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Annals of the New York Academy of Sciences

Information Mechanics Perspective on Some Assumptions in Classical Mechanics and Quantum Mechanics about Measurement

Frederick W. Kantor

Published Dec 1, 1986• 1 citation
Publisher
DOI
10.1111/j.1749-6632.1986.tb12467.x

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In classical information theory (represented by Shannon's framework), the study of information transmission typically presupposes a fixed "channel" endowed with absolute attributes. This assumption implicitly holds that the properties of the channel are determinate and observer-independent, remaining unchanged regardless of perspective or the state of the channel itself. However, contemporary physics---particularly the development of quantum mechanics---fundamentally challenges the very notion of "absoluteness." As Carlo Rovelli has emphasized in one of his core arguments, quantum mechanics compels us to abandon the conception of states and properties as "absolute" and "observer-independent." The insistence on such absoluteness is precisely what underlies many of the paradoxes and interpretative difficulties that plague quantum theory. Rovelli extends this general philosophical critique of "absoluteness" consistently into the domain of information theory, thereby provoking a profound re-examination and critique of the classical presupposition of the "absolute channel." From this relational perspective, information should not be conceived as an abstract entity existing independently of physical relations, but rather as an observable measure of relative relations between systems. Accordingly, the reconstruction of classical information theory on the basis of relational ontology---namely, the reconstruction of information theory itself---is not only a demand of theoretical coherence but also a necessary step in responding to the challenge of quantum reality and in building a more universal theory of information.
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name principle of infinite precision). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on finite information quantities (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem.'' We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').
In quantum mechanics, the measurement problem is commonly regarded as reason for deep concern. It seems that, either, the problem can be solved and there is hope for quantum mechanics, or the theory better be left behind in search of another one. We investigate the prospect of finding a solution to the measurement problem—within quantum mechanics, as well as in theoretical frameworks beyond it. As we do so, there emerges a perspective on doing physics drawing from considerations in the philosophy of language and in epistemology. Developing this perspective for further aspects in physics reveals: The notion of a system is similarly problematic. Eventually, the question arises whether these are problems of specific physical theories, or rather of specific stances towards physics. In this regard, we examine in particular the role and understanding of assumptions.