Gravity as an Emergent Response to Topological Obstruction in Internal Time

This work presents a framework in which gravity is not fundamental but emerges as a long-wavelength response to topological obstruction in an internal notion of time orientation. The theory is defined on a spacetime manifold equipped with an auxiliary Lorentzian structure and an internal field taking values in S3≃SU(2)S3≃SU(2), interpreted as an internal orientation of time rather than a spacetime vector or metric. Because of the topology of the target space, the internal field admits conserved, integer-valued homotopy sectors. Nontrivial topology obstructs global trivialization and enforces irreducible internal gradients and localized energy density. Assuming locality, internal isotropy, diffeomorphism covariance, and a finite correlation length, coarse-grained correlations of the internal field necessarily define an emergent Lorentzian spacetime geometry. Long-wavelength fluctuations of this emergent geometry include a massless spin-2 mode with universal coupling, and general consistency requirements uniquely select Einstein gravity as the infrared effective theory. The Einstein–Hilbert action arises as an induced effective action, with Newton’s constant determined by the microscopic correlation length.