Revisiting the Identity Principle of Quantum Mechanics

Identity principle is a fundamental postulate of quantum mechanics. In this paper, from a philosophical point of view, we revisit the identity principle of quantum mechanics. We attribute the identity to the existence of a precision limit for observation: the microscopic objects become indistinguishable when the difference between them is lower than the precision limit. This precision limit is determined not by the measuring apparatus, but by the action quantum h behand the objective physical law. We deduce logically how to relate the identity principle with the probabilistic interpretation, uncertainty principle, quantization in quantum mechanics, attempting to sorting out some logic for quantum theory. The indistinguishability of identical particles makes it impossible to accurately obtain all the details about the microscopic objects at the same time, and consequently the microscopic objects can only be described statistically, leading to the probabilistic determinism and indeterminacy of initial state in quantum mechanics. By reviewing Bohmian mechanics, one of the nonlocal hidden variable theories, we discuss the possibility of restoring determinism and causality in quantum mechanics by restoring the determinacy of initial state. However, any hidden variable theory constructed by using only the terminologies of classical physics cannot reproduce the quantum mechanical predictions. It is the identity principle that makes it impossible to restore causality and determinism, and is the root that makes quantum mechanics different from classical physics. Finally, the boundary between the so-called classical and quantum worlds is discussed. We hope these philosophical arguments can provide a kind of epistemic understanding for quantum mechanics.