See query–and I’m not certain the premise is even true. I read it in a shitty article on physical constants not even worth citing. But the topics e.g. “why is c c and not x” come up here a lot, always fruitfully.
In a nutshell, it’s based on the fact that 1,800 is approximately equal to 1.
Which makes it sound crazy, so let me elaborate. If you take all of the known constants of nature, and combine them in various ways to get various dimensionless numbers, you can get many different numbers, but they seem to be somewhat clumped. For instance, if you take the ratio of the mass of the proton to the mass of the electron, you get about 1800. And most particles are roughly in that mass range, to within a few orders of magnitude. Or things like the fine structure constant, approximately 1/137. So you end up with a bunch of numbers within a few orders of magnitude of 1.
But you also get some numbers that are much larger, in the vicinity of 10^40, like the ratio of the electric force between two electrons to the gravitational force between them, or the ratio of the age of the Universe to the Planck time. And unless you do cute things like taking the square root of the ratio of those forces, you never get numbers in between, like 10^20 (or even 10^30 or 10^10).
Well, it’s easy enough to handwave away the clump of numbers near 1. But what about those numbers near 10^40? Is there some reason why there’d be a clump near there? Well, there are two broad categories of those big numbers. Like, instead of looking at the ratio of electric force to gravity, we could look at the ratio of one of the nuclear forces to gravity, but since the nuclear forces have a strength within a few orders of magnitude of electromagnetism, that’s not really a different category.
But there is another category: Some of those big numbers depend on the age of the Universe, but they still come out to around 10^40. Coincidence? Well, maybe. But if not, if there’s something fundamental tying those two numbers together, then it must mean that at least one of the fundamental constants must vary with time, because the age of the Universe (of course) varies with time. And the only way you can make it work with only one constant varying is if that constant is big G.
Now, observations and measurements since then (actually, analyses of observations) have ruled out the possibility that G is varying in the way that Dirac predicted (though there are still some more complicated models along the same lines that just might work). And it might in fact just be a coincidence. Alternately, it might not be a coincidence, but might be due to the anthropic principle, if there’s some reason that intelligence could only evolve in that epoch of the Universe when those big numbers are in the same neighborhood.
Oh, and I should also mention that in addition to the observational evidence, the original argument has since been weakened. We now know that neutrinos have nonzero mass (in Dirac’s lifetime, they were either unknown, or assumed to be massless), which means that we can look at, say, the ratio of the neutrino mass to the mass of some larger particle. But while we don’t know the exact mass of the neutrino, we do know that it’s less than about 1 eV. Meanwhile, there are other fundamental particles, like the Higgs, which have a mass up around 10^11 eV, so we do indeed have at least one dimensionless constant that’s significantly in between the small numbers and the big ones.
Thank you Chronos.
I have to chew on some of that.