Where Did the Mysteries of Quantum Mechanics Arise?

Quantum mechanics came to employ complex probability amplitudes and the abstract state space known as Hilbert space because the behavior of electrons and light could not be described by the intuition of classical three-dimensional space alone. Complex numbers retain the magnitude and phase of an amplitude within a single quantity, while Hilbert space unifies linear superposition, inner products, observables, and time evolution in one mathematical framework. This made it possible to describe point-like particle detections and wave-like interference within the same theory. Yet this mathematical success also raised an ontological question: should the state structure in Hilbert space be read as physical reality itself? That question developed into long-standing debates over Schrödinger’s cat, the measurement problem, quantum entanglement, and nonlocality. This paper traces that history for a general readership and applies to quantum theory the distinction, emphasized by NNRT in relativity, between “successful mathematics” and “the physical reality of the mathematical object.” It then argues that physics remains incomplete at that stage: the next central task is to identify the physical mechanism—what acts on what, and how—that gives rise to the observed phenomena.

File1 in English; File 2 in Japanese under consideration