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From: Russell Standish <rks.domain.name.hidden>

Date: Wed, 25 Oct 2000 10:21:50 +1100 (EST)

Christoph Schiller wrote:

*>
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*>
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*>
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*> Russel Standish wrote:
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*>
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*> - My understanding of QM is that it is based on a set (the Hilbert space
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*> - of "wavefunctions") that is neither a space-time set nor a particle
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*> - set. It has infinite dimensionality while space-time sets are finite,
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*> - and is continuous while particle sets are discrete.
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*>
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*> - Let me know if I'm missing something here, but I would have thought
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*> - that this does kill your argument.
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*>
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*> I think there are several ways to see that the Hilbert space falls
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*> under the argument nevertheless.
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*>
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*> Different wavefunctions differ by the values of the corresponding
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*> observables, and for these observables the argument still holds;
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*> in fact, there are minimum measureable values for most observables.
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*> (I do not dare to say "all", because I would need to
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*> look into the matter in more detail.)
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*>
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*> In addition, wavefunctions can be seen as functions over
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*> space and time, so that the minimum measureable intervals
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*> which make it impossible to say that space and time are sets,
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*> allows to deduce that it is impossible that Hilbert spaces
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*> are sets.
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^^^ I beg to pick a rather pedantic point here - Hilbert spaces are

sets by definition - see any elementary functional analysis textbook

for an exposition - the one by Erwin Kreysig will do.

Hilbert spaces have a distance measure defined on them (the norm of the

difference), and the distance between two elements of a Hilbert space

is only zero when the two elements are identical.

I think your problems arise when you introduce observers. Quantum

Mechanics is a very nice theory, and works extremely well when there

are no observers to complicate the picture!

Of course, you may wish to say that QM is merely a mathematical

description, that doesn't really relate to the real universe at all,

however I tend to take the opposing view that QM is more fundamental

than the "pseudo"-classical reality that we perceive.

Hope this gives food for thought (and further discussion :)

Cheers

*>
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*> Thanks for the point - I hadn't thought of it in this way yet.
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*>
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*> Christoph Schiller
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*>
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*>
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*>
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*> ---
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*>
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*> Have a look at my free physics textbook, written to be
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*> surprising and challenging on every page:
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*>
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*> http://www.dse.nl/motionmountain/contents.html
*

*>
*

*> ---
*

*>
*

*> ------------------------------------------------------------
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*> --== Sent via Deja.com http://www.deja.com/ ==--
*

*> Before you buy.
*

*>
*

*>
*

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

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Received on Tue Oct 24 2000 - 16:53:50 PDT

Date: Wed, 25 Oct 2000 10:21:50 +1100 (EST)

Christoph Schiller wrote:

^^^ I beg to pick a rather pedantic point here - Hilbert spaces are

sets by definition - see any elementary functional analysis textbook

for an exposition - the one by Erwin Kreysig will do.

Hilbert spaces have a distance measure defined on them (the norm of the

difference), and the distance between two elements of a Hilbert space

is only zero when the two elements are identical.

I think your problems arise when you introduce observers. Quantum

Mechanics is a very nice theory, and works extremely well when there

are no observers to complicate the picture!

Of course, you may wish to say that QM is merely a mathematical

description, that doesn't really relate to the real universe at all,

however I tend to take the opposing view that QM is more fundamental

than the "pseudo"-classical reality that we perceive.

Hope this gives food for thought (and further discussion :)

Cheers

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

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Received on Tue Oct 24 2000 - 16:53:50 PDT

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