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?