How to be causal: time, spacetime, and spectra

Details How to be causal: time, spacetime, and spectra How to be causal: time, spacetime, and spectra

2011-06-09

arxiv.org/abs/1106.1792v2

Eur. J. Phys. 32, 1687 (2011)

Physics

Classical Physics

Comments welcome

Scientific paper

10.1088/0143-0807/32/6/022

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 eqations 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 casual properties are sometimes debated.

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