Revisiting the Applicability of Metaphysical Identity in Quantum Mechanics

Abstract

We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics (QM) might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties when considering the syntactic level of the theory.

arXiv commentwelcome!

References in corpus (6)

• Macroscopicity of Mechanical Quantum Superposition States
• How Classical Particles Emerge From the Quantum World
• The Paraconsistent Logic of Quantum Superpositions
• Why Should we Interpret Quantum Mechanics?
• Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach
• On the Importance of Interpretation in Quantum Physics. A Reply to Elise Crull

Cited by in corpus (4)

• Against 'Particle Metaphysics' and 'Collapses' within the Definition of Quantum Entanglement
• Beyond Purity and Mixtures in Categorical Quantum Mechanics
• The Logos Categorical Approach to Quantum Mechanics: III. Relational Potential Coding and Quantum Entanglement Beyond Collapses, Pure States and Particle Metaphysics
• Against Collapses, Purity and Separability Within the Definition of Quantum Entanglement