>From: Russell Standish <[EMAIL PROTECTED]>
>Subject: Re: why can't we erase information?
>Date: Mon, 10 Apr 2006 18:34:42 +1000
>On Mon, Apr 10, 2006 at 12:03:47AM -0700, Brent Meeker wrote:
> > Russell Standish wrote:
> > > Unitary evolution preserves information. It is only through
> > > measurement by an observer that information can be created or
> > > destroyed. Usually, the second law is interpreted as the destruction
> > > of information (anyone observing a closed system will over time know
> > > less information about the system), so it puzzles me that you have the
> > > sign the other way.
> > What? You're saying that if I observe a system, then I know less about
> > must be using some non-standard meaning of "know".
> > Brent Meeker
>Yes - in the case of milk being stirred into coffee. Strange as it may
>seem, you know more information when the system is initially
>structured than after that initial structure has dispersed.
>And yes you need to observe it. Entropy is undefined without an
As I understand it, you don't need exactly need an observer, you just need
to identify various macro-variables (like pressure and temperature) which
can be used to "coarse-grain" the phase space of the system, with entropy
being proportional to the logarithm of the number of possible detailed
"microstates" (detailed descriptions of the positions and momenta of all the
particles, within the limits of the uncertainty principle) compatible with a
given "macrostate" (descriptions of the system which only tell you the value
of the macro-variables). Once you have chosen your set of macro-variables,
they should have well-defined values for any system, regardless of whether
it's being observed by anyone or not. Of course, the choice of variables is
based on what properties we human observers are actually capable of
measuring in practice, so I don't necessarily disagree with your statement,
but I think it needs a little clarification.
Likewise, I think "the second law is interpreted as the destruction of
information" needs a bit of clarification--as entropy increases, there are
more and more microstates compatible with a given macrostate so the observer
is losing information about the microstate, but information is not really
being lost at a fundamental level, since *in principle* it would always be
possible to measure a system's exact microstate.
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