re:Re: Quantum Probability and Decision Theory

From: Marchal Bruno <>
Date: Mon, 30 Dec 2002 17:56:29 +0100 (MET)

Dear Stephen,

> When what is [relevant]?
>> Quantum computer can be emulated by classical computer (see below).
> Please point me to some paper, other than yours, that gives something
>better than a hand-waving argument of this statement.

See Deutsch 1985. (precise ref in my thesis)

>> Quantum computer does not violate Church thesis. The set of
>> quantum computable functions is the same as the set of classically
>> computable functions.
> This is one statement that I found:
>"Church's thesis. All the models of computation yet developed, and all those
>that may be developed in the future, are equivalent in power. We will not
>ever find a more powerful model."
> Statements of this kind are found in religious dogma and are not
>acceptable in mathematical and logical circles unless they have adjoining
>caveats and attempted proofs. No where do I find this. It reminds me of
>Kronecker's statement "God made the integers; all else is the work of man."

Church thesis is indeed a non trivial hypothesis in the foundation
of computer science. The main conceptual argument is the closure of the
set of partial recursive functions for the diagonalisation procedure.
An empirical argument is that all attempt to define the set of computable
functions leads to the same class of functions. A relevant book is Webb 1980.

> I do not intend to be impolite here, Bruno, but, Please, give me some
>reference that discusses how it is that "The set of
>quantum computable functions is the same as the set of classically
>computable functions."

It is perhaps up to you to show me a quantum computable function not
being classicaly computable. But if you succeed you will give me
something like an unitary transformation, and then I will show
you how to write a classical program emulating this unitary transformation.
See Pour El and Richard's book on how to conceive differential equations
with non computable solutions (but still locally generable by the UD though),
but anyway, linear quantum waves are classicaly emulable. It is a tedious
but conceptually not so hard exercise.

> I can not see how this is possible given that (as Svozil et at state in
> )
>"for quantum systems representable by Hilbert spaces of dimension higher
>than two, there does not exist any such valuation s: LŪ {0,1} ... there
>exist different quantum propositions which cannot be distinguished by any
>classical truth assignment."
> If there does not exist a unique Boolean valuation for QM systems that
>can be taken to exist a priori and given that UTMs, including UD, demand the
>existence of such for their definition, how is it that you can continue to
>make this statement?

Because the physical world is a first person modality. The accessible
probable worlds can not *appear* in a boolean way from inside. Apparantly
it appears in some quantum logical way. The physical world is not
include in the UD; it emerges from the inside modal first person
statistics from the machines point of view. Those modalities are made
non trivial by the constraints of theoretical computer science and
logic of provability.

> Can UD run them all simultaneously or in some concurrent way that would
>give us some way of finding solutions to the "foliation of space-like
>hypersurfaces" problem of GR? Also, what are the "physical resource"
>requirements of UD? What consitutes it's "memory" and its "read/write head"?

Good question. I hope so :)

>Also, what are the "physical resource"
>requirements of UD? What consitutes it's "memory" and its
>"read/write head"?

I do not need the hypothesis of the existence of "physical resource".
The UD has no other requirement than arithmetical truth. You know,
infinity of primes, and other chinese theorems ...

> I like this part of your thesis and my interest in it makes me ask these
>very pointed questions. Additionally, I hope you would agree that there may
>be an additional problem of how the "Principle of Least action" of physics
>come about. Could it be considered, within your thesis, as just another
>1-person aspect?

Absolutely. Unless comp is false, and that's what makes comp testable.

> Appeals to polls and beliefs should not be made. It would be more
>helpfull if we considered such things as G. Chaitin's Omega when discussing
>random sequences. Can UD compute Omega?

No. But it trivially generates it. Uninterestingly, 'cause we cannot
recognize it. If you dont't like polls you can use the betting manner
of defining probabilities by iterating duplication of population of

>> Now, the simple reason why the quantum is turing-emulable is that the
>> solutions of Schroedinger or Dirac Wave Equation(s) are computable.
> Where is this explained? Please, some papers that you did not write...

See ref above. Deutsch 1985. Or Deutsch FOR book.

> When is your thesis going to be available to those people, like myself,
>who can not read French? Could you try a "machine" translation?

I am writing a paper. Hope to finish it soon ...
The main non technical explanations are online, and more numerous
than in my french very concise thesis.

Hope this helps. Anyway thanks for letting me know your interest.

Received on Mon Dec 30 2002 - 11:59:57 PST

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