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) . The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct.

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 ----------------------------------------------------------------------------