Re: what is faster

Jim Black wrote:

[snip]

If my analysis above is correct, it is impossible for this dispersion
relationship to hold over the entire frequency range, because it would
allow superluminal information transfer. I suspect that the departure
of the refractive index from this linear approximation at higher
frequencies is crucial to understanding why causality is not violated.

You might well be right about that, I'll have to think about this more
carefully. I was aware that the response of the monochromatic
components to the shutter was an approximation -- and it's certainly
not compatible with anomalous dispersion across all frequencies. The
model the applet represents is that the anomalous dispersion
relationship holds only for the band of frequencies explicitly
portrayed, while the overall dispersion function, whatever it might be,
is such that the approximation used for the shutter response isn't too
inaccurate. I know that's not very precise, but it's simple to
implement, and I think it's actually quite physically reasonable.

I'm vaguely aware of something called the Kramers-Kronig relations,
which were mentioned in a recent thread on sci.physics.research on
"Fourier analysis and causality". I believe they put some kind of
restriction on dispersion functions in order for them to be compatible
with causality, so perhaps they would be one way to rule out this
dispersion relationship holding true for all frequencies.

In any case, if I can work out a slightly more realistic response to
the shutter I might add that to the applet when I get a chance. I
doubt it will make any qualitative difference to any of the behaviour,
but it *would* be more satisfying to have an explicit dispersion
relationship to explain the response to the shutter.

.

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