A Quantum Mechanical Analogy for Interpersonal Understanding ——Operators, Representations, and Eigenvalues

A Quantum Mechanical Analogy for Interpersonal Understanding: Operators, Representations, and Eigenvalues

Authors: Zhang Mingkai · Yu Qing (Co-first Authors)

Abstract

This work proposes a conceptual framework for interpersonal understanding inspired by the mathematical formalism of quantum mechanics. Rather than applying quantum theory to human cognition in a physical sense, the paper employs operators, eigenvalues, unitary transformations, matrix elements, and spectral decomposition as rigorous analogical tools for analyzing interpersonal differences and the practice of tolerance.

Within this framework, each individual is represented as a unique operator acting on experience. The same external event may yield different eigenvalues when observed through different operators, reflecting the diversity of human responses. Understanding another person is reformulated as performing an internal unitary transformation that allows one to express the same phenomenon within another representation and thereby approximate the other's eigenvalues.

The framework further argues that matrix elements—the detailed internal structures through which experiences acquire meaning—remain fundamentally inaccessible to external observers. Consequently, the inverse problem of reconstructing another person's internal matrix elements solely from observed eigenvalues is mathematically ill-posed. The paper distinguishes between rigid and flexible matrix elements and interprets tolerance as an ongoing process of spectral decomposition and reconstruction.

The objective is not to claim a scientific equivalence between quantum mechanics and psychology, but rather to provide a mathematically structured philosophical language for discussing understanding, disagreement, empathy, and tolerance.

Keywords

Quantum Mechanics; Interpersonal Understanding; Operator Theory; Eigenvalues; Unitary Transformation; Matrix Elements; Spectral Decomposition; Philosophy of Physics; Tolerance

Citation

Zhang, M., & Yu, Q. (2026). A Quantum Mechanical Analogy for Interpersonal Understanding: Operators, Representations, and Eigenvalues.

License

MIT License

June 2026