Re: A theoretical physics FAQ (information in a particle)
- From: "Juan R." <juanREMOVE-THIS@xxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 10 Jan 2008 23:52:40 +0000 (UTC)
Gerard Westendorp wrote {478147e2$0$85782$e4fe514c@xxxxxxxxxxxxxx} on Sun,
06 Jan 2008 20:44:26 -0500:
Arnold Neumaier wrote:
The theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
Quite readable stuff on some of the most tricky subjects!
One question on the "information in one particle". The FAQ reads:
[..]
A pure state of an electron is defined by its wave function (up to a
phase). Thus knowing all about an electron requires in the traditional
interpretation to know all about this wave function - an infinite
amount of information.
How does this relate to the entropy formula S = k ln(Omega)?
Gerard
General definition of entropy is
S = - k Tr{RHO {LN RHO}}
for a *isolated* system *at equilibrium*
RHO = 1 / OMEGA
Substituting
S = k Tr{RHO {LN OMEGA}} = k {LN OMEGA} Tr{RHO} = k {LN OMEGA}
Textbooks often take this like definition for entropy but the general
definition is that of above.
An electron at pure state |PSI> is
RHO = |PSI><PSI|
and
S = - k Tr{RHO {LN RHO}} = 0
--
I follow http://canonicalscience.com/guidelines.txt
.
- References:
- A theoretical physics FAQ
- From: Arnold Neumaier
- A theoretical physics FAQ
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