Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a gauge-invariant functional that depends on the electron and photon fields and their first derivatives only. In this scenario, as well-known, it is not possible to set up a Lorentz invariant gauge theory containing a massive photon. We show nevertheless that there exist two radically different electrodynamics, namely, the Chern-Simons and the Podolsky formulations, in which this problem can be overcome. The former is only valid in odd space-time dimensions, while the latter requires the presence of higher-order derivatives of the gauge field in the Lagrangian. This theory, usually known as Podolsky electrodynamics, is simultaneously gauge and Lorentz invariant; in addition, it contains a massive photon. Therefore, a massive photon, unlike the popular belief, can be adequately accommodated within the context of a gauge-invariant electrodynamics.Comment: 10 page

Beyond simulation: designing for uncertainty and robust solutions

Simulation is an increasingly essential tool in the design of our environment, but any model is only as good as the initial assumptions on which it is built. This paper aims to outline some of the limits and potential dangers of reliance on simulation, and suggests how to make our models, and our buildings, more robust with respect to the uncertainty we face in design. It argues that the single analyses provided by most simulations display too precise and too narrow a result to be maximally useful in design, and instead a broader description is required, as might be provided by many differing simulations. Increased computing power now allows this in many areas. Suggestions are made for the further development of simulation tools for design, in that these increased resources should be dedicated not simply to the accuracy of single solutions, but to a bigger picture that takes account of a design’s robustness to change, multiple phenomena that cannot be predicted, and the wider range of possible solutions. Methods for doing so, including statistical methods, adaptive modelling, machine learning and pattern recognition algorithms for identifying persistent structures in models, will be identified. We propose a number of avenues for future research and how these fit into design process, particularly in the case of the design of very large buildings