Is diamagnetism really acausal?

TL;DR

This paper addresses the apparent paradox between the existence of diamagnetism and the principle of causality, providing a full resolution to this longstanding puzzle.

Contribution

It offers a novel explanation resolving the conflict between diamagnetism and causality constraints in physics.

Findings

Diamagnetism exists without violating causality.

The paradox is resolved through a new theoretical framework.

Previous explanations were insufficient or incomplete.

Abstract

Diamagnetism, in which the magnetisation in a medium opposes the direction of an applied magnetic field, is a weak but familiar effect in a wide class of materials. Being weak it is also a linear response to any applied field. The problem is that the existence of diamagnetism is in direct conflict with the requirements of causality as embodied in the familiar Kramers-Kronig relations. Nature does not care about our confusion and diamagnetism exists and physics is constrained by the requirements of causality (that effect cannot precede its cause). This puzzle has received intermittent attention from time to time, with a variety of arguments made to resolve the paradox. None of these, no matter how plausible, reveal the mechanism that resolves the existence of diamagnetism without sacrificing causality. The full resolution is presented in this letter.