Year: 2014
Type: article
Abstract: We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables, which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenters' performances are not self-consistent. This self-inconsistency is an effect of the language of QM differing greatly from the language of human performances. The former is the language of a mathematical theory that uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The latter language consists of performative propositions that are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic that is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: the difference between a mathematical theory and a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics.
Source: Physica Scripta
Authors: Andrei Khrennikov, Andrew Schumann
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Award: G464291786
OpenAlex ID: W2013724686