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on the occasion of adding one more recent reference (Wells 18) I gave the paragraphs criticizing the concept their own subsection Problems with the concept.
And then I took the liberty to add what I think is the key problem, which is however generally overlooked in these discussions, away from the small community of mathematical field theorists: Dependence on the renormalization scheme
added pointer to yesterday’s
added the following pointer to this preprint, updated today:
This already appeared last year, and was recorded then at hierarchy problem, but it deserves to go here into naturalness, too. The authors conclude:
The aim of this work has been to stress that there is no physical sense in the naturalness criterion.
added pointer to:
with this quote:
[pp 135:] “it is unlikely that the microscopic equations contain various free parameters that are carefully adjusted by Nature to give cancelling effects such that the macroscopic systems have some special properties. This is a philosophy which we would like to apply to the unified gauge theories: the effective interactions at a large length scale, corresponding to a low energy scale $\mu_1$ should follow from the properties at a much smaller length scale, or higher energy scale $\mu_2$, without the requirement that various different parameters at the energy scale $\mu_2$ match with an accuracy of the order of $\mu_1/\mu_2$. That would be unnatural.”
and appended to the item
this quote:
“we seem to have to dial various renormalized quantities to small values. The situation of having numerous arbitrary dimensional parameters is even more humiliating when some of them are very small. […] First of all, we’d like to interpret small or nearly symmetric quantities as coming from a slightly broken symmetry; otherwise they don’t make sense to us. […] When we can’t avoid dialing some renormalized quantity to a small value […] that situation has recently been described as a problem of ’naturalness’.”
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