Title: Re: [Fis] QUANTUM INFORMATION

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 Bellís (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 ëfixedí 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 donít 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

--
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Ted Goranson
Sirius-Beta

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