On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote:
> Dear Russel,
>
> The reference page is about the necessary resources for quantum
> computation in general. The "result" that "our space-time structure can
> emerge from a computation on a Hilbert space" is not complicated, we just
> prove that the class of all possible evolutions of QM systems includes QM
> computations.
> Then we take Deutsch's work showing how classical systems can be
> simulated by quantum computations and identify the subset(class) of
> simulations with the subset(class) of our experiences of "our world" and
> figure out how to switch from a 3rd person to a 1st person representation
> (something like what Bruno Marchal proposes) .
Ahh, that little word "can". I was taking your previous statement as
stating something much more profound - that 4D space-time must emerge
from a Hilbert space computation. Still - perhaps it is possible. I
was at dinner a couple of weeks ago with a quantum theorist who
claimed exactly that, starting from a standard QED formulation, and
taking the h->0 limit. Alas, they tend not to teach QED at
undergraduate level, so my ability to evaluate this claim is
impoverished.
> The hard part is taking the idea that Hilbert space is a representation
> of something that has ontological reality - not just a mental construct.
>
Its not so hard. If we accept ensembles of descriptions as having the
ultimate ontological reality (similar, if not equivalent, to Bruno's
arithmetic realism), then Hilbert spaces emerge as the highest measure
structure under fairly mild assumptions about the nature of
consciousness. (detailed in my "Why Occam's Razor paper).
> Kindest regards,
>
>
> Stephen
>
> ----- Original Message -----
> From: "Russell Standish" <R.Standish.domain.name.hidden>
> To: "Stephen Paul King" <stephenk1.domain.name.hidden>
> Cc: <everything-list.domain.name.hidden>; <issues.domain.name.hidden.org>
> Sent: Sunday, February 22, 2004 6:04 PM
> Subject: Re: Is the universe computable?
>
> 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
>
> ----------------------------------------------------------------------------
> A/Prof Russell Standish Director
> High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
> UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
> Australia R.Standish.domain.name.hidden
> Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
> International prefix +612, Interstate prefix 02
> ----------------------------------------------------------------------------
>
--
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A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
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Received on Sun Feb 22 2004 - 23:26:28 PST