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Re: Imaginary reality



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).