How to be causal: time, spacetime and spectra

ISSN： 0143-0807

Source： European Journal of Physics, Vol.32, Iss.6, 2011-11, pp. : 1687-1700

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers–Kronig relations. The specification of causality in terms of temporal differential equations then shows us the way to write down dynamical models so that their causal nature in the sense used here should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers–Kronig relations applicable not only to just temporal causality, but also to spacetime 'light-cone' causality based on signals carried by waves. I also apply this causal reasoning to Maxwell's equations, which is an instructive example since their causal properties are sometimes debated.