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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.
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Have a look at my free physics textbook, written to be
surprising and challenging on every page:
http://www.dse.nl/motionmountain/contents.html
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Received on Tue Oct 24 2000 - 06:08:52 PDT