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From: Osher Doctorow on 25 Jul 2010 12:10
From Osher Doctorow

A good "motivation" for this subsection or section is Wikipedia's
online "Incompleteness" or "Incompleteness Theorem" and "Peano
Axioms".

In Quantum (Mechanics) Theory, the Classical Nonrelativistic Physics
is characterized by:

1) h --> 0 (or h " = " 0) is (Nonrelativistic) Classical from Quantum
physics.

On a scale of [0, 1], however, as is usual in Probability and Probable
Causation/Influence (PI), the "opposite" holds, scaling h > 0 to 1:

2) h --> 1 (or h " = " 1) is Quantum (Mechanics) from Classical
Nonrelativistic physics.

Let us now define an "Observation" operator or expression O(x) for
some physical object or observable or physical "anything" x:

3) O(x) = h (Planck's constant)

Then we get:

4) |O(Quantum) - O(Classical Nonrelativistic) | = 1.

Here "Quantum" means "Quantum (Mechanics) physics", etc.

We see that:

5) From (4), Quantum (Mechanics) and Classical Nonrelativistic Physics
differ maximally in Observation from each other's perspective, which
also (1) is the maximum possible difference in probabilities (which
are in the scale [0, 1] always).

A similar argument, this time without h but with a normalized distance
scale variable R on [0, 1] replacing h, yields:

6) Classical Nonrelativistic Physics and Relativistic Physics differ
maximally in Observation from each other's perspective.

Regarding each type of physics as the "Universe" (relatively from its
"viewpoint"), the other types are then either Null Sets or sets of
Probability 0. Formally:

7) The 3 types of Physics, Classical Nonrelativistic, Quantum, and
Relativistic, differ from each other approximately as the Universe
(Probability 1) differs from either Null Sets or sets of Probability
0.

From the previous last few posts, P(0 --> U) = 1 and P(U --> 0) = 0
where the 0 inside P( ) is a set of probability 0 including the
possibility of it being the null set. Therefore, from the viewpoint
of each type of physics in (7), the "other type" (0) appears to
generate or create it, while it cannot generate or create the other
type. Formally:

8) From the viewpoint of each type of physics in (7), the other types
appear to generate it, while it cannot generate the other types. In
short, the other types can be regarded as (relatively poor or even
extremely poor) approximations to the type in question which
incorrectly seem to be more effective than they are.

Osher Doctorow
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