Dear Russell, 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 ...

## Advertising

Kindest regards, Stephen ----- 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 can > find online? I do need to do better than "can"! I need a "must"! ;-) > > Stephen > > ----- 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 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" <[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 > 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 [EMAIL PROTECTED] > > Room 2075, Red Centre > http://parallel.hpc.unsw.edu.au/rks > > International prefix +612, Interstate prefix 02 > > --------------------------------------------------------------------------