary in only a minuscule way, the universe would look far different than it does now, even to the extent that life like us could not possibly exist. These non-life-universe arguments appear sound, remembering they are all conditional on assumed physical theory.
It turns out that only an exceedingly narrow range of the standard constants allow a universe anything like this one. Using an entropy argument well summarized in Robert Spitzer’s New Proofs for the Existence of God (pp 52-59; we’ll be going through this whole book), Penrose shows the creation of the constants had to have the “accuracy of one part in 1010123“, which is mighty precise! (In case your browser does not render that math, it’s 10 to the 10 to the 123rd power.)
This argument is not only premised on assumed physical theory, which is uncontroversial, but it also assumes there was a choice possible in the value of the constants.
There is no way to know or prove this choice existed, even for God. It could be, do not forget, that one or more of the values of the constants might be deducible, we just yet do not know how. We might some day discover how. In that case, we will have proven this constant had to have this particular value, with no choice about it. Penrose’s number would be reduced by some amount for each new deduction. If we could deduce all the constants, then it would appear the universe was inevitable, under Penrose’s interpretation.
But this is all doing it the hard way. That the universe exists at all, rather than nothing, is sufficient proof of the existence of God.
One possible line of escape, used by some and also summarized by Spitzer, is to assume all the “universes” which had the “allowable” values of constants really do or did exist; thus, they say, solving the choice problem. Or quantum mechanical arguments imply the constants are chosen “randomly”.
It should be obvious these are fallacies. The same unproven premise is there, that the constants could be different than they are, that a choice was possible. If a choice was possible, there had to be a chooser, or some simpler, more basic mechanism that led to the particular values.
But then what accounts for this constant chooser? It could be God directly, or other more fundamental still physical processes. If the latter, these had to come from somewhere: they could not have come from nothing.
Every path taken by these arguments leads to the same origin, which is Ultimate Chooser, the real true and sole reason the way things are are The Way Things Are. The nature of nature has to have an explanation, and that explanation can never, not ever, be nothing. The explanation has to be something outside nature, and the only candidate for that is God.
Incidentally, I do not agree with any probabilistic argument used to prove God’s existence, e.g. this one from Swineburn.