Representations of empirical set theories

Hirokazu Nishimura

Gábor Hofer‐Szabó

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical representation of classical conditional probabilities is situated within the broader frame of noncommutative representations. To this goal, we adopt some parts of the quantum formalism and ask whether empirical data can constrain the rest of the representation to conform to quantum mechanics. We will show that as the set of empirical data grows, conventional elements in the representation gradually shrink and the noncommutative representations narrow down to the unique quantum mechanical representation.

Foat Sultanbekov

Giovanni Battista Rossi, Francesco Crenna

Measurement can be defined on the basis of the notion of empirical relation, which appears as a primitive term in the representational theory. Here a language is introduced for dealing with empirical relations and a probabilistic logic is applied to statements concerning them.

Christian DE RONDE

In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the theory of quanta, but rather a direct consequence of the empirical-positivist understanding of physical theories when applied to the orthodox quantum formalism. In contraposition, we discuss a representational realist account of both physical 'theories' and 'measurement' which goes back to the works of Einstein, Heisenberg and Pauli. After presenting a critical analysis of Bohr's definitions of 'measurement' we continue to discuss the way in which several contemporary approaches to QM --such as decoherence, modal interpretations and QBism-- remain committed to Bohr's general methodology. Finally, in order to expose the many inconsistencies present within the (empirical-positivist) presuppositions responsible for creating the quantum measurement problem, we show how through these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics.

Satoko Titani, Haruhiko Kozawa