Date: Tue, 19 Aug 2003 13:50:55 -0500
Subject: Re: (urth) Father Inire's Mirrors and Wolfe Physics
From: Michael Buice 


On Tuesday, August 19, 2003, at 12:21  PM, Tony Martinez wrote:
> I don't have a copy of the book on hand, so forgive any
> misrememberings.  I seem to remember the argument goes something like
> this: light is, mathematically, made up of lots of different
> frequencies, from 0 upto infinity.  This means that some of the
> components of light travel *faster than light*.  I remember this scene
> as a speculation that if you could remove all the frequencies which,
> added together, slow down the sum total, you'd have the ones which
> travel faster than light. (*)

The fact I believe you are trying to get at is the concept that group 
velocity and phase velocity are distinct.  This is not directly Quantum 
Mechanics, per se, just wave mechanics (classical physics; however, it 
does apply to QM).

Drop a stone into a pond.  You will see circular waves propagating from 
the impact point.  These wave fronts are moving at a certain speed, the 
speed of "sound" in water.  The velocity of those wave fronts is called 
the "group velocity" and is the analogous speed referred to by the 
"speed of light" for wave packets of light, when it is viewed as an 
electromagnetic wave.

These same waves you see on the pond can also be seen as a combination 
of waves which each have precise frequencies of oscillation.  These 
constituent waves travel at all sorts of different speeds, and the same 
situation is true of light as an electromagnetic wave.  Propagating 
through a given material, there are components which travel faster and 
slower than the speed of light in that material.  This velocity is 
called the "phase velocity".  There have been many experiments which 
have measured these two velocities and received far more press than 
they should have for reporting such things as "speed of light broken" 
and so forth.  You can't "separate" these components in the sense that 
you can't use them to transmit any useful information faster than light 
speed, which is one colloquial manner of stating the limits placed on 
velocity by Lorentz invariance (i.e. special relativity).

The rub is that, under QM, all of these behaviors apply to matter and I 
seem to recall more than a few descriptions of wave mechanical nature 
(or at least what Severian can piece together from what he's been told) 
in New Sun.

Michael


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