Christoph Schiller wrote:
>
>
>
> 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.
^^^ 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
>
> 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.
>
>
----------------------------------------------------------------------------
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
----------------------------------------------------------------------------
Received on Tue Oct 24 2000 - 16:53:50 PDT