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).