Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Tracing controversies in hacker communities: ethical considerations for internet research

This paper reflects on the ethics of internet research on community controversies. Specifically, it focuses on controversies concerning gendered, social interaction in hacking communities. It addresses the question how internet researchers should treat and represent content that individuals controversially discussed online. While many internet sources are likewise technically public, they may yet suggest distinct privacy expectations on the part of involved individuals. In internet research, ethical decision-making regarding which online primary sources may be, e.g., referenced and quoted or require anonymisation is still ambiguous and contested. Instead of generalisable rules, the context dependence of internet research ethics has been frequently stressed. Given this ambiguity, the paper elaborates on ethical decisions and their implications by exploring the case of a controversial hackerspaces.org mailing list debate. In tracing data across different platforms, it analyses the emerging ethico-methodological challenges

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea