No evidence of “new physics” was found so far by LHC experiments, and this situation has led some voices in the physics community to call for the abandonment of the “naturalness” criterion, while other scientists have felt the need to break a lance in its defense by claiming that, at least in some sense, it has already led to successes and therefore should not be dismissed too quickly, but rather only reflected or reshaped to fit new needs. In our paper we will argue that present pro-or-contra naturalness debates miss the fundamental point that naturalness, despite contrary claims, is essentially a very hazily defined, in a sense even mythical notion which, in the course of more than four decades, has been steadily, and often not coherently, shaped by its interplay with different branches of model-building in high-energy physics and cosmology on the one side, and new incoming experimental results on the other. In our paper we will endeavor to clear up some of the physical and philosophical haze by taking a closer look back at (real or alleged) origin of naturalness in the 1970s and 1980s, with particular attention to the early work of Kenneth Wilson. In doing this, we aim to bring to light how naturalness belongs to a long tradition of present and past physical and philosophical criteria for effectively guiding theoretical reflection and experimental practice in fundamental research.
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For a detailed discussion of the discovery/non-discovery of weak neutral currents see .
Georgi and Pais’s definition is the earliest systematic use we could find of the term naturalness in particle physics, although its characterization has little in common with later notions.
If the simplifying assumption that \(m \sim 0\) was dropped, then the value was predicted for \(\lambda \sim m\).
It must be recalled that Wilson was writing before the establishment of Quantum Chromodynamics as a theory of strong interactions, and that he was not making any specific assumption on the form of the strong Lagrangian. However, since it was known that strong forces had a SU(3) symmetry (the quark model) broken at low energy, the unknown Lagrangian must have an SU(3)-symmetry and contain smaller, SU(3)-breaking terms.
Here Wilson assumed that electromagnetic interactions were those responsible for the fact that at the cutoff \(\Lambda \) strong interactions could not be anymore studied in isolation, and that therefore their renormalization group equation was not valid anymore at those high momenta.
More precisely, parameters known to break at low momenta an internal symmetry of strong interactions were expected to also break a symmetry common to strong interactions and to the forces that became relevant at the cutoff \(\Lambda \), for example electromagnetism. This conclusion did not follow necessarily from the analysis, but appeared plausible when considering that the same function of momentum was expected to satisfy two renormalization group equations: the one of strong interactions at lower energy, and the one for the theory valid above the cutoff at higher energies. The former equation required the parameters to become smaller and smaller when momenta increased, and the easiest way in which a seamless connection between the two ranges could take place, Wilson assumed, was that the two theories shared a symmetry broken by the parameters in question, which guaranteed that they would only receive small radiative corrections when nearing the cutoff.
In 2005 Wilson wrote that this paper contained “three blunders”: the statements on scalar particles, the failure to recognize the possibility of asymptotic freedom and the idea that limit cycles might be physically significant [34, p. 12]. Interestingly Peskin in 2014 also said that Wilson spoke of “three errors”, but beside limit cycles and asymptotic freedom, he counted the idea that one might predict coupling constants instead of the critique to scalar particles [22, pp. 658–659].
See for example  and references therein.
Note that Nelson distinguishes between a “structural naturalness”, which has essentially to do with simplicity (p. 60), and a “numerical naturalness”, which is, in fact, the today’s meaning of the concept. We will focus, therefore, only on his numerical naturalness.
As acknowledged by Nelson himself, at p. 66.
For an overview and examples of approaches to model-building from the 1990s onward see .
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We are grateful to the participants of the 2018 Aachen workshop on “Naturalness, Hierarchy, and Fine Tuning” and to the anonymous referee for very helpful comments and suggestions. Arianna Borrelli wishes to acknowledge funding by the project “Exploring the “dark ages” of particle physics: isospin, strangeness and the construction of physical-mathematical concepts in the pre-Standard-Model era (ca. 1950–1965)” (German Research Council (DFG) Grant BO 4062/2-1), and the Institute for Advances Studies on Media Cultures of Computer Simulation (MECS), Leuphana Universität Lüneburg (DFG research Grant KFOR 1927).
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Borrelli, A., Castellani, E. The Practice of Naturalness: A Historical-Philosophical Perspective. Found Phys 49, 860–878 (2019). https://doi.org/10.1007/s10701-019-00287-7
- Historical contextualization
- Renormalization Group
- Kenneth Wilson
- Physics beyond the Standard Model