- #1

Couchyam

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*quantum*electrodynamics over reasonably short time and length scales), so presumably every activity or thought that we have has something akin to an "electromagnetic signature", however faint, which can be expanded in a complete basis of harmonics to the vacuum Maxwell equations (and/or Green functions.) It might be interesting to consider that the "signature" of a typical lived experience (as opposed to our subconscious existence), such as browsing a website, or reading the chapter of a book, encompasses roughly the same volume as the inner solar system, and that of our moment-to-moment existence (spanning a few milliseconds) is roughly on the order of the size of the Earth.

Would our experiences be nearly as complex and multifaceted as they are if the Earth were encased by a perfectly rigid and conducting (i.e. non-deformable, non-resistive) shell?* I suspect not, at least if ordinary, massive baryonic matter isn't modeled as having a life of its own. Given that insurmountable practical and ethical hurdles rule out any sort of experiment, I would be interested in hearing other thoughts on this.

A more specific (though somewhat less viscerally 'real') question could be framed as follows:

Given a compact domain with nonempty interior

*and smooth boundary*say (or whatever conditions we know are required in order to solve Maxwell's equations in a compact domain with Dirichlet or v.N. boundary conditions),

(a) Given a charged continuous medium with a smooth constitutive relation or equation of state, with or without charged point-like particles with appropriately defined/regularized dynamics, are there limits to how singular or irregular a solution can become over the course of a single orbit,

(b) What if the boundary doesn't have to be smooth?

*Incidentally, Earth's

*ionosphere*almost acts as a perfectly conducting shell, but isn't perfectly opaque, hence our lived experience (according to my hunch.)