Re: Imaginary reality

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Huh?  The index is complex if the wave is traveling in an absorbing
medium.  What's to conserve?

The complex index of refraction is a property of the medium.  Slater and
others showed in the 'twenties that the real and imaginary parts satisfy
an integral relationship (now popularized as a "dispersion relation").

But then I don't know what John meant by his caveat "in detail".
                                Regards,
                                        Jack

Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
                          Mark Twain, <Extract from Eve's Autobiography>

On Fri, 21 Apr 2000, John S. Denker wrote:

> At 11:31 AM 4/21/00 -0700, Bernard G. Cleyet & Nancy Ann Seese wrote:
> > People!
> >
> > Remember, also, that indices of refraction are complex!
>
>
> Hmmmm.
> The way I remember it, indices are sometimes sorta kinda complex.  Maybe.
>
>
> This is a nice illustration of a point I hinted at earlier today:
> Sometimes the formalism does an excellent job of expressing the real
> physics;  sometimes it doesn't.
>
> An imaginary piece to the index of refraction is an _imperfect_ shorthand
> for representing absorption.  It is easy to see how it produces an
> imaginary part to the wavenumber (k), which leads to a wavefunction that
> decays in magnitude as it goes along.
>
> It is also easy to see that this representation cannot possibly be correct
> in detail.  It suggests that the equation of motion is non-unitary.  It
> doesn't conserve phase space.  It violates the fluctuation-dissipation
> theorem.  It violates the 2nd law of thermodynamics.  It violates the
> uncertainty principle.  But if you don't look too closely, you might not
> notice the violations.
>
> This is in stark contrast with the representation that uses complex numbers
> to combine the sine and cosine phasor components of the wavefunction into a
> single equation, which is rigorously correct (given relatively reasonable
> assumptions about linearity et cetera).