.
# mass and charge
and so the story goes: materials are made of mass, mass is made of atoms, atoms
are made up of "massive" particles, some with charge; the deeper the questions
we ask about everyday matter, the stanger the properties of matter get,
according to the latest theories.
but no one really knows what is mass, or charge. what are these? "these are
properties of matter", some might say.
where are they located? we consider there is a mass density, a charge density.
# light in a medium
when light enters a medium it slows down, some say - "we can measure it".
others, like famous physicist and nobel price winner, Richard Feynman, say that
fundamentally there is no reason why a material should slow light: light should
just pass through (they argue on the principles of linearity and superposition,
perhaps); the slowdown of the speed of light in a material, they argue, happens
because the material gets polarized by light and emits a secondary wave that
interacts with the first one, changing its phase.
# polarization
because of the principle of superposition, two electromagnetic waves are said
not to interact with each other.
when light enters a material, it is believe that the electric and magnetic
fields of the light wave excites the electrons of the material, which because
they are accelerated charged particles in phase with the incoming light, produce
a secondary electromagnetic wave that *does* interact with the incident wave.
there is no mystery on any of this, it is described in every physics text book,
as Maxwell Equations inside a material.
the response of a polarizable material, the so-called "polarization" of a
dielectric- to an electric field $E$ is written as
$$
P = \chi E
$$
where $\chi$ is a way to express the way a material responds to the electric
field. If the material is "linear", then $\chi$ is just a number (if not is
something more exotic)
So, polarization is just an electric field produced by the material.
Nothing in Maxwell equations prescribes the $P$ has to be produced by matters.
So, it stands to reason that two electromanetic waves do interact.
# is the universe expanding?
having established, in prose, that em waves can interact, we might ask "how?"
superposition doesn't mean non-interaction.
two waves can add up (superposition) and interact via the energy density
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