FOM: Alice, Carol and Leibniz
Insall
montez at rollanet.org
Tue Apr 16 19:34:00 EDT 2002
I have been assuming that I understood what each person meant by
``indistinguishable'', in terms of an inability to linguistically ``pin
down'' a particular object as being ``distinct from'' some other particular
object. (This reminds me of urelemente, in set theory. The language has no
individual names for specific urelements, and so the assumption of the
existence of urelements in one's set-theoretic universe provides a way to
deny various hypotheses that are significantly affected by the ability to
``name'' objects, such as the axiom of choice.) Can you please explain what
you mean by that term in the quote below? Would you say that any two
electrons are indistinguishable, no matter what is their degree of
separation, and no matter what states they are in? It seems that protons
are distinguishable, for otherwise, it seems to me that NMR spectrosopy
would need a different explanation than the one I was given in organic
chemistry class as an undergraduate student, which indicated that one learns
from an NMR spectrum about different ``environments'' for individual protons
in a given molecule or in a given small collection of molecules. (It is not
clear to me that one needs to be able to ``name'' the individual protons in
order to ``discover'' distinguishing properties for them.)
Matt Insall
-----Original Message-----
From: owner-fom at math.psu.edu [mailto:owner-fom at math.psu.edu]On Behalf Of
Miguel A. Lerma
Sent: Tuesday, April 16, 2002 12:07 PM
To: fom at math.psu.edu; lrwiman at ilstu.edu
Cc: Dean.Buckner at btopenworld.com
Subject: Re: FOM: Alice, Carol and Leibniz
But if the particles are indistinguishable,
then the state of the total system is not just the product
of the states of the individual particles, but the symmetrized
or antisymmetrized product of their states (depending on the
statistics, symmetrized for bosons, antisymmetrized for fermions)
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