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IEEE International Conference on Cognitive Infocommunications

On Uncertainty and the ‘Space-Time-Information’ Continuum : The role of the Probabilist and/or Philostochus

Péter Várlaki, Péter Bárányi

Published Sep 23, 2020• 0 citations
Publisher

Abstract

The paper deals with the `old' physical worldview of the space-time continuum paradigm and argues that it may need to be supplemented with underlying notions of information and uncertainty. Using this approach, we very briefly discuss a quantum physics case's interpretation possibility and uncertainty-interpretational possibility of Russell's paradox with its `philosophical' problems, too.

DOI
10.1109/coginfocom50765.2020.9237902

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The paper deals with the old' physical worldview of the space-time continuum paradigm and argues that it may need to be supplemented with underlying notions of information and uncertainty. Using this approach, we very briefly discuss a quantum physics case's interpretation possibility and uncertainty-interpretational possibility of Russell's paradox with its philosophical' problems, too.
A vast number of internal “time” quantities, intrinsically associated with some particular phenomena, is all that can be consistently defined in physics. This leads us to interpret the notion of “uncertainty in time” specifically, for each of the considered phenomena. However, a universal conception of “time” can be proposed from the unifying point of view of the Observer, considering only the information process underlying any phenomenon. A change in the available information relative to that phenomenon can be calculated with the use of a universal “time”-information operator. This operator computes the algorithmic information content of the predictive tool associated with any experimental situation. Its standard deviation is then used to interpret the notion of “uncertainty in time” as a limit of predictability for any evolution. Heisenberg’s principle of “time”-energy uncertainty can then be rigorously regarded as a cognitive principle governing the evolution of any physical system.
I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.
In this chapter, we consider the way quantum theory represents deterministic, statistical, and probabilistic aspects of Nature. After a discussion in Section 3.1 of uncertainty in general, we discuss in Sections 3.2-3.4 several formal notions of classical probability, their relation to the probability concept used in applied statistics, and their dependence on the description used. Section 3.5 briefly discusses various examples, where probabilistic features emerge from fully deterministic situations-a theme to be taken up in much more detail in Chapter 11. Section 3.6 then shows how the statistical aspects of the quantum formalism naturally follow from the weak law of large numbers. The notions of c-probability in the classical case and of q-probability in the quantum case are formally defined in Section 3.7. Historically, the concept of classical probability (including its use in stochastic processes) was given an undisputed formal mathematical foundation in 1933 in terms of the measure-theoretic setting of Kolmogorov [164]. Apart from this traditional axiomatic foundation of classical probability theory, there is a less well-known equivalent axiomatic treatment by Whittle [302] in terms of expectations. Here probabilities appear as the expectations of statements, {0, 1}-valued random variables. von Plato [240] discusses the history of the concept of probability. Krüger et al. [169] discuss the history of probability in the various fields of application. Sklar [275] discusses the philosophical problems of the probability concept, with an emphasis on statistical mechanics.
Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.
The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems.