Suppose there were 5 numbers randomly selected between 1 and 10^40. What are the odds that those numbers would be off by orders of magnitude? The answer is quite low. The vast majority of numbers between 1 and 10^40 are within an order of magnitude of each other. In fact, for any N, the vast majority of numbers between 1 and N are within an order of magnitude of each other.

Suppose that one is deciding, prior to observation, what the strengths of the fundamental forces are likely to be. There are a few possibilities:

They might assign a uniform probability distribution across all the strengths they could be. Thus, they’d think that gravity is just as likely to be its actual strength as 5 times its strength or 25 times its strength, and so on. But if this is true, then all the forces will be guaranteed to be infinite. To see this, suppose that they were finite. For any finite number they could be, the odds that they’d be that number or below would be zero, for there are infinite numbers greater than that number. Thus the odds of it being any finite number are zero. Now, maybe you think this is wrong—you assign aleph null the same probability of being the strength of gravity as its current strength. But then there’s a paradox—the odds of getting infinite are zero as are the odds of getting any finite number. I take that this establishes that this proposal is unworkable.

Think that laws of physics that are pretty weak—roughly in the same ballparks ours in terms of strength—are more inherently likely. Thus, the odds you’d get laws like ours are high. The problem is that this makes it likely that all the laws would be roughly similar strengths, for the reasons I described, which is false. Now, maybe you think that the probability distribution for strengths of laws differs by the law—but why would this be? It seems like same factors that would motivate some probability distribution of some possible strengths of one law would be pretty general.

You might think that the probability distribution would be such as to get a reasonable probability of laws like ours. For instance, maybe the probability distribution is skewed such that most of the forces will be of roughly the same strength as our fundamental laws happen to be. Problem: this is clearly ludicrous. No one in a dark room who hadn’t observed the universe would think that the strength of gravity, the weak nuclear force, the strong nuclear force, and electromagnetism are just inherently more likely numbers than other numbers.

Thus, if the laws are fundamental, you’d either expect the forces to be of infinite strength or all of similar strength. The fact that we don’t see that is a good reason to think that the laws aren’t fundamental. A designer, in contrast, might have a reason to design laws this way—maybe they’re more mathematically elegant, provide greater discoverability, or something. So this is good evidence for a designer.

Appealing to fundamental laws doesn’t help solve this puzzle, because the fundamental laws could result in any of a great range of higher-order laws, by which I mean laws that are emergent properties of the most fundamental laws. Any reasonable probability distribution over the higher-order laws, so it will still be weird that the strength of the laws of physics are so varied.

However, even once one has very varied forces, there’s another puzzle: why aren’t there any redundant forces? Gravity holds across great scales, but is very weak at small scales. Thus, gravity plays little role in determining actions at the level of atoms, but it rules the day when it comes to larger objects like plants. But it could have been otherwise. If gravity was as strong as it currently is but its force dropped off as quickly as the strong nuclear force, then it would be basically irrelevant. So the question: why aren’t there any irrelevant forces?

You might think that there are these mostly impotent laws. But that’s a less simple hypothesis. It requires positing more fundamental stuff. I guess maybe the way out of this is to posit that the laws result from more fundamental stuff, so positing redundant laws doesn’t require positing anything fundamental. But this requires believing something speculative about physics for which we have no evidence. I’m hesitant to do this.

All of this is pretty speculative and I don’t know exactly what to think about it. Still, it’s definitely some evidence for God—and maybe pretty good evidence. I’ll have to think about it more, and would be curious to hear what others think.

Your ideas are incredibly creative and are simply begging for more math and science exposure on your part.

Interesting, but I think a better understanding of particle physics undermines the premises on which your argument is based. I'm just going to state the physics, even though it probably mostly sounds like magical gobbledygook. But feel free to ask questions.

If classical physics were true, all 4 forces would fall off at the same rate (Force = const/r^2), basically because the force lines spread out, and in 3 space dimensions the area of a sphere is proportional to r^2. But in QFT, there are also corrections due to virtual particles, that can make the so-called "constants" change as you vary the distance/energy you measure them at. (The equations involve a logarithm, so the constant only changes a bit, even over many orders of magnitude. These changes, known as the "renormalization group flow", can be calculated explicitly in the Standard Model; i.e. if you know what the constant is at any given scale, you can figure out what it is at another scale.)

The three fundamental forces of the Standard Model, namely:

- the SU(3) strong force between quarks,

- the SU(2) electroweak force, and

- the U(1) hypercharge force

actually DO all have roughly similar sizes! (The elecromagnetic field we know and love, is actually a combination of the SU(2) force and the U(1) force.) If you use units where c = hbar = 1, you can make a dimensionless constant, and then (if we extrapolate them from the LHC scale back to the Planck scale, assuming no new physics happens in between) they are all about the same size (roughly in the range alpha = 1/30 to 1/50). But even if we measure them at the LHC scale, their range lies within a single order of magnitude.

The number strengths that are quoted by people like Collins are very phenomeological low energy measurements, that are affected by the fact that the strong force becomes confining while the weak force becomes spontaneously broken by the Higgs. For purposes of this conversation, those numbers are insufficiently fundamental, and you should be considering the number range in my previous paragraph.

What about gravity? This is sometimes quoted as being about 10^40 times weaker than the other forces. But this is a meaningless nonsense claim, since it compares quantities with different units. The problem is that gravity is unique in that the size of the force depends, not on a charge, but on the MASSES of the two objects (ultimately because it is mediated by a spin-2 boson, not a spin-1 boson). This means you have to specify what mass of objects you are considering, or you can't even compare it to the other forces! This is a somewhat arbitrary choice. If the two objects both have the Planck mass, then the force is about the same strength as the other forces. if they are stars, it would be much bigger. If they are electrons or protons, then you get numbers like 10^(-40).

There are some legitimate fine-tuning questions in the vicinity of this big number, but it ought to be expressed as the question of why the electron and proton are so light compared to the Planck mass. They turn out to be light for completely different reasons, though. The electron is light because it couples very weakly to the Higgs boson (nobody knows why, since this is an arbitrary parameter, but it is "technically natural" in the sense that if you assume it starts off small, then quantum corrections don't mess that up), and also because the Higgs boson is itself fine-tuned to be very light compared to the Planck scale (this is "technically unnatural" and easy to spoil with quantum corrections, and requires fine-tuning to about 1 part in 10^30 in the fundamental constants, unless supersymmetry exists).

For the proton, on the other hand, there is no fine-tuning required to make it light, due to the fact that as you go down in energies, the SU(3) force gradually inches its way up to being strongly interacting, and then as soon as it gets strong enough (when alpha ~ 1) there is a confinement phase transition, and the proton appears at around that energy scale. In other words the Standard Model predicts that the proton mass should be about e^(-50#) where the # is some order unity number that I'd have to do a calculation to know what is, and the 50 comes from the fact that the strong force is about 1/50 at the Planck scale. But it is a notable coincidence (and anthropically important) that the proton mass ends up being so close to the electron mass.

Note that none of the physics in the previous 2 paragraphs had anything to do with gravity per se (other than stopping the fine-tuning analysis once we down get to the Planck length, since smaller distance scales might not exist). So saying that "gravity is 10^40 times weaker than the other forces" is just not a good way of putting things.