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arXiv:0804.3592 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Typicality derived

Don Nelson Page

Published Jul 11, 2008• 13 citations
arXivHTMLPDF

Abstract

Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate normalized probabilities for alternatives obeying what I call the principle of observational discrimination, that each possible complete observation or data set should uniquely distinguish one element from the set of alternatives.

DOI
10.1103/physrevd.78.023514

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•Jan 1, 2012•0 citations
Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate normalized probabilities for alternatives obeying what I call the principle of observational discrimination, that each possible complete observation or data set should uniquely distinguish one element from the set of alternatives.
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain events. These experiments are referred to as \textit{typicalistic} (instead of probabilistic) experiments. As probabilistic experiments are represented by probability spaces, typicalistic experiments can be represented by \textit{typicality spaces}, where a typicality space is basically a probability space in which the probability measure has been replaced by a much less structured typicality measure TTT. The condition T(A)≈1T(A) \approx 1T(A)≈1 defines the typical sets, and a typicality space is related to a typicalistic experiment by associating the typical sets of the former with the nearly certain events of the latter. Some elements of a theory of typicality, including the definition of typicality spaces, are developed in the first part of the paper. The second hypothesis is that the evolution of a quantum particle (or of a system of quantum particles) can be considered a typicalistic phenomenon, so that it can be represented by the combination of typicality theory and quantum mechanics. The result is a novel formulation of quantum mechanics that does not present the measurement problem and that could be a viable alternative to Bohmian mechanics. This subject is developed in the second part of the paper.
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind ("identical particles") are completely indistinguishable from each other and lack identity. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of "particle" in ordinary language and in classical physical theory, but also with how this term is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by "particles" in the classical limit of quantum mechanics. Elaborating on earlier work, we here analyze the premises of the standard view and discuss an alternative that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory.
The EPR controversy between Albert Einstein and Niels Bohr about the completeness of the quantum mechanics is one of the most essential contemporary debates in physics with respect to the issue of realism. Initially considered as a though-experiment, the EPR paradox was meant to evidence the inadequacy of quantum mechanics with respect to the traditional leading principle of physics such as locality, independence of the system elements of reality with respect to the observer or semantic reference of theories to elements of the reality in itself. Bell’s mathematical inquiry opened the possibility to empirically discriminate between the view of Bohr and Einstein through the so-called Bell’s inequalities. Based on these inequalities, the experimental test provided in particular by the work of Alain Aspect settled the debate in favor of Bohr and the completeness of quantum mechanics. The previously evident assumption that physical theories are describing the reality in it-self can thus be questioned. Several approaches have been proposed to face that challenge, such as the orthodox quantum physics formulation coupled with the interpretation of Bernard d’Espagnat , the non-local theory of De Broglie-Bohm or the quantum mechanics approach with extended probability of James B. Hartle . In this paper, we consider the idea according to which the field of experiments and measurements on quantum systems is a research context where several epistemic values traditionally leading the scientific activity are in conflict. Instead of conceiving the transition from classical to quantum physics along Thomas Kuhns’ theory of revolutionary paradigm change , characterized by a strong incommensurability between the old and the new approaches, we argue that this epistemological shift could be rationally understood as an incremental evolution of the epistemic values leading scientific activity. As the analysis in this paper aims to show, such a rational reconstruction shows a process of gradual change, where core epistemic values are maintained, while others are broadened to account for the new scientific approaches. The settling of the EPR controversy could be understood as the indication that the previously assumed epistemic values cannot be consistently held together in the quantum context. The values of logical consistency and empirical adequacy remained universally shared, but the controversy leads to question the other traditionally admitted principles, such as the locality, the requirement of semantic references to the reality in itself and the independence of experimental results with respect to the observer, all tightly connected with the realistic conceptions of the world. This first part of the paper characterizes the selected contemporary approaches in quantum context with respect to the modification of the epistemic principles they adopt to restore their consistency. While the de Broglie-Bohm theory explicitly follows the requirement of referring to the reality in itself at the expense of the locality principle, the approaches of d’Espagnat and of Hartle give priority to the values of theoretical framework simplicity and predictive power. In the case of d’Espagnat, the descriptive purpose of the scientific activity remains, but only in a weak objectivity perspective, restricted to the “empirical reality” in which the observer is involved. In the case of Hartle, the extended probability formulation of quantum mechanics is conceived as “an extension of familiar probability theory that incorporates negative probabilities”6, which relies on the Bayesian conception of “probabilities as instruction for betting” (negative probability is thus associated to the instruction “don’t bet”). In a second part, the paper uses this reconstruction of the various theories in order to address the epistemic status of the principles of descriptive power and of independence of the observed system with respect to the observer. In particular, our analysis aims to assess if a reference to the observer is part of the reality description or if such reference is avoidable. This is of prior interest in exploring the main characteristics of a realistic approach that would be applicable in the context of experiments and measurements on quantum systems. In that perspective, we argue that the direct holistic realism, developed by Hilary Putnam in The Threefold Cord , could be a promising intermediate option between a classical realism, which assumes that theoretical structures are describing the reality in it-self, and a more instrumentalist view, focusing mainly on the modeling of the empirical reality as a result of experimental operations while rejecting access to the reality in itself.