Topological Origin of Singlet Correlations: Entanglement as a Global Invariant of an SU(2) Field

We propose that the fundamental reality is a smooth, continuous SU(2) operator field on three‑dimensional space. Particles are not independent objects but localized topological defects (knots) in this field. Entanglement between two particles is not a mysterious non‑local connection; it is the direct consequence of a global topological constraint: the total winding number of the field over all space is fixed to zero. For a pair of defects created from the vacuum, this forces opposite topological charges and, through quantization of the rotational collective coordinates, a total spin of zero. The unique state satisfying these requirements is the spin singlet, from which the standard Bell correlations follow automatically. In this framework, measurement is a geometric projection onto the local orientation of the defect. Because the two defects are parts of a single continuous field, the two defects remain constrained by the same global topological invariant, ensuring that the correlation persists under local unitary transformations. The model provides a local, realist, and geometric alternative to the Copenhagen interpretation, resolving the EPR paradox without invoking superluminal signals or wave‑function collapse.