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)

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Abstract

This paper develops an analogical framework that borrows the mathematical formalism of quantum mechanics...

Key Results

1. Axiomatic foundation: Three postulates formalizing the individual as an operator
2. Proposition 1: Observer-independence constraint
3. Proposition 2: Non-uniqueness of eigenvalue sets — ill-posed inverse problem
4. Proposition 3: Inexhaustibility of understanding
5. Spectral decomposition: Three-phase operational theory of tolerance

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License: MIT © 2026 Zhang Mingkai & Yu Qing

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)

---

Abstract

This paper develops an analogical framework that borrows the mathematical formalism of quantum mechanics...

Key Results

1. Axiomatic foundation: Three postulates formalizing the individual as an operator
2. Proposition 1: Observer-independence constraint
3. Proposition 2: Non-uniqueness of eigenvalue sets — ill-posed inverse problem
4. Proposition 3: Inexhaustibility of understanding
5. Spectral decomposition: Three-phase operational theory of tolerance

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License: MIT © 2026 Zhang Mingkai & Yu Qing

v1.0 — A Quantum Mechanical Analogy for Interpersonal Understanding

v1.0 — A Quantum Mechanical Analogy for Interpersonal Understanding

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

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Abstract

This paper borrows the mathematical structure of quantum mechanics——operators, eigenvalues, unitary transformations, and matrix elements——to construct an analogical framework for understanding interpersonal differences and tolerance.

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Contents

File	Language
matrix-interpersonal.pdf	🇨🇳 中文 (4 pages)
matrix-interpersonal.tex	🇨🇳 LaTeX source
matrix-interpersonal-en.pdf	🇬🇧 English (4 pages)
matrix-interpersonal-en.tex	🇬🇧 LaTeX source

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License

MIT © 2026 Zhang Mingkai & Yu Qing

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)

---

Abstract

This paper proposes a novel analogical framework that borrows the mathematical structure of quantum mechanics——operators, eigenvalues, unitary transformations, and matrix elements——to systematically model interpersonal differences and the practice of tolerance.

Each person is treated as a unique operator acting on a common state space; the same external event collapses into different eigenvalues across different operators, with no implication of fault on either side. Understanding another person is reframed as performing a unitary transformation within one's own representation to obtain the other's core logic (eigenvalues), while accepting that the inner texture of their experience (matrix elements) is irreversibly inaccessible.

The paper further demonstrates that reconstructing matrix elements from eigenvalues alone is a mathematically ill-posed inverse problem, draws a distinction between rigid and flexible matrix elements, and formalizes tolerance as a dynamic process of spectral decomposition——recognizing, expanding, and accommodating different eigenspectra.

Presenting the hardest scientific language as a vehicle for the softest truths, this work suggests that genuine understanding is perpetual approximation rather than once-and-for-all arrival.

Bilingual (Chinese and English).

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