Re: [Fis] QUANTUM INFORMATION

Re: [Fis] QUANTUM INFORMATION

From: Ted Goranson <[email protected]>
Date: Sat 03 Jun 2006 - 15:14:57 CEST

Andrei Khrennikov wrote on 5/15/06:
>11th FIS Discussion Session:
>
>QUANTUM INFORMATION
>Andrei Khrennikov & Jonathan D.H. Smith

Friends,

Thank you to Andrei for the solid beginning of
this session. If I understand it correctly, he is
using the platform of FIS (interest in the
fundamental nature of information AND how that
could lead to new perspectives in science) to
present some views on QI.

QI is usually a term applied to information in
the usual sense, processed or manipulated in
artificially designed systems using QM effects
and behavior, and that is how the introduction
begins.

Then the shift is made here: "Therefore 'Quantum
Information' gives a new great chance for
reconsideration of quantum foundations." And we
are referred to a particular frequency view of
the Bell inequity wherein the EPR paradox is
resolved and QM is seen as a complete theory,
bolstering the notion that a useful view of
information can be distilled from it.

This view depends on Bell�s (and others)
assertions against local reality.(Smith's half of
the introductory message wonders openly about
quantum communication and computation and
suggests that either QM is "necessary" or can be
replaced by classical "tricks." He then asks
about the limits and nature of Q computation.)

Sri, in a side conversation, introduces the
notion of ontological precedence, which I would
like to extend beyond his notion a bit here.

Because I think our non-physicist colleagues may
get lost in all this, the relevant key concepts
here are due to Kolmogorov, a rather amazing
mathematician whose insights targeted the
mathematics of description and mapped discrete
probabilities onto topological spaces ordinarily
associated with logic. In so doing, he spanned
two traditions in mathematical philosophy:

One which is based in numbers and asserts that
science is a matter of measurement, and a second
tradition which asserts that science is a matter
of comprehending causality (causality in this
context being a matter of logical explication).

Classical physics broke when following the first
tradition and was fixed (still within that
tradition) by QM, which has proved to be
amazingly useful in physics, but not in other
sciences. That uncomfortable fact, plus some odd
QM paradoxes in physics, drive QM champions to
repair or extend QM by adding geometric features
from the "second" thread of mathematical
philosophy.

This had been done earlier in a simpler way in
the application of symmetry from what we'll call
the second tradition here. The result was of this
cross-tradition meld was the so-called "standard
model."

(Einstein, incidentally, was purely in the
geometric tradition, and there are still a number
of physicists, albeit shrinking, with similar
views. The international symmetry society ISIS-S
seems to collect a critical mass of these folks;
their next meeting is in Buenos Aires, November
2007.) Kolmogorov provided tools that went much
further in this synthetic vein of
cross-tradition, so is the basis of first resort
when coming to matters of QI.

So for the non-specialist in this area, the
challenge is to understand Kolmogorov's ideas. I
do not myself think it essential or even
important to recount the historical steps in
physics in this matter. What probably matters to
the reader is knowing where the levels of
abstraction are, in each of the instances where
one theoretical thread has been �fixed� using the
other. In other words, when the conceptual space
is reshuffled, which abstractions are then closer
to reality and which are at the other end of
elaborations, in the mechanics of representation.

I think the key is in tracing ontological
precedence, which would make this explicit.

Unhappily, working physicists don�t normally make
these distinctions. If a theory works, it is
effectively collapsed into reality, regardless of
the internal dependencies of abstraction therein.
Worse, different theoretical formulations array
these dependencies contrarily depending on their
own foibles, academic political alliances and the
nature of the problem.

To my mind, information is a layered thing in any
formulation, and there is always a gradation
between the way things are and the machinery we
use to represent it. In fact, the way we chose to
represent phenomena could be thought of as a
second kind of information. It might even be that
the steps from reality to theory are discrete, or
appear to be so. In the case of theorists who
collapse representation into reality, these steps
are becoming tangled.

I suggest that if FIS really does come up with
something new and useful, it will be in inventing
or discovering these steps, or alternatively
proposing a new formulation of information
abstraction with specific steps. This way, when
we speak of information, at least we'll know what
type of information we are dealing with, before
we try to press into styles and forms.

Examples: ordinary, Copenhagen QM applies and
observer shift; gravitation field theorists
suggest hidden dimensions; information theorists
with a direct view insert Bell's "hidden
variables"; I expect Koichiro soon to suggest a
tense-based notion.

The proposal I am making here is to allow more
than one insertion level, and to provide for
different ontologies at each level, while also
allowing the ontologies to be linked in a
derivative way. This is not such a radical
proposal - if there is a gradation, then we
assume that the levels are linked. If there are
levels, we may find that different "behaviors"
characterize each stage, and that behavior must
be factored into any analysis of the information
we find there. And finally, because it is already
in the discussion, I propose that we use
Kolmogorov manifolds as a referent structure for
this.

Here's another way to look at it: whatever
"language" entities in the world use to
communicate with each other (and their enveloping
systems), it is ontologically unreachable to us.
It has an unachievably high Kolmogorov
complexity, meaning that the description is
bigger than the thing it describes.

So in keeping with the sensibilities of
physicists, the first ontological layer will
impose what we've called the "first tradition"
and reduce the complexity of the description.
What you have here is the view that many
physicists have of the world, a distributed
existence characterized as probabilities. Not
manageable information yet, not in the sense of
an FIS-like information science.

So we add another ontological transform that
further reduces the complexity, a layer that adds
logical ontological structure. This is
generalized from a notion of Levin's which deals
with one such ontological feature: constraints.
The result is topological manifolds with real
phenomenon on one fold and logical information
related to that phenomenon on another.

Any number of such ontological layers are
possible and I suppose as system scale increases
(physical, chemical, biological and so on...) new
ones are added, possibly with constant semantic
distance.

The point here is as stated at the beginning,
that "ontological precedence" is key in
unwrapping how QM and information inform each
other, if I can use such a reflexive notion.

Best, Ted

-- 
__________
Ted Goranson
Sirius-Beta

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Received on Sat Jun 3 15:17:38 2006


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