Towards Understanding Fine-Tuning in Fundamental Physics
The standard models of particle physics and cosmology are enjoying wild success, but are beset by surprising features. Chief among these are the mysterious smallness of general relativity's cosmological constant (known as the cosmological constant "problem"), and the mysteriously tremendous strength of all other forces relative to gravity (known as the hierarchy "problem"). Both are instances of a physically relevant quantity that (due to quantum effects) is a sum of many (unknown) quantities; in both cases, these summands seem to cancel out to remarkable precision to give a much smaller sum, a phenomenon called fine-tuning.
The size of the cosmological constant has proved robust against explanation on the grounds of physical principles like symmetry. Such explanations of the electroweak/gravity hierarchy abound, but recent experimental efforts have ruled many of them out, or forced them to introduce new fine-tuning. In both cases, arguments about selection effects and priors have emerged.
Here, a dialectic approach is taken to understanding this apparent fine-tuning in nature: First, symmetry is employed. Supersymmetry famously resolves the hierarchy problem, but is under siege by increasing experimental constraints ruling out much of its natural parameter space. A class of supersymmetry models with supersymmetry broken at a low scale is proposed which evade experimental constraints without needing fine-tuning. The key ingredient is some anti-correlation between supersymmetry-breaking effects and electroweak-breaking effects on a field, e.g. if the symmetry-breaking fields are localized at different points along an extra
Then, a careful argument employing selection effects and Bayesian reasoning is undertaken to show that the size of the cosmological constant is not surprising. Previous such arguments have suggested many different probability measures on the space of different possibilities, but a careful review of quantum mechanics shows a unique measure consistent with the Born rule that determines quantum-mechanical probability.
Finally, the harmony of these two approaches is briefly assessed. Upon reflection, the quantities observed in nature must have their values due to both underlying principles and selection effects. Implications are very briefly discussed.