In physics, naturalness is the property that the dimensionless ratios between free parameters or physical constants appearing in a physical theory should take values "of order 1" and that free parameters are not fine-tuned. That is, a natural theory would have parameter ratios with values like 2.34 rather than 234000 or 0.000234. This is in contrast to current theory like the standard model, where there are a number of parameters that vary by many orders of magnitude, and require extensive "fine-tuning" of those values in order for the theory to predict properties resembling those observed for the universe we live in.
The requirement that satisfactory theories should be "natural" in this sense is a current of thought initiated around the 1960s in particle physics. It is an aesthetic criterion, not a physical one, that arises from the seeming non-naturalness of the standard model and the broader topics of the hierarchy problem, fine-tuning, and the anthropic principle.
It is not always compatible with Occam's razor, since many instances of "natural" theories have more parameters than "fine-tuned" theories such as the Standard Model. Naturalness in physics is closely related to the issue of fine-tuning, and over the past decade many scientists argued that the principle of naturalness is a specific application of Bayesian statistics.
In particle physics, the assumption of naturalness means that, unless a more detailed explanation exists, all conceivable terms in the effective action that preserve the required symmetries should appear in this effective action with natural coefficients.
where d is the dimension of the field operator; and c is a dimensionless number which should be "random" and smaller than 1 at the scale where the effective theory breaks down. Further renormalization group running can reduce the value of c at an energy scale E, but by a small factor proportional to ln(E/Λ).
Some parameters in the effective action of the Standard Model seem to have far smaller coefficients than required by consistency with the assumption of naturalness, leading to some of the fundamental open questions in physics. In particular:
- The naturalness of the QCD "theta parameter" leads to the strong CP problem, because it is very small (experimentally consistent with "zero") rather than of order of magnitude unity.
- The naturalness of the Higgs mass leads to the hierarchy problem, because it is 17 orders of magnitude smaller than the Planck Mass that characterizes gravity. (Equivalently, the Fermi Constant characterizing the strength of the Weak Force is very very large compared to the Gravitational Constant characterizing the strength of gravity.)
- The naturalness of the cosmological constant leads to the cosmological constant problem because it is at least 40 and perhaps as much as 100 or more orders of magnitude smaller than naively expected.
In addition, the coupling of the electron to the Higgs, the mass of the electron, is abnormally small, and to a lesser extent, the masses of the light quarks.
In models with large extra dimensions, the assumption of naturalness is violated for operators which multiply field operators that create objects which are localized at different positions in the extra dimensions.
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