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Article 6076 of comp.ai.philosophy:
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>From: clarke@acme.ucf.edu (Thomas Clarke)
Newsgroups: comp.ai.philosophy
Subject: Re: Quantum mechanics (no AI here, sorry)
Message-ID: <1992Jun4.124417.12957@cs.ucf.edu>
Date: 4 Jun 92 12:44:17 GMT
References: <1992Jun03.203556.4561@spss.com>
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In article <1992Jun03.203556.4561@spss.com>  writes:
> In article <1992Jun2.161131.11780@guinness.idbsu.edu> holmes@opal.idbsu.edu 
> (Randall Holmes) writes:
> >If you think that the waves are real physical phenomena, then FTL
> >signalling is involved.  I think it is quite reasonable to suppose
> >that the universe has "real states"; the particle side of the
> >particle-wave duality is real; the wave side encodes restrictions on
> >what information we can have about the real situation.  
> > Stuff Deleted  
> 
> I'm not sure I understand you, but I suspect you're wrong.  It's not just
> a matter of observing a correlation across a huge distance.  It's that
> you and another observer do something (twist a calcite crystal) and
> immediately, before any signal could move from one to the other, the
> correlation rate changes, in a way that can't be explained by local
> properties of the particles.  There's something non-local going on here.
> I don't see what difference it makes if you call it "phyical" or not.

My two cents.  The particle picture and the wave picture are mathematically
equivalent.  I think it was Dirac who dicovered that Heisevberg's and
Schrodinger's views could be reconciled in the arena of Hilbert space; 
von Neuman dotted the mathematical i's and crossed the t's.  

Heisenberg has an infinitely long vector of amplitudes which represent the
strength of various particle states (square magnitude for probability).
Mathematically Heisenberg's vectors are in l2, the space of square summable
infinite sequences with dot product equal to sum of products.

Schrodinger has wave functions whose amplitude represents state amplitude
at a given point in space (square for probability density).  Mathematically
Schrodinger's wave functions are in L2, the space of square integrable 
functions with dot product equal to the integral of the product.

In functional analysis it is proved that L2 is isomorphic ot l2 (at least
for the "nice" cases involved in quantum mechanics).  Whatever happens
in l2 has a corresponding result in L2.  (Think of the Fourier transform
of a periodic continuous signal which results in a infinite series of 
Fourier coefficients).

Thus it seems to me the mathematics says that if waves give you heartburn,
then particles will give you indigestion.

--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu


