Emergent quantum entanglement from higher-dimensional geometric projection

Quantum entanglement is a fundamental feature of quantum mechanics whose underlying physical interpretation remains an active topic of research. In this work, we develop a geometric framework in which physical states are defined on a higher-dimensional manifold, while observable states arise from a coherent projection onto spacetime. We show that this projection acts as a non-injective mapping on the underlying state space, generically transforming separable higher-dimensional states into non-factorizable states in the observable domain. Within this construction, quantum correlations emerge as a consequence of interference along a compact dimension. Under conditions of phase coherence, the standard quantum predictions are recovered. More generally, incomplete phase cancellation leads to a well-defined deviation from the usual correlation structure, introducing an additional angular dependence beyond the relative measurement settings. The framework is fully compatible with the standard quantum formalism at the effective level, while extending it through experimentally testable predictions. Moreover, the presence of such additional angular contributions provides a potential signature of projection-induced effects. These results suggest that quantum entanglement may be interpreted as an emergent phenomenon associated with geometric projection, in which effective nonlocal behavior arises from dimensional reduction.