correction: philosophy and the vacuum (and index matching)

[John Denker <jsd@MONMOUTH.COM>]

At 03:27 PM 9/8/00 -0400, I wrote:
> >If vacuum polarization effects affect this, then can we
> >assign a non-unity index of fraction to certain vacuums?
>
> Yes.  As an application: the index formulation is an acceptable way to
> describe the scattering when waveguides are joined with an impedance
> mismatch at the joint.
...
> In a waveguide or lumped circuit that has inductance per
> unit length (L) and capacitance per unit length (C) the impedance is
>    Z = sqrt(L/C)
> and the speed of waves is
>    c_1 = 1/sqrt(LC)

Fine so far....

> which means the index is
>    n = c/c_1 = c*sqrt(LC)

The last line is not right.  In the usual waveguide-splicing situation, the
important matching criterion involves impedance-matching, not speed-matching.

For ordinary optical materials, the speed and the index vary together, but
that's not a general requirement.

I'm not 100% clear on
 -- when impedance matching is the important idea
 -- when speed matching is the important idea
 -- whether it makes sense to attach the word "index" to one or the other
of those.

Perhaps a less-confusing way of saying it is that people are familiar with
the principle of least time, and commonly apply it to optics problems
without thinking too hard about it.  But that principle is not true in
general;  the gold standard is the principle of least action.  Messing with
waveguide impedance is a fine way to illustrate the non-equivalence of the
two principles.