Re: Provable vs Computable

From: George Levy <GLevy.domain.name.hidden>
Date: Fri, 01 Jun 2001 22:06:17 -0700

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

juergen.domain.name.hidden 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:

> George, thanks for your reply, which is almost as convoluted and
> 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
Received on Fri Jun 01 2001 - 22:07:59 PDT