Duality in Physics

We propose an ontological interpretation of quantum mechanics based on the principle of subjective incompleteness—a fundamental limitation arising from the fact that the observer is part of the world being observed. By formalizing consciousness as a set of states Subj and the world as a self-mapping W:Subj→Subj, we construct an ontological configuration space whose structure naturally gives rise to the Hilbert space of quantum states. Within the proposed model, the hidden parameters in the representation of an observable operator are the eigenvalues of its canonical conjugate. In particular, the coordinate and momentum representations complement each other to form a complete ontological description, with the corresponding variables appearing as mutually hidden. From this perspective, the phenomenon of duality in physics, exemplified by pairs such as coordinate–momentum or time–energy, reflects the underlying subject–object structure of reality. The model offers a new justification of Bohr’s principle of complementarity and provides a geometrical account of noncommutativity in terms of subjective incompleteness. Furthermore, the entropic uncertainty relations of Hirschman–Everett are reinterpreted as quantitative measures of subjective incompleteness. This approach links the growth of thermodynamic entropy with the “motion” of the observer’s consciousness along the gradient of ontological states, thereby providing a natural explanation of the thermodynamic arrow of time. Thus, the key features of quantum mechanics emerge from the fundamental principle of subjective incompleteness. This article continues a series of works devoted to the role of the observer and consciousness in physics.