From: Amara Graps (Amara.Graps@mpi-hd.mpg.de)
Date: Wed Mar 27 2002 - 07:05:56 MST
Hal Finney:
>Actually, information is not quantized.
Would you accept entropy being *conserved* in quantum mechanics ..?
There's an interesting thread on sci.physics.research on this topic.
Here's one part:
=============================================================
>From "Geoffrey A. Landis" <geoffrey.landis@sff.net>
Newsgroups sci.physics.research,sci.space.tech
Subject Conservation of information [Re: Experiments in creating worm holes.]
Date Mon, 18 Mar 2002 23:11:58 +0000 (UTC)
James Logajan wrote:
>
> I never encountered any "conservation of information" laws in undergraduate
> physics; must be one of those graduate courses I missed since I didn't go
> for a doctorate. Lucky me, since as a result I can sleep soundly.
Not surprising; it might be covered in a graduate quantum-mechanics
course, but then it might not, since it's not really central to physics.
You use the information/entropy connection from statistical mechanics
and information theory, then when you define entropy in quantum
mechanics you see immediately that entropy is *conserved* in quantum mechanics.
This seems quite surprising, really, since in our macroscopic world
entropy *increases*. But since quantum mechanics is time-reversable, it
shouldn't have been unexpected: entropy increase is a manifestation of
time *non* reversability, and all time-reversable processes conserve
entropy (and information)-- in fact, in statistical mechanics,
entropy-increasing processes are known as "irreversable".
>I wouldn't know how one goes about defining, measuring, or quantifying the
> physical manifestation of "information".
Per Claude Shannon, you just count the possible number of states, N. An
eight-bit message, for example, has 256 possible states. It's then
convenient to express information in terms of entropy, S = k ln N
--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis
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Amara Graps, PhD | Max-Planck-Institut fuer Kernphysik
Heidelberg Cosmic Dust Group | Saupfercheckweg 1
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Amara.Graps@mpi-hd.mpg.de * http://www.mpi-hd.mpg.de/dustgroup/~graps
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