There is a large discrepancy between the weak force and gravity. Why is the weak force 10^24 times stronger than gravity? When faced with such a large number as 10,000,000,000,000,000, ten quadrillions, the question that physicists are naturally led to ask is: where did that number come from? 2
Although they represent a significant problem for particle physics theories, the observed hierarchies of the fundamental parameters are a distinguishing feature of the cosmos, and extreme hierarchies are required for any universe to be viable: The strength of gravity can vary over several orders of magnitude, but it must remain weak compared to other forces so that the universe can evolve and produce structure, and stars can function. This required weakness of gravity leads to the hierarchies of scale that we observe in the universe. In addition, any working universe requires a clean separation of the energies corresponding to the vacuum, atoms, nuclei, electroweak symmetry breaking, and the Planck scale. In other words, the hierarchies of physics lead to the observed hierarchies of astrophysics, and this ordering is necessary for a habitable universe. The universe is surprisingly resilient to changes in its fundamental and cosmological parameters. 1
I respect Ethan Siegel for the excellent articles and books that he writes and his knowledge and expertise in regards to physics. I disagree however that there are just two fine-tune problems.
There are many constants that cannot be predicted, just measured. That means, the specific numbers in the mathematical equations that define the laws of physics cannot be derived from more fundamental things. They are just what they are, without further explanation. Why is that so? Nobody knows. What we do know, however, is, that if these numbers in the equations would be different, we would not be here. Another example is the mass of the fundamental particles, like quark masses which define the mass of protons, neutrons, etc. There would be almost an infinite number of possible combinations of quarks, but if protons had other combinations, there would be no stable atoms, and we would not be here.
One of the two Ethan mentions is the hierarchy problem. I think that one alone is sufficient to infer a creator, an intelligent designer, as the best explanation of the existence of our life permitting universe.
Ethan Siegel: The only "impressive" examples of fine-tuning that I know of are the hierarchy problem and the coincidence problem. That's it. The hierarchy problem basically says, "why are the Planck scale and the mass/energy scale of what appears in the Universe so far apart?" The coincidence problem basically says, "why are the normal matter, dark matter, radiation, and dark energy densities, today, NOT so far apart from one another?" That's it. Those are the only tunings that cannot be derived from other tunings. The difference of gravity to electromagnetism is a restatement of the hierarchy problem. Why are these numbers so different from one another? We don't know.
Wikipedia: Hierarchy problem
In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 10^24 times stronger than gravity.
A simple example:
Suppose a physics model requires four parameters which allow it to produce a very high-quality working model, generating predictions of some aspect of our physical universe. Suppose we find through experiments that the parameters have values:
404,331,557,902,116,024,553,602,703,216.58 (roughly 4×10^29).
We might wonder how such figures arise. But in particular, we might be especially curious about a theory where three values are close to one, and the fourth is so different; in other words, the huge disproportion we seem to find between the first three parameters and the fourth. We might also wonder, if one force is so much weaker than the others that it needs a factor of 4×10^29 to allow it to be related to them in terms of effects, how did our universe come to be so exactly balanced when its forces emerged? In current particle physics, the differences between some parameters are much larger than this, so the question is even more noteworthy.
Matt Strassler The Hierarchy Problem
What is the Hierarchy Problem?
An important feature of nature that puzzles scientists like myself is known as the hierarchy, meaning the vast discrepancy between aspects of the weak nuclear force and gravity. There are several different ways to describe this hierarchy, each emphasizing a different feature of it. Here is one:
The mass of the smallest possible black hole defines what is known as the Planck Mass. The masses of the W and Z particles, the force carriers of the weak nuclear force, are about 10,000,000,000,000,000 times smaller than the Planck Mass. Thus there is a huge hierarchy in the mass scales of weak nuclear forces and gravity.
When faced with such a large number as 10,000,000,000,000,000, ten quadrillions, the question that physicists are naturally led to ask is: where did that number come from? It might have some sort of interesting explanation.
But while trying to figure out a possible explanation, physicists in the 1970s realized there was actually a serious problem, even a paradox, behind this number. The issue, now called the hierarchy problem, has to do with the size of the non-zero Higgs field, which in turn determines the mass of the W and Z particles.
The non-zero Higgs field has a size of about 250 GeV, and that gives us the W and Z particles with masses of about 100 GeV. But it turns out that quantum mechanics would lead us to expect that this size of a Higgs field is unstable, something like (warning: imperfect analogy ahead) a vase balanced precariously on the edge of a table. With the physics we know about so far, the tendency of quantum mechanics to jostle — those quantum fluctuations I’ve mentioned elsewhere — would seem to imply that there are two natural values for the Higgs field — in analogy to the two natural places for the vase, firmly placed on the table or smashed on the floor. Naively, the Higgs field should either be zero, or it should be as big as the Planck Energy, 10,000,000,000,000,000 times larger than it is observed to be. Why is it at a value that is non-zero and tiny, a value that seems, at least naively, so unnatural?
This is the hierarchy problem.