We critically analyze the rationale of arguments from finetuning and naturalness in particle physics and cosmology, notably the small values of the mass of the Higgs-boson and the cosmological constant. We identify several new reasons why these arguments are not scientifically relevant. Besides laying out why the necessity to define a probability distribution renders arguments from naturalness internally contradictory, it is also explained why it is conceptually questionable to single out assumptions about dimensionless parameters from among a host of other assumptions. Some other numerological coincidences and their problems are also discussed.
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Here and in the following “consistency” refers to the absence of internal contradictions in a theory’s regime of applicability. It does not imply that a theory has empirical support.
This raises the question how much effort should be made to work out details of theories that have not yet been tested, but this is a question which shall not concern us here.
In practice one does not, of course, study the space of all possible quantum field theories, but only that of certain classes of theories, typically chosen by field-content and symmetry-requirements.
In units in which the speed of light and Planck’s constant are equal to 1.
Or at least the problem we will discuss here. The literature distinguishes several cosmological constant problems, but the other ones aren’t so relevant for what follows.
These corrections are often said to be due to “quantum fluctuation,” which is not wrong but sometimes causes confusion by bringing up the question just what is fluctuating and why. Suffices to say that this is just a word given to some terms in an equation.
In many cases the question whether a problem really is a problem can be answered by observing what economists refer to as “revealed preferences.” It means, in brief, look at what they do, don’t listen to what they say. I think this criterion is of great use also in theoretical physics.
The reader be warned that what was once called “invisible axion” is now in the literature often referred to as just “axion.”
A “measure” is what’s necessary to assign weights to the elements of a set. For all practical purposes it’s the same as a probability distribution.
One may find value in other types of explanations, but discussing those is beyond the scope of this present work. It would be interesting to know, of course, if a not-finetuned theory has some other kind of explanatory value.
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I thank the Munich Center for Advanced Studies and the Munich Center for Mathematical Philosophy for hospitality and gratefully acknowledge support from the Foundational Questions Institute and the German Research Foundation.
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Hossenfelder, S. Screams for explanation: finetuning and naturalness in the foundations of physics. Synthese 198 (Suppl 16), 3727–3745 (2021). https://doi.org/10.1007/s11229-019-02377-5