Gerald Pollack on Organic Chemistry of Water

This is all about large-scale structure in aqueous solutions. These electrically charged structures produce very different chemical conditions than those produced by considering water as a collection of identical H2O molecules where temperature, heat capicity and pressure are the only macroscopic measurable properties. 

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See also John Stuart Reid on Sound and Mithuna Yoganathan's attempts to measure the speed of light in water in this post of mine: Ice. The point I'm trying to make is that when you explain a physical effect, such as that light slows down in water, you explain it in terms of some context which includes physical models of "light" and "water", as well as " speed", and the explanation is really only an explanation in so far as it relates to those particular models. So those models are themselves explanations of the phenomena. Then the mathematical models give us a language in which we can express the relations between the measurements we make, and the process of reduction of the phenomena is not really reducing the phenomena themselves, but rather it is a reduction of the statements in the different languages, one to another. See Hilary Putnam on Philosophy And our Mental Life.

Here's Grant Sanderson's animation of the explanation in the Feynman Lectures chapter 31: The Origin of the Refractive Index in which "speed" is v = fλ where lambda is the Wavelength, "light" is a plane electromagnetic wave and "water" is an array of simple harmonic oscillators called "electrons". Here's his supplemental video.

 

Here's Mithuna explaining how she modeled the passage of light through water, in this case "light" is either a plane wave, or a wave packet made by a Fourier series. This is probably closer to the actual process by which LIDAR measurements are made, which would almost certainly use a train of regular pulses and some sort of averaging of a series of measurements of the flight times. Again, "water" is an array of harmonic oscillators. Then "speed" is a complicated superposition of the original wave and the wave produced by the moving charges in the "water".

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In the course I studied (which I did not understand very well) "light" was an electromagnetic wave and "water" was a soup of electric dipoles which induced displacement and magnetizing fields in the Macroscopic Formulation of Maxwell's Equations. Then the speed of the wave was related to the permittivity and permeability constants of the different media on either side of an interface. This could also model some of the properties of polarized light and how they changed when waves are reflected of different surfaces such as metals and dielectrics.

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Ray Fleming has an explanation of Einstein's Theory of General Relativity as an optical phenomenon:

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Here's a Geometric Algebra interpretation of the macroscopic formulation of Maxwell's equations:

See his blog and his book Geometric Algebra for Electrical Engineers.

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See also this post of mine: Martin Roelphs on Projective Geometric Algebra.

See also Spacetime algebra as a powerful tool for electromagnetism by Justin Dressel, Konstantin Y. Bliokh and Franco Nori.

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.

And here is a series of lectures on this paper. The guy has clearly been hanging out with Mexicans. He says modulo like a Mexican would say it if it was a Spanish word!

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