# Superoscillations: a scale physics perspective

## TL;DR

This paper investigates the likelihood and observability of superoscillations in functions using scale physics, revealing that both probability and detectability decrease sharply with increasing scale, following power-law decay patterns.

## Contribution

The study introduces a scale physics perspective to analyze superoscillations, combining numerical and analytical methods to quantify their probability and detectability.

## Key findings

- Superoscillation probability decreases quadratically with scale.
- Detectability of superoscillations diminishes with a fourth-order power-law.
- Superoscillations are increasingly rare and hard to detect at larger scales.

## Abstract

Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the total power in the field that is located at regions of superoscillations. It is found that the probability for a superoscillation of a particular scale follows a quadratic power-law decay curve above the scale of the bounded support of the spectrum. The detectability is found to be even more severely suppressed, following a fourth-order power-law decay curve above the scale of the spectrum.