Quantum Non-Objectivity from Performativity of Quantum Phenomena

TL;DR

This paper explores the non-objectivity of quantum observables by examining the logical foundations of quantum mechanics, highlighting the difference between the formal mathematical language and the performative language of experiments, and proposing non-classical logics to resolve inconsistencies.

Contribution

It introduces a novel perspective on quantum non-objectivity by linking it to the performative nature of quantum phenomena and applies non-classical self-referent logics to address logical inconsistencies.

Findings

Quantum observables lack objectivity due to the absence of logical atoms.

Quantum formalism is self-consistent mathematically but not in experimental performative language.

Non-classical logics can resolve the self-inconsistency in quantum descriptions.

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 experimenter's performances are not self-consistent. This self-inconsistency is an effect of that the language of QM differs much from the language of human performances. The first is the language of a mathematical theory which uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The second language consists of performative propositions which are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic which is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: from a mathematical theory to a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics.