Russell Standish wrote:
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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
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.

Geor ge


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?
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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
t he 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.


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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


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