QM is far more than a "set of equations"! It is a very predictive and falsifiable collection of principles and relationships. The most cunning of experimenters have been trying for almost 90 years to find a falsification, none yet has even been hinted. When a quantum gravity theory is found that unifies QM and General Relativity theory's realms of prediction, it will not contradict them, but will extend them. We see the same situation when we compare QM and GR to Newton's theory.
It is one thing for a quantum computation to solve NP-Complete problems in polynomial time. It is something else to compute simulations of behaviors "faster" than Nature itself can complete them. The non-commutativity issue is a very important aspect of any theory that hopes to explain phenomena, it follows from the small but non-zero value of the Plank constant. From what I have studied of superstring theory (or its M-theory incarnation), the non-commutativity of canonically conjugate observables (such as position and momentum) is something that we should not expect to vanish.
This is Not a "time dependency", it is a "concurrency" problem. It involves the order of operations that naturally can not be avoided when more that one event is considered. In order to do simulations of consciousnesses that involve shuffling the ordering, it is necessary for each conscious event is computationally simulable independent of all others and this would include any possible experience including experiences of events that involes order sensitive measurements. If we could assume that "all possible experienciable events" exists, like a pile of shapshots, then we claim have to prove that for any given first person experience of living in a world with time there exists some sequence of snapshots that exist a priori in the pile, but this is not enough, we must be able to show the necessity of first person experiences.
Why is it that I have a first experson experience of a world in which there is an asymmetry between past and future if the entire content of this experience exists priori to me? Why bother with an illusion of time?
BTW, the N-boby problem is completely intractible in a world that takes Plank's constant to be zero because the number of solutions becomes infinite if the energy differences can be infinitely small. The problem is non-integrable.
QM solves this problem partially by only allowing energy (involved in emmision and absorbtion events, which encompasses any and all interactions) to be integer multiples of the plank constant. All of this can be learned from a good QM for laymen book such as Roger Penrose's "The Emperor's New Mind" or John Gribbin's "Schroedinger's Kittens".
----- Original Message ----- From: "Tianran Chen" <[EMAIL PROTECTED]>
To: "Stephen Paul King" <[EMAIL PROTECTED]>; <firstname.lastname@example.org>
Sent: Wednesday, January 26, 2005 9:48 PM
Subject: Re: Belief Statements
Stephen Paul King wrote:Dear Hal and Tianran,
Assuming there is some aspect of consciousness that requires QM ( I side with Penrose on this) these out of order computations are impossible. This boils down to the fact that for systems that have time-like relationship with each other will have observable that are not commutative.
We could ignore Penrose and make the same argument by pointing out that is the simulated consciousnesses, for example those of Alice and Bob of the EPR experiment, are to involve any hint of QM phenomena then the non-commutativity will rear its ugly head and nip off the idea in the bud. I am surprised that Greg Egan didn't notice this...
Logically speaking, QM (not its interpretations) is simply a branch of applied mathematics (use the definition given by <<Foundation of Mathematics>>) that happen to agree with some observed facts. In another word, QM is a set of equations we used to describe phenomenon. If there is time dependency, then it is in the structure of those equations, not in the phenomenon. It is totally possible that later on, some totally different theories will be proposed that can describe the same set of observations and yet do not suffer from such time dependency problem. Isn't it?
Let us suppose, later on, the super-string theory become favored by most serious physicsts, and let us pretend that there are some equation in the super-string theory that can support consciousness, and can be solved in constant steps with some turing machine. However unlikely, such possible shall not be ruled out.
Also from another direction, isn't it possible that later some type of computation model (say quantum computer) can actually solve hard problems (say multi-body gravity problem) in constant time, then it can also simulate consciousness-supporting world out of order.
I only had chance read a few sections novel, so sorry if I misunderstood some important details here. But the novel did not explicitly say which theory of physics the simulator was using, right?