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From: Christoph Schiller <christoph_schiller.domain.name.hidden>

Date: Tue, 24 Oct 2000 01:46:04 -0700

('binary' encoding is not supported, stored as-is) Russel Standish wrote:

- My understanding of QM is that it is based on a set (the Hilbert space

- of "wavefunctions") that is neither a space-time set nor a particle

- set. It has infinite dimensionality while space-time sets are finite,

- and is continuous while particle sets are discrete.

- Let me know if I'm missing something here, but I would have thought

- that this does kill your argument.

I think there are several ways to see that the Hilbert space falls

under the argument nevertheless.

Different wavefunctions differ by the values of the corresponding

observables, and for these observables the argument still holds;

in fact, there are minimum measureable values for most observables.

(I do not dare to say "all", because I would need to

look into the matter in more detail.)

In addition, wavefunctions can be seen as functions over

space and time, so that the minimum measureable intervals

which make it impossible to say that space and time are sets,

allows to deduce that it is impossible that Hilbert spaces

are sets.

Thanks for the point - I hadn't thought of it in this way yet.

Christoph Schiller

Date: Tue, 24 Oct 2000 01:46:04 -0700

('binary' encoding is not supported, stored as-is) Russel Standish wrote:

- My understanding of QM is that it is based on a set (the Hilbert space

- of "wavefunctions") that is neither a space-time set nor a particle

- set. It has infinite dimensionality while space-time sets are finite,

- and is continuous while particle sets are discrete.

- Let me know if I'm missing something here, but I would have thought

- that this does kill your argument.

I think there are several ways to see that the Hilbert space falls

under the argument nevertheless.

Different wavefunctions differ by the values of the corresponding

observables, and for these observables the argument still holds;

in fact, there are minimum measureable values for most observables.

(I do not dare to say "all", because I would need to

look into the matter in more detail.)

In addition, wavefunctions can be seen as functions over

space and time, so that the minimum measureable intervals

which make it impossible to say that space and time are sets,

allows to deduce that it is impossible that Hilbert spaces

are sets.

Thanks for the point - I hadn't thought of it in this way yet.

Christoph Schiller

--- Have a look at my free physics textbook, written to be surprising and challenging on every page: http://www.dse.nl/motionmountain/contents.html --- ------------------------------------------------------------ --== Sent via Deja.com http://www.deja.com/ ==-- Before you buy.Received on Tue Oct 24 2000 - 01:46:36 PDT

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