# Re: Provable vs Computable

John and Hal, Bruno and all everythingers, sorry for the delay guys, I was travelling and had lots of work. Bruno, I just scanned your post quickly. It seems to me we are going in the right direction but I shall need time to digest what you wrote. I shall reply to you later

Let me first reply to John and Hal because it is the shortest reply. Let's go back to the original Juergens' post

[EMAIL PROTECTED] wrote:

> Example: a never ending universe history h is computed by a finite
> nonhalting program p. To simulate randomness and noise etc, p invokes a
> short pseudorandom generator subroutine q which also never halts. The
> n-th pseudorandom event of history h is based on q's  n-th output bit
> q(n) which is initialized by 0 and set to 1 as soon as the n-th element
> of an ordered list of all possible program prefixes halts.  Whenever q
> modifies some q(n) that was already used in the previous computation of
> h, p appropriately recomputes h since the n-th pseudorandom event.
>
> Such a virtual reality or universe is perfectly well-defined.

I replied:

>Such a universe would violate Bell' inequality theorem. Quantum randomness
>cannot be simulated by hidden variables. We have to move beyond
>realism......to get a model of objective reality we must first develop a
>model of consciousness.

A purely mechanical model no matter how complicated, including random variables, cannot replicate the results generated by Quantum mechanics + probability theory. This is exactly what Bell's inequality implies. In fact Bell proved his inequality using Quantum theory and probability.

Therefore,  Juergens' erector (fr: meccano) set approach using pseudo-random generators, would definitely violate Bell's inequality theorem, and would not be phenomenally or experimentally equivalent to quantum mechanics. Some of his (our) choices are:

1) Quantum mechanics + probability -> Bell's inequality and give up on a mechanical hidden variable, on pseudo random generators, and more generally, on realism.

2) Something else of power equivalent to Quantum mechanics in describing nature....Good Luck!!!  I do not believe the route to this solution is the erector set technique. Many a 19th and early 20th century physicist has broken a tooth on that bone!

George

jamikes wrote:

hard-to-follow as was my question. You wrote:

> I am not restricting anything. I am only saying that Juergens has to
choose
> between violating Bell's  inequality theorem and all that this implies, or
not
> and all that this implies. My stand is that we shouldn't.
>  George
>
So ;let me rephrase the question:
is your stand that if an imaginary universe would violate eg. Bell's
theorem, it should be excluded from consideration as a possibility,
- or -
we should rather conclude that Bell's theorem (or any other fundemntal
"human" rule) has a limited validity and does not cover every possible
universe?
John