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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 11th 2018
   • (edited Sep 11th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexon the occasion of adding one more recent reference ([Wells 18](https://ncatlab.org/nlab/show/naturalness#Wells18)) I gave the paragraphs criticizing the concept their own subsection _[Problems with the concept](https://ncatlab.org/nlab/show/naturalness#ProblemsWithTheConcept)_. 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](https://ncatlab.org/nlab/show/naturalness#DependenceOnRenormalizationScheme)_ <a href="https://ncatlab.org/nlab/revision/diff/naturalness/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/naturalness/18">v18</a>, <a href="https://ncatlab.org/nlab/show/naturalness">current</a>

   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

   diff, v18, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 5th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to yesterday's * Goran Senjanovic, _Natural Philosophy versus Philosophy of Naturalness_ ([arXiv:2001.10988](https://arxiv.org/abs/2001.10988)) <a href="https://ncatlab.org/nlab/revision/diff/naturalness/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/naturalness/26">v26</a>, <a href="https://ncatlab.org/nlab/show/naturalness">current</a>

   added pointer to yesterday’s

   • Goran Senjanovic, Natural Philosophy versus Philosophy of Naturalness (arXiv:2001.10988)

   diff, v26, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the following pointer to this preprint, updated today: * [[Sander Mooij]], [[Mikhail Shaposhnikov]], _QFT without infinities and hierarchy problem_ &lbrack;[arXiv:2110.05175](https://arxiv.org/abs/2110.05175)&rbrack; 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. <a href="https://ncatlab.org/nlab/revision/diff/naturalness/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/naturalness/30">v30</a>, <a href="https://ncatlab.org/nlab/show/naturalness">current</a>

   added the following pointer to this preprint, updated today:

   • Sander Mooij, Mikhail Shaposhnikov, QFT without infinities and hierarchy problem [arXiv:2110.05175]

   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.

   diff, v30, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 7th 2023
   • (edited Aug 7th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Gerard 't Hooft]], *Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking* In: G. 'Hooft et al., *Recent Developments in Gauge Theories*, NATO Advanced Study Institutes Series **59**, Springer (1980) &lbrack;[doi:10.1007/978-1-4684-7571-5_9](https://doi.org/10.1007/978-1-4684-7571-5_9)&rbrack; with this quote: > &lbrack;pp 135:&rbrack; "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 * [[Murray Gell-Mann]], introductory talk at _[Shelter Island II](https://en.wikipedia.org/wiki/Shelter_Island_Conference)_ (1983) 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. &lbrack;...&rbrack; 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. &lbrack;...&rbrack; When we can't avoid dialing some renormalized quantity to a small value &lbrack;...&rbrack; that situation has recently been described as a problem of 'naturalness'." <a href="https://ncatlab.org/nlab/revision/diff/naturalness/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/naturalness/31">v31</a>, <a href="https://ncatlab.org/nlab/show/naturalness">current</a>

   added pointer to:

   • Gerard ’t Hooft, Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking In: G. ’Hooft et al., Recent Developments in Gauge Theories, NATO Advanced Study Institutes Series 59, Springer (1980) [doi:10.1007/978-1-4684-7571-5_9]

   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

   • Murray Gell-Mann, introductory talk at Shelter Island II (1983)

   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’.”

   diff, v31, current