Let me add that I do not think that it is sufficient to embed space-time
in Hilbert space, we also need some way of explaining how space-time
phenomena acts on the Hilbert space's vectors. The infamous "back-action"...
I have an idea but it is pure vapor at this point ...
----- Original Message -----
From: "Stephen Paul King" <[EMAIL PROTECTED]>
To: "Russell Standish" <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Sunday, February 22, 2004 11:39 PM
Subject: Re: Is the universe computable?
> Dear Russel,
> Does this "quantum theorist " have anything published on this that i
> find online? I do need to do better than "can"! I need a "must"! ;-)
> ----- Original Message -----
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: "Stephen Paul King" <[EMAIL PROTECTED]>
> Cc: "Russell Standish" <[EMAIL PROTECTED]>;
> <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
> Sent: Sunday, February 22, 2004 11:22 PM
> Subject: Re: Is the universe computable?
> 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
> > prove that the class of all possible evolutions of QM systems includes
> > 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"
> > figure out how to switch from a 3rd person to a 1st person
> > (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
> > The hard part is taking the idea that Hilbert space is a
> > 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" <[EMAIL PROTECTED]>
> > To: "Stephen Paul King" <[EMAIL PROTECTED]>
> > Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
> > 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
> > to
> > > be "big enough" to allow us to fit QM into it. On the other hand, it
> > > been shown that a QM system, considered as a quantum computational
> > > can simulate, with arbitrary accurasy, any classical system, given
> > > sufficient "Hilbert space" dimensions - which play the role of
> > > resources" for QM systems.
> > >
> > > See: http://arxiv.org/abs/quant-ph/0204157
> > >
> > >
> > >
> > > This leads me to the idea that maybe space-time itself is
> > that
> > > is secondary. It and all of its contents (including our physical
> > > 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
> > > 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
> > UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
> > Australia [EMAIL PROTECTED]
> > Room 2075, Red Centre
> > International prefix +612, Interstate prefix 02