Finetuned Cancellations and Improbable Theories

TL;DR

This paper uses a statistical analysis of the $x-y$ cancellation model to argue that finetuned points are not inherently improbable, but highly finetuned regions are less likely, supporting a moderate naturalness perspective.

Contribution

It introduces a statistical framework for understanding finetuning in physical theories, challenging the notion that finetuned points are inherently unlikely.

Findings

Finetuned points are as probable as any other point in parameter space.

Highly finetuned regions have lower probability than non-finetuned regions.

The probability of landing in a finetuned region is invariant under parameter ranges.

Abstract

It is argued that the $x-y$ cancellation model (XYCM) is a good proxy for discussions of finetuned cancellations in physical theories. XYCM is then analyzed from a statistical perspective, where it is argued that a finetuned point in the parameter space is not abnormal, with any such point being just as probable as any other point. However, landing inside a standardly defined finetuned region (i.e., the full parameter space of finetuned points) has a much lower probability than landing outside the region, and that probability is invariant under assumed ranges of parameters. This proposition requires asserting also that the finetuned target region is a priori established. Therefore, it is surmised that highly finetuned theories are generally expected to be highly improbable. An actionable implication of this moderate naturalness position is that the search for a non-finetuned explanation to supplant an apparently finetuned theory is likely to be a valid pursuit, but not guaranteed to be. A statistical characterization of this moderate position is presented, as well as those of the extreme pro-naturalness and anti-naturalness positions.