On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote:
> 
>     Again, that does not work because we can not take space-time (ala GR) to
> be "big enough" to allow us to fit QM into it. On the other hand, it has
> been shown that a QM system, considered as a quantum computational system,
> can simulate, with arbitrary accurasy, any classical system, given
> sufficient "Hilbert space" dimensions - which play the role of "physical
> resources" for QM systems.
> 
> See: http://arxiv.org/abs/quant-ph/0204157
> 
> 
> 
>     This leads me to the idea that maybe space-time itself is something that
> is secondary. It and all of its contents (including our physical bodies)
> might just be a simulation being generated in some sufficiently large
> Hilbert space. This idea, of course, requires us to give Hilbert space (and
> L^2 spaces in general?) the same ontological status that we usually only
> confer to space-time. ;-)
> 
> 

Interesting speculation. I'm not sure that it follows from the ref you
give above, however if indeed our space-time structure can emerge from
a computation on a Hilbert space as you suggest, then this would be a
powerful result. I have already shown (viz my Occam's Razor paper)
that the Hilbert space stucture follows from Anthropic arguments on
ensemble theories. Getting the space time structure is the next big
task to be solved.

                                                Cheers

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