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All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned. But where you draw the line between fine tuned and not fined ...

The argument for fine tuning is far broader than just the Higgs. For example it's argued that the existance of any elements heavier than lithium relies on a fine tuned resonance in the carbon 12 nuclues that allows three helium nuclei to stay together long enough to form a carbon nucleus. There are lots of books that explore these ideas. A good start would ...

The hierarchy problem is not only about big numbers, such as $M_{pl}/M_{EW}$, per se'. In fact in QCD there is no hierarchy problem associated to the ratio $M_{pl}/\Lambda_{QCD}$. The problem is actually about the quantum numbers of certain operators in a Wilsonian EFT. The point is that we understand the SM as an effective low-energy description of the ...

It's the same problem because the low scale matches in both definitions; and the high scale matches in both definitions, too. Both problems are the puzzle why the two scales are so much different. First, the low scale. In the Higgs fine-tuning, you define the low scale as the Higgs mass. But the Higgs mass can't be parameterically greater than the Z-boson ...

To me, it seems like there are 3 different concepts being discussed: (1) fine-tuning, (2) wanting unitless constants to be of order unity, and (3) wanting theories to have a simple form. The WP link defines "naturalness" as #2, although I don't think that's universally understood. A very old example of #3 would be the history of models of the solar system, ...

1) The cosmological constant in the context of quantum field theory is a set of calculations and leads to a sum that will look something schematically like this cc = 3-5+22-120+3042-50242+... +O(M^4) where M is some heavy mass scale The problem is we don't know the exact numbers in the sum, we can only calculate a few of them and the best we can do is ...

Analogously to the use of SU(2) instantons for describing tunelling between topologically distinct vacuum sectors, I've heard people talk about gravitational instantons as describing a tunneling process connecting "nothing" with an expanding Minkowski signature universe. People talk heuristically of a universe having emerged by tunnelling from "nothing". ...