"It was only an observation that planes of linear polarization,
into which a beam of light is decomposed, are usually not
arbitrary. This becomes an issue in crystal optics, for example,
when the index ellipsoid is constructed for a crystal like calcite.
The optical axis, z, and principal axes, x,y (defined in terms
of two mutually perpendicular principal planes) are imposed
by the internal atomic structure. The unique x,y,z axes turn
out to be mutually perpendicular while the cleavage surfaces
are not. This was counterintuitive to me. My impression used to
be that x and y are arbitrary directions perpendicular to the z axis."
Hi Ludwik,
Consider that a (2 dimensional) vector may be decomposed into arbitrary
x/y components. However a certain decomposition may make the physics more
lucid/easy for a particular problem. Eg. The forces on an object sliding
along an inclined plane, vs the forces on a car rounding a banked curve.
Either problem can be done using various x/y choices, but for each a
certain choice facilitates the calculation ( and the conception). The
same is true of your optics situation.