Sorry I responded to your last message before reading this one!
Its also slightly confusing to use the term wavefunction, which most
people would think of as a member of C(R^n), however this could be
fixed by using the term "state" in its place.
My initial response to your latest post is that even if a single
observer cannot distinguish between two states, there is a another
observer who can. If one includes the totality of observers (which may
or may not be a set :), then the set of states is a set (in fact a
Hilbert space), at least according to the conventional view.
PS: to make sense of the totality of observers as really existing
demands a many worlds or many minds type interpretation.
Cheers
Christoph Schiller wrote:
>
>
>
> Oops, sorry for the typo. I did *not* intend to say:
>
> 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.
>
> But:
>
> 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,
> allow to deduce that it is impossible that wavefunctions
> form sets. (At Planck scales, of course)
>
> In particular, at Planck scales, wavefunctions do not form
> Hilbert spaces. (In fact, it is unclear whether wavefunctions
> make sense at all in these conditions.)
>
> Of course, at usual energies, the Hilbert space is a good
> approximation for the description of nature.
>
>
>
>
>
> ---
>
> 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.
>
>
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Received on Tue Oct 24 2000 - 17:26:20 PDT