Is there a conflict between causality and diamagnetism?

TL;DR

This paper resolves a long-standing paradox between the observed diamagnetism in materials and the causality constraints imposed by the Kramers-Kronig relations, clarifying the underlying physics.

Contribution

The authors identify flaws in previous analyses and provide a new explanation reconciling diamagnetism with causality principles.

Findings

Diamagnetism is compatible with causality after correcting earlier assumptions.

The absence of dia-electric responses is explained by the proposed resolution.

Previous paradoxes were due to oversights in theoretical analyses.

Abstract

There is a long-standing apparent conflict between the existence of diamagnetism and causality as expressed through the Kramers-Kronig relations. In essence, using causality arguments, along with a small number of seemingly well-justified assumptions, one can show that diamagnetism is impossible. However, experiments show diamagnetic responses from magnetic media. We present a resolution to this issue, which also explains the absence of observed dia-electric responses in media. In the process, we expose some of the short-comings in earlier analyses that have kept the paradox alive.