Time and space, frequency and wavevector: or, what I talk about when I talk about propagation

TL;DR

This paper clarifies the concept of negative frequency in wave propagation, explaining its meaning and relevance in optics and water waves, and discusses the contexts where it appears.

Contribution

It provides a conceptual framework for understanding negative frequency in wave physics, addressing recent debates and clarifying its significance.

Findings

Negative frequency has meaningful interpretations in wave physics.

The paper explains the contexts where negative frequency appears.

It clarifies misconceptions about wave propagation and frequency.

Abstract

The existence of waves with negative frequency is a surprising and perhaps controversial claim which has recently been revisted in optics and for water waves. Here I explain a context within which to understand the meaning of the "negative frequency" conception, and why it appears in some cases.