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From: George Levy <GLevy.domain.name.hidden>

Date: Tue, 10 Sep 2002 10:13:17 -0700

Russell Standish wrote:

*>George Levy wrote:
*

*>...
*

*>As it stand, the comp hypothesis is only a philosophical exercise
*

*>because it does not reproduce the same phenomenon as QM in particular
*

*>the phenomenon of complementarity. Therefore, to establish a meaningful
*

*>relevance between comp and QM we must show that such phenomena can be
*

*>incorporated in comp.
*

*>
*

*>The following thought experiment is an attempt to illustrate how
*

*>complementarity can be incorporated into a duplication experiment. This
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*>experiment raises some interesting questions regarding the relationship
*

*>between the scientific MW and the philosopical plenitude.
*

*>
*

*>Thought Experiment:
*

*>
*

*>
*

*>....
*

*>
*

*>>Questions
*

*>>This thought experiment, attempt to provide a model of how MW relates to
*

*>>the Comp hypothesis. Many questions arise.
*

*>>1) Why is it that the Plenitude is not directly accessed by QM as
*

*>>explained by comp. Why is there a need for an intermediate MW
*

*>>characterized by complementarity?
*

*>>2) Why is complementarity two-dimensional? Could it be
*

*>>three-dimentional? or higher?
*

*>>3) Is the two-dimensionality of complementarity fact-like? Are there
*

*>>other worlds in the Plenitude which have a complementarity with a higher
*

*>>dimensionality?
*

*>>4) Is the MW only one instance in the Plenitude? How many levels do we
*

*>>have to go from the scientifically determined MW to the philosophically
*

*>>determined Plenitude?
*

*>>5) Is complementarity anthropically necessary?
*

*>>
*

*>>This is only a feable attempt in the generation of a physical model to
*

*>>relate comp to the MW. I hope that we can improve on it through our
*

*>>discussions.
*

*>>
*

*>>George
*

*>>
*

*>
*

*>I would like to point out that my "Why Occam's Razor" paper answers
*

*>about 90% of your question (with the other 10% being the most
*

*>difficult bit, or course :).
*

*>
*

*>Complementarity is a property of any two quantum operators that are
*

*>related by the Fourier transform (x <-> id/dx). The proof is well
*

*>known, and can be found (eg) in Shankar's book.
*

*>
*

Come on! This is circular reasoning. Conventional QM complementarity

requires 2D Fourier. Therefore 2D Fourier must describe complementarity.

True for conventional QM. I was talking about other MWs within the

Plenitude. Could their complementarity be described by Hadamar

transforms for example?

*>
*

*>That momentum is represented by derivative operator (P=id/dx) is
*

*>called the correspondence principle, and is usually given as an axiom
*

*>(see Shankar). Henry gave a "derivation" of this correspondence
*

*>principle about 10 years ago, (Bruno kindly sent me a copy), but I
*

*>believe his derivation is faulty. To date, I still gregard the
*

*>correspondence principle as a mystery.
*

*>
*

*>The other "axioms" of quantum mechanics can be derived from a simple
*

*>model of observation (set out in Why Occams razor). Observers select
*

*>an observation purely at random from an ensemble of choices, subject
*

*>to the anthropic constraint. This is analogous to Darwinian evolution,
*

*>where natural selection selects from natural variation. It is my
*

*>supposition that this generalized evolutionary process is the only
*

*>possible creative process - the only means of generating the complex
*

*>(information rich) structures from the simple ones that are favoured in
*

*>the Schmidhuber ensemble.
*

*>
*

*>It is the anthropic principle that requires us to live in an
*

*>information rich world. The AP is a mystery - one that I believe to be
*

*>equivalent to the famous "mind-body" problem, ie why should we observe
*

*>a correspondence between our mind and a a complex structure called the
*

*>brain?
*

*>
*

*>So to answer your dot points:
*

*>
*

*>1) The above mechanism is why we need an intermediate Multiverse.
*

*>2) The complementarity is 2D because the Fourier transform is its own
*

*>inverse.
*

*>
*

I don't agree with this reasoning. It is circular.

*>A 3D complementarity relationship would require a 3-cycle
*

*>transformation between operators:
*

*>
*

*> X-->Y
*

*> ^ /
*

*> \v
*

*> Z
*

*>
*

*>
*

*>(ASCII characters are _so_ limited...)
*

*>
*

*>To fully answer this question requires answering "Why the correspondence
*

*>principle?"
*

*>
*

*>3) appears to be related to 2) ...?
*

*>
*

*>4) The Multiverse appears to be the only one containing conscious
*

*>observers (subject to the above model of consciousness being necessary).
*

*>
*

*>5) I believe yes (subject to an adequate derivation of the
*

*>correspondence principle existing).
*

*>
*

Interesting but you haven't convinced me.

George

Received on Tue Sep 10 2002 - 10:14:16 PDT

Date: Tue, 10 Sep 2002 10:13:17 -0700

Russell Standish wrote:

Come on! This is circular reasoning. Conventional QM complementarity

requires 2D Fourier. Therefore 2D Fourier must describe complementarity.

True for conventional QM. I was talking about other MWs within the

Plenitude. Could their complementarity be described by Hadamar

transforms for example?

I don't agree with this reasoning. It is circular.

Interesting but you haven't convinced me.

George

Received on Tue Sep 10 2002 - 10:14:16 PDT

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